diff --git a/Lab3-policy-gradient.ipynb b/Lab3-policy-gradient.ipynb
index 4529e50..d76b099 100644
--- a/Lab3-policy-gradient.ipynb
+++ b/Lab3-policy-gradient.ipynb
@@ -3,9 +3,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# Automatically reload changes to external code\n",
@@ -28,14 +26,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "[2017-09-12 22:50:43,560] Making new env: CartPole-v0\n"
+      "[2017-11-07 13:50:11,632] Making new env: CartPole-v0\n"
      ]
     }
    ],
@@ -103,14 +101,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/Users/andrew/miniconda2/envs/cedl/lib/python3.5/site-packages/tensorflow/python/ops/gradients_impl.py:95: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
+      "/Users/Howard/anaconda/envs/cedl/lib/python3.5/site-packages/tensorflow/python/ops/gradients_impl.py:95: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
       "  \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
      ]
     }
@@ -133,7 +131,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Problem 3\n",
+    "### Problem 3\n",
     "\n",
     "Use baseline to reduce the variance of our gradient estimate.\n",
     "\n",
@@ -152,10 +150,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 4,
+   "metadata": {},
    "outputs": [],
    "source": [
     "class PolicyOptimizer(object):\n",
@@ -214,21 +210,25 @@
     "            Sample solution should be only 1 line.\n",
     "            \"\"\"\n",
     "            # YOUR CODE HERE >>>>>>\n",
+    "            a = r - b\n",
     "            # <<<<<<<<\n",
     "\n",
     "            p[\"returns\"] = r\n",
     "            p[\"baselines\"] = b\n",
     "            p[\"advantages\"] = (a - a.mean()) / (a.std() + 1e-8) # normalize\n",
-    "\n",
+    "            p[\"advantage_variance\"] = np.var(a) # My additional code for plotting advantage variance.\n",
+    "            \n",
     "        obs = np.concatenate([ p[\"observations\"] for p in paths ])\n",
     "        actions = np.concatenate([ p[\"actions\"] for p in paths ])\n",
     "        rewards = np.concatenate([ p[\"rewards\"] for p in paths ])\n",
     "        advantages = np.concatenate([ p[\"advantages\"] for p in paths ])\n",
+    "        advantage_variances = np.array([ p[\"advantage_variance\"] for p in paths ])\n",
     "\n",
     "        return dict(\n",
     "            observations=obs,\n",
     "            actions=actions,\n",
     "            rewards=rewards,\n",
+    "            advantage_variances=advantage_variances,\n",
     "            advantages=advantages,\n",
     "        )\n",
     "\n",
@@ -236,16 +236,25 @@
     "    def train(self):\n",
     "        loss_list = []\n",
     "        avg_return_list = []\n",
+    "        avg_advantage_variance_list = []\n",
+    "        \n",
     "        for i in range(1, self.n_iter + 1):\n",
     "            paths = []\n",
+    "            \n",
     "            for _ in range(self.n_episode):\n",
     "                paths.append(self.sample_path())\n",
+    "                \n",
     "            data = self.process_paths(paths)\n",
     "            loss = self.policy.train(data[\"observations\"], data[\"actions\"], data[\"advantages\"])\n",
     "            avg_return = np.mean([sum(p[\"rewards\"]) for p in paths])\n",
-    "            print(\"Iteration {}: Average Return = {}\".format(i, avg_return))\n",
+    "            avg_advantage_variance = np.mean(data[\"advantage_variances\"])\n",
+    "            \n",
+    "            print(\"Iteration {}: Average Return = {} | Average Advantage Variance: {}\".format(i, avg_return, avg_advantage_variance))\n",
+    "            \n",
     "            loss_list.append(loss)\n",
     "            avg_return_list.append(avg_return)\n",
+    "            avg_advantage_variance_list.append(avg_advantage_variance)\n",
+    "            \n",
     "            # CartPole-v0 defines \"solving\" as getting average reward of 195.0 over 100 consecutive trials.\n",
     "            if avg_return >= 195:\n",
     "                print(\"Solve at {} iterations, which equals {} episodes.\".format(i, i*100))\n",
@@ -253,103 +262,99 @@
     "\n",
     "            if self.baseline != None:\n",
     "                self.baseline.fit(paths)\n",
-    "        return loss_list, avg_return_list"
+    "        return loss_list, avg_return_list, avg_advantage_variance_list"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Iteration 1: Average Return = 14.85\n",
-      "Iteration 2: Average Return = 15.59\n",
-      "Iteration 3: Average Return = 16.61\n",
-      "Iteration 4: Average Return = 17.43\n",
-      "Iteration 5: Average Return = 17.08\n",
-      "Iteration 6: Average Return = 17.24\n",
-      "Iteration 7: Average Return = 21.3\n",
-      "Iteration 8: Average Return = 21.42\n",
-      "Iteration 9: Average Return = 20.62\n",
-      "Iteration 10: Average Return = 26.82\n",
-      "Iteration 11: Average Return = 28.0\n",
-      "Iteration 12: Average Return = 28.41\n",
-      "Iteration 13: Average Return = 28.96\n",
-      "Iteration 14: Average Return = 28.15\n",
-      "Iteration 15: Average Return = 30.64\n",
-      "Iteration 16: Average Return = 36.2\n",
-      "Iteration 17: Average Return = 38.13\n",
-      "Iteration 18: Average Return = 34.5\n",
-      "Iteration 19: Average Return = 40.37\n",
-      "Iteration 20: Average Return = 35.78\n",
-      "Iteration 21: Average Return = 47.81\n",
-      "Iteration 22: Average Return = 47.21\n",
-      "Iteration 23: Average Return = 43.34\n",
-      "Iteration 24: Average Return = 46.1\n",
-      "Iteration 25: Average Return = 50.25\n",
-      "Iteration 26: Average Return = 51.02\n",
-      "Iteration 27: Average Return = 59.81\n",
-      "Iteration 28: Average Return = 57.49\n",
-      "Iteration 29: Average Return = 61.39\n",
-      "Iteration 30: Average Return = 62.26\n",
-      "Iteration 31: Average Return = 61.98\n",
-      "Iteration 32: Average Return = 62.16\n",
-      "Iteration 33: Average Return = 59.89\n",
-      "Iteration 34: Average Return = 73.46\n",
-      "Iteration 35: Average Return = 78.51\n",
-      "Iteration 36: Average Return = 72.79\n",
-      "Iteration 37: Average Return = 78.74\n",
-      "Iteration 38: Average Return = 86.95\n",
-      "Iteration 39: Average Return = 94.08\n",
-      "Iteration 40: Average Return = 97.58\n",
-      "Iteration 41: Average Return = 103.42\n",
-      "Iteration 42: Average Return = 101.17\n",
-      "Iteration 43: Average Return = 112.39\n",
-      "Iteration 44: Average Return = 115.09\n",
-      "Iteration 45: Average Return = 134.65\n",
-      "Iteration 46: Average Return = 138.92\n",
-      "Iteration 47: Average Return = 147.15\n",
-      "Iteration 48: Average Return = 152.35\n",
-      "Iteration 49: Average Return = 149.66\n",
-      "Iteration 50: Average Return = 148.15\n",
-      "Iteration 51: Average Return = 144.82\n",
-      "Iteration 52: Average Return = 144.43\n",
-      "Iteration 53: Average Return = 153.21\n",
-      "Iteration 54: Average Return = 163.66\n",
-      "Iteration 55: Average Return = 154.28\n",
-      "Iteration 56: Average Return = 155.07\n",
-      "Iteration 57: Average Return = 161.53\n",
-      "Iteration 58: Average Return = 166.28\n",
-      "Iteration 59: Average Return = 174.05\n",
-      "Iteration 60: Average Return = 172.8\n",
-      "Iteration 61: Average Return = 170.78\n",
-      "Iteration 62: Average Return = 179.58\n",
-      "Iteration 63: Average Return = 174.84\n",
-      "Iteration 64: Average Return = 175.74\n",
-      "Iteration 65: Average Return = 174.99\n",
-      "Iteration 66: Average Return = 187.7\n",
-      "Iteration 67: Average Return = 178.94\n",
-      "Iteration 68: Average Return = 182.74\n",
-      "Iteration 69: Average Return = 181.42\n",
-      "Iteration 70: Average Return = 182.19\n",
-      "Iteration 71: Average Return = 184.58\n",
-      "Iteration 72: Average Return = 181.9\n",
-      "Iteration 73: Average Return = 184.29\n",
-      "Iteration 74: Average Return = 188.8\n",
-      "Iteration 75: Average Return = 190.46\n",
-      "Iteration 76: Average Return = 188.89\n",
-      "Iteration 77: Average Return = 187.9\n",
-      "Iteration 78: Average Return = 190.19\n",
-      "Iteration 79: Average Return = 186.28\n",
-      "Iteration 80: Average Return = 189.1\n",
-      "Iteration 81: Average Return = 188.16\n",
-      "Iteration 82: Average Return = 191.32\n",
-      "Iteration 83: Average Return = 192.03\n",
-      "Iteration 84: Average Return = 195.45\n",
-      "Solve at 84 iterations, which equals 8400 episodes.\n"
+      "Iteration 1: Average Return = 25.59 | Average Advantage Variance: 48.351865612557724\n",
+      "Iteration 2: Average Return = 24.8 | Average Advantage Variance: 20.65048949168897\n",
+      "Iteration 3: Average Return = 28.74 | Average Advantage Variance: 22.13545724245825\n",
+      "Iteration 4: Average Return = 30.85 | Average Advantage Variance: 21.29429545367064\n",
+      "Iteration 5: Average Return = 31.25 | Average Advantage Variance: 23.602730478502558\n",
+      "Iteration 6: Average Return = 35.95 | Average Advantage Variance: 30.556859174015543\n",
+      "Iteration 7: Average Return = 33.98 | Average Advantage Variance: 34.52406210704295\n",
+      "Iteration 8: Average Return = 34.02 | Average Advantage Variance: 26.42146686387153\n",
+      "Iteration 9: Average Return = 37.86 | Average Advantage Variance: 28.0064356959493\n",
+      "Iteration 10: Average Return = 36.7 | Average Advantage Variance: 29.125894655094726\n",
+      "Iteration 11: Average Return = 39.24 | Average Advantage Variance: 34.92325058502597\n",
+      "Iteration 12: Average Return = 38.12 | Average Advantage Variance: 24.663745918726278\n",
+      "Iteration 13: Average Return = 42.16 | Average Advantage Variance: 25.53625249684122\n",
+      "Iteration 14: Average Return = 43.46 | Average Advantage Variance: 29.64068299230753\n",
+      "Iteration 15: Average Return = 45.5 | Average Advantage Variance: 30.83696088879085\n",
+      "Iteration 16: Average Return = 46.07 | Average Advantage Variance: 30.24291413071842\n",
+      "Iteration 17: Average Return = 46.46 | Average Advantage Variance: 29.51328026333303\n",
+      "Iteration 18: Average Return = 43.61 | Average Advantage Variance: 25.81055223826167\n",
+      "Iteration 19: Average Return = 44.4 | Average Advantage Variance: 24.8791987022585\n",
+      "Iteration 20: Average Return = 46.12 | Average Advantage Variance: 21.62926278843614\n",
+      "Iteration 21: Average Return = 50.32 | Average Advantage Variance: 28.89130832504027\n",
+      "Iteration 22: Average Return = 50.97 | Average Advantage Variance: 29.981063663366204\n",
+      "Iteration 23: Average Return = 50.99 | Average Advantage Variance: 30.533226049515214\n",
+      "Iteration 24: Average Return = 52.97 | Average Advantage Variance: 27.958060870176336\n",
+      "Iteration 25: Average Return = 54.41 | Average Advantage Variance: 28.94597635253092\n",
+      "Iteration 26: Average Return = 51.62 | Average Advantage Variance: 28.633312416525147\n",
+      "Iteration 27: Average Return = 53.03 | Average Advantage Variance: 31.999785701999205\n",
+      "Iteration 28: Average Return = 56.47 | Average Advantage Variance: 33.23399687032651\n",
+      "Iteration 29: Average Return = 58.33 | Average Advantage Variance: 33.04375247199863\n",
+      "Iteration 30: Average Return = 60.46 | Average Advantage Variance: 38.41737196380684\n",
+      "Iteration 31: Average Return = 55.87 | Average Advantage Variance: 30.71584113213717\n",
+      "Iteration 32: Average Return = 54.53 | Average Advantage Variance: 26.270106880027967\n",
+      "Iteration 33: Average Return = 55.43 | Average Advantage Variance: 24.529012871853457\n",
+      "Iteration 34: Average Return = 62.98 | Average Advantage Variance: 30.933791732505302\n",
+      "Iteration 35: Average Return = 64.06 | Average Advantage Variance: 29.75019719598117\n",
+      "Iteration 36: Average Return = 65.37 | Average Advantage Variance: 34.906276477947955\n",
+      "Iteration 37: Average Return = 63.68 | Average Advantage Variance: 24.97192303518823\n",
+      "Iteration 38: Average Return = 67.27 | Average Advantage Variance: 29.10197455101781\n",
+      "Iteration 39: Average Return = 62.2 | Average Advantage Variance: 23.51568610205659\n",
+      "Iteration 40: Average Return = 64.5 | Average Advantage Variance: 29.397292723362742\n",
+      "Iteration 41: Average Return = 66.59 | Average Advantage Variance: 30.827112918615736\n",
+      "Iteration 42: Average Return = 74.06 | Average Advantage Variance: 36.27106717823759\n",
+      "Iteration 43: Average Return = 71.47 | Average Advantage Variance: 26.904280040963823\n",
+      "Iteration 44: Average Return = 75.28 | Average Advantage Variance: 32.88512072801452\n",
+      "Iteration 45: Average Return = 80.71 | Average Advantage Variance: 36.74875583700775\n",
+      "Iteration 46: Average Return = 75.5 | Average Advantage Variance: 30.2503334654542\n",
+      "Iteration 47: Average Return = 83.53 | Average Advantage Variance: 38.30691962090316\n",
+      "Iteration 48: Average Return = 92.73 | Average Advantage Variance: 41.97650402253011\n",
+      "Iteration 49: Average Return = 94.93 | Average Advantage Variance: 38.0379064308017\n",
+      "Iteration 50: Average Return = 101.97 | Average Advantage Variance: 41.66995555483244\n",
+      "Iteration 51: Average Return = 104.87 | Average Advantage Variance: 42.54672396156329\n",
+      "Iteration 52: Average Return = 121.97 | Average Advantage Variance: 48.900139867641634\n",
+      "Iteration 53: Average Return = 125.1 | Average Advantage Variance: 36.83724214710699\n",
+      "Iteration 54: Average Return = 134.13 | Average Advantage Variance: 33.7458095438153\n",
+      "Iteration 55: Average Return = 139.2 | Average Advantage Variance: 23.045907284422455\n",
+      "Iteration 56: Average Return = 137.74 | Average Advantage Variance: 14.940458118392126\n",
+      "Iteration 57: Average Return = 134.88 | Average Advantage Variance: 18.009932982638652\n",
+      "Iteration 58: Average Return = 137.1 | Average Advantage Variance: 20.751132151412023\n",
+      "Iteration 59: Average Return = 135.17 | Average Advantage Variance: 15.564235765139122\n",
+      "Iteration 60: Average Return = 145.11 | Average Advantage Variance: 17.140943990974357\n",
+      "Iteration 61: Average Return = 150.32 | Average Advantage Variance: 15.342877797472518\n",
+      "Iteration 62: Average Return = 156.91 | Average Advantage Variance: 14.73913973560266\n",
+      "Iteration 63: Average Return = 153.94 | Average Advantage Variance: 12.286257958297703\n",
+      "Iteration 64: Average Return = 165.22 | Average Advantage Variance: 18.768308757568146\n",
+      "Iteration 65: Average Return = 167.32 | Average Advantage Variance: 7.276832422595179\n",
+      "Iteration 66: Average Return = 174.24 | Average Advantage Variance: 8.850345262283955\n",
+      "Iteration 67: Average Return = 173.77 | Average Advantage Variance: 6.451348940935663\n",
+      "Iteration 68: Average Return = 180.25 | Average Advantage Variance: 8.639755530502491\n",
+      "Iteration 69: Average Return = 184.07 | Average Advantage Variance: 4.033395584839485\n",
+      "Iteration 70: Average Return = 189.84 | Average Advantage Variance: 3.832568130570312\n",
+      "Iteration 71: Average Return = 193.89 | Average Advantage Variance: 2.5091744144243204\n",
+      "Iteration 72: Average Return = 189.19 | Average Advantage Variance: 2.6248013848304925\n",
+      "Iteration 73: Average Return = 192.4 | Average Advantage Variance: 2.535109936893029\n",
+      "Iteration 74: Average Return = 194.18 | Average Advantage Variance: 1.1413285550473464\n",
+      "Iteration 75: Average Return = 192.26 | Average Advantage Variance: 0.6477926859310129\n",
+      "Iteration 76: Average Return = 194.8 | Average Advantage Variance: 1.1958804409420545\n",
+      "Iteration 77: Average Return = 194.09 | Average Advantage Variance: 0.6822225681858246\n",
+      "Iteration 78: Average Return = 194.31 | Average Advantage Variance: 0.5343218591276616\n",
+      "Iteration 79: Average Return = 193.96 | Average Advantage Variance: 0.7315534130350639\n",
+      "Iteration 80: Average Return = 196.09 | Average Advantage Variance: 1.0495728827492738\n",
+      "Solve at 80 iterations, which equals 8000 episodes.\n"
      ]
     }
    ],
@@ -366,19 +371,19 @@
     "                     discount_rate)\n",
     "\n",
     "# Train the policy optimizer\n",
-    "loss_list, avg_return_list = po.train()"
+    "loss_list, avg_return_list, avg_advantage_variance_list = po.train()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w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\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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x3nnn8Td/8zejsidtRFzyiu70DZ0QSstA2QpPXPwJuvPDqNLwqoAx8lx0fx+h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\nSUVORK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107bac18>"
+       "<matplotlib.figure.Figure at 0x1207fba58>"
       ]
      },
      "metadata": {},
@@ -386,9 +391,19 @@
     },
     {
      "data": {
-      "image/png": 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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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qyKVicfToUXr06FFiW+3atctcSlUIUTn06UzYsRnVORpluNy6LITLXPpUhYWF\nceDAgRLb9u3bR3h4uFtCCSHKR29YDaYpTVDCbVzqs7jvvvuIi4ujb9++FBUVsWTJEr777jsef/xx\nd+cTQrhA/7ASrmqOatDY6iiimnLpyuLGG2/k+eef5/Tp07Ru3ZpTp07x9NNP0759e3fnE0KUQR/e\nBz/vR0Vd/kJkQpTFpSuL06dP07RpU1ljQggb0iv+A961pAlKuJVLxSI2NpY2bdrQvXt3OnXqRO3a\ntd2dSwhxHp2VAefOouo1KLn9TC56w2pUVG+Uj69F6URN4FIz1OzZs+nQoQPffvsto0aNYubMmWzc\nuJHi4mJ35xOixtOF5zCn/QVzylPo7MySz61bBoXnUL1kBTzhXi6vlHfrrbcyefJk4uPjufrqq1mw\nYAGjRo1ydz4hajz9zaeQehzO5qMXzP19u2miV/4HmrdCNW5qYUJRE5T7huzs7GyysrLIycnB11cu\ne4VwJ33yGPqbT1E3RaPuGIreuAa95X+OJ3f+CKnH5apCVAqX+iyOHj3KmjVrWLt2LefOnSMqKopn\nnnmG5s2vbK78Y8eOMWPGDOfj1NRUBg8ezJkzZ1i2bBn+/v4ADB06lA4dOlzRuYSoarTWmB/9A7xq\nOWaR9fVDJ3+P+dEcjGvaYq74GuoGoDp0tTqqqAFcKhZ/+9vf6Ny5M6NGjaJNmzbOJVavVEREBNOm\nTQMcK/I9/vjj3HTTTaxYsYL+/ftz5513Vsh5hKiKdPL3sPNH1P2PowKCADAeGof52jOY78+ErRtR\nt9+D8vKyOKmoCVwqFnPnznXOCeUu27ZtIzw8nLCwMLeeR4iqQOedQS961zHQLvo253bVtCWqzx3o\npC9AGaiet1qYUtQkLlUAT09PsrKy2LdvHzk5OWitnc/dfHPFDARau3Yt3bp1cz5eunQpq1evJjIy\nkuHDh+Pn51ch5xHC7rRpoj/6B5zOxhj3N5ThUeJ5ddcD6B83oJo0Q4XIH1eicih9/m/+i9iwYQNv\nvvkmDRo04MiRIzRu3JgjR45w7bXX8uKLL15xiKKiIh5//HHi4+MJDAwkKyvL2V+xcOFCMjMziY2N\nLXVcUlISSUlJAMTFxV3RxIaenp4UFRVd9vHuYtdcYN9sds0Fv2czc06Tu/AdfG4dhGfjq0vsk/Ph\nHPI+m4ffsNH4/mn4BV/HzM9DeXqivLwrNJcd2TWbXXNB+bJ5e7v2GXLpymLhwoXExsYSFRXFww8/\nzN///ndWrFjBkSNHXDpJWTZv3kzTpk0JDHSsGfzb/wH69OnD1KlTL3hcTEwMMTExzsdpaWmXnSE0\nNPSKjncXu+YC+2azay74PZuI8Z/pAAAY0ElEQVSZ+CH660/JT/oa9dA4jE7dATBX/Rf92TxUz9vI\n63k7+ZX0PqrC98xu7JoLypctIiLCpf1c6qlOS0sjKiqqxLbo6GhWr17t0knK8scmqMzM3wcebdiw\ngcaNZXI0UX3os2fRq76Ba9tBo6vQ//w75sJ30JvXoz+aA207Ojq1lbI6qhBOLl1Z+Pv7k5WVRWBg\nIGFhYezZs4e6detimuYVBygoKGDr1q0lBvh9+OGHHDp0CKUUYWFhMvhPVCv6h+WQm4Nxx1CIbIn+\n9AN00heOTuurmmOMegbl4VH2CwlRiVwqFn369GHXrl106dKF/v378/LLL6OUYsCAAVccoHbt2rz3\n3nslto0bN+6KX1cIO9Km6SwKtGiNUgo1ZCRm5DXoDasxHhyDql3H6phClOJSsRg4cKDz6+joaNq0\naUNBQQGNGjVyWzAhqqNzm9bByV9QI58u0cxk3NQTbuppYTIhLu2yBk+EhoZWdA4haoQzXyyA4FAZ\ndS2qHFmsV4hKog/vp/CnFFSfO1BuHuQqREWTYiHEZdBaY365APPD2bgwVMlxzHeJqNo+qO63uDmd\nEBVP/rwR4jLorxeiv/jY8eDqFqjufS++b1EheukSdPL3+PS/l7OySJGogqRYCHEB+uxZdMo6OLwP\n1bUPqkmk8zlz+Vfozz9GRfVGp59CL3oP3aYDKiik9Ovs3YE5PwGOH4Ebu+I7+GHOFlz+TANCWEWK\nhRC/0lrDkYPoNd+i16+C/DOgDPSyL6FDV4w7hqCPHkJ/8k+4vjPqofGo9JOYL4/H/HA2xti/Ou9w\n0gV56MUfoFf/F4LDMMb+DdW+E4afPxTYc9SvEJcixULUaFprOLwPnbIOnbIeTv4Cnl6oDl1RPW+B\nRk3RyxwD5syUdaAMuKbt7wPn6kWg7n4QvfBd9P9Worr0Ru/Z7phCPP0Uqu9dqDvvl7ETosqTYiFq\nLF2Qjzn1OTh6CAxHEVAxd6A69UD51nXup+68H93nDvS3n8Op46jhY0pM4KduHoDeuBb9yVzMQ/vQ\ny7+C0PoYz76Kat7agncmRMWTYiFqLL12GRw9hLrvMVSXXig//4vuq3zrou4eduHnDA+Mh8Zj/r8/\no5d9iep5G+reh+VqQlQrUixEjaTNYvSyLyDyGoyYK1+RUTVohDHub6AUqlX7CkgohL1IsRBVls45\njV70LvrQHoynpqACg10/+MdkOHUCY9CF14u4HKr19RX2WkLYjQzKE1WO1hrzhxWYLzyBTl4NaamY\n781Al2MWZDPpcwipBzdElb2zEEKKhaha9IlfMN94Cf3eDKgXgfG3maiho2Dnj+hvl7j2Gof3w57t\nqJv7y1TgQrhImqFElaBzTqO/WuBYNMjTGzV0FKrX7Y71qSOaoHdsRid+iL6mLZQx0aVO+hxq1ZFp\nN4QoBykWwtYc6z98jv5qERTko3regrpzKMo/yLmPUgrjwbGYB/dizp2O2Wb+xV8vKx2d/D2qVz+U\nTLshhMukGUrYljZN9Iez0Yvfh+atMF6ahTEstkSh+I3y9cMY+TSkp5I97f/Qh/dd+DWXfwWmiepz\nh7vjC1GtyJWFsCWtNXrBP9Hff4vqPxhj4IXHOJxPNW+Fuu8xzn32L9iyAa5qjup5K8rPH71zC3rH\nFkg9Dh2iUGHhlfAuhKg+pFiISqML8tDrlqNX/Ad8/TBGT7rg7a5aa/Ti99Ar/oO69W7UXQ+4fA7j\n5gEE9/8TaV9/hl69FD0/AQ1Qqza0vA7Vuz+qa5+Ke1NC1BBSLITb6fRT6O8S0WuToCDfsf700UOY\nrz6NMfb/UE2a/b7v2bPoLz5Cf/e5Y5GgP40osfyoKwzfuhg3D0D37g+H9kJhIUS2RHl6VfRbE6LG\nsEWxGDNmDLVr18YwDDw8PIiLiyM3N5cZM2Zw6tQpwsLCmDBhAn5+flZHFeWgC8851nH4ZjEUF6Nu\n7I7qMwAVeQ36yEHMtyZjTp2E8egEaByJXvkNes13kJeLir7NMQ1HOQvF+ZRS0LRlBb4jIWouWxQL\ngBdffBF//9/n5klMTKRt27YMHDiQxMREEhMTGTas7HZrYQ1dWAhmMWgTNLDnJ8yF78CpE3BjV4x7\nH0GF1HPurxo3xXg+HnP2q5j/iAOlHFNldOiK6t0fWrS+okIhhKhYtikWf5ScnMxLL70EQHR0NC+9\n9JIUCxvRe7ZzZuUhindug5/3Q9rJ0js1aIwxcfJF50pSAUEYT09BL5kPtWo7JuC7wAJCQgjr2aZY\nTJkyBYC+ffsSExNDdnY2QUGOWyQDAwPJzs62Mp44j/n9t+h5b5ELUK8B6qrm0LUPeHsDjisE/ANQ\nHXugPC/9EVNe3qjBj1ZGbCHEFbBFsZg8eTLBwcFkZ2fzyiuvEBERUeJ5pdQFmySSkpJISkoCIC4u\njtAyRu5eiqen5xUd7y52y1W4ZzsZH7+N9/U3ETIpDrNWbasjlWK379n57JrNrrnAvtnsmgvck80W\nxSI42HH7ZEBAAJ06dWLfvn0EBASQmZlJUFAQmZmZJfozfhMTE0NMTIzzcVra5S9XGRoaekXHu4ud\ncunTmZivTYLAYIpG/BmzVm3bZDufnb5nf2TXbHbNBfbNZtdcUL5sf/zj/GIsH8FdUFBAfn6+8+ut\nW7fSpEkTOnbsyKpVqwBYtWoVnTp1sjJmjaeLijDnTIW8HIzY50usJCeEqP4sv7LIzs5m+vTpABQX\nF9O9e3euv/56mjVrxowZM1i+fLnz1llxeXRONhz7GX38KGScgoxT6IxTUDcQY9gTqLoBlz6+qBD9\nyVzYuwP12FOoxk0rKbkQwi4sLxb169dn2rRppbbXrVuXF154wYJE1YPe+SPmfz+DIwch57ybAzw8\nIDAEgkNh20bM157BGPcCqkGj0q9RXIxevwL95QJIT0XdcjdG5+hKfBdCCLuwvFiIiqWzM9GL3kNv\nWAXBYah2naDhVaiIJtCgEQQGO6b1BvSB3ZhvveIoGE9MQrVqj9YaTh5D796G/jYRUo/BVc0xhj0B\nbTpY/O6EEFaRYlFN6LMF6DXfoT//CArPoQYMQd3+J5R3rYseoyKvwXh+Ouas/4f5xkvQ+gbH9Bi/\nXYk0vApjzPPQvrMMkBOihpNiUYVpreHQPvSab9EbVjvmXWrVHuP+0ajwhi69hgqtjzHp75gfvAFH\nD6HadHCMnm7RGsIbSZEQQgBSLKosnZ+HOetl2LcTvL0d8y5173tZ02QoH188Yp93U1IhRHUgxaIK\n0mYx5jvxcGA3ashIVNTNsuqbEMKtpFhUQfrf82FrMuqB0Ri9+lkdRwhRA0ixsDG9fxf5W0+jm16L\nqusYwW6uW45e+m9Ur9uRQiGEqCxSLGxIm8Xorxaiv1rIaa3BMODadqiW16G/WgDXtEXdN9LqmEKI\nGkSKhYX0prWYn3+ManMD6qaecHULyMl29Efs/BEV1ZuggfeTuXIpeuMaxxrSYeEYo58rczZXIYSo\nSPIbxyJ67w5HUfAPRK/8DzrpCwgLh3PnHCvFDR+L6t4Xr7AwjOD66LsfhF8OgX8gyq/0pIpCCOFO\nUiwqkDZNdOKHEByK6nErysPjwvud+AUzYQqE1MeYNBUMA715vXOshPHnF0vNv6SUgkYyJ5MQwhpS\nLCqQXv4l+ptPHV+vWooxdBSqZZuS++RkO8ZHGAbG+BecVwmqWwx0iyn1mkIIYQdSLCqIPnoQ/dm/\noP1NGF16YS5+D3PaX37vizBNME10yjrIysB46hVUvQZWxxZCCJdIsagA+txZzHdeBx8/jIfGoeoG\nYLTtiP7mU/TSJbBh9e87e3tjPDYR1exa6wILIUQ5SbGoAPrf8+CXw46+hl/XhlC1aqMGDkP3uxeK\nCh23vyoP8PCQO5mEEFWO/Na6TNoshqxM9K6t6GVfovrcgbruxlL7Ke9acImZX4UQoiqQYlEOOj8P\n/flH6C3/g6x0KC52PNHwKtSfHrI2nBBCuJEUCxfpzesxP34bsjPg+s6OjuuQeqiQMGjeCuXlbXVE\nIYRwGykWZdCnMzE//AdsXg+NrnasKBd5jdWxhBCiUkmxuARdkI858yU48QvqTw+hYu6SzmkhRI1k\n6W++tLQ0EhISyMrKQilFTEwM/fr1Y9GiRSxbtgx/f8eAtaFDh9KhQ+Wu/+xcM+LoYYxxf0O1Ld15\nLYQQNYWlxcLDw4MHH3yQyMhI8vPzmTRpEu3atQOgf//+3HnnnZZl05/Ngx83oIaMkkIhhKjxLC0W\nQUFBBAUFAVCnTh0aNmxIRkZGpWbQGacw50wlp11HdKOm0LyVY56mb5egevfD6DOgUvMIIYQd2aYB\nPjU1lYMHD9K8eXN27drF0qVLWb16NZGRkQwfPhw/Pz/3nPhMLnh4kPf1YsfgOQCloM0NsmaEEEL8\nSmmttdUhCgoKePHFFxk0aBCdO3cmKyvL2V+xcOFCMjMziY2NLXVcUlISSUlJAMTFxXHu3LnLzuBh\nFpO/axuFO7dSnHYSv2FPYPi6qUCVg6enJ0VFRVbHuCC7ZrNrLrBvNrvmAvtms2suKF82b2/Xbvu3\nvFgUFRUxdepU2rdvz4ABpZt8UlNTmTp1KvHx8WW+1rFjxy47R2hoKGlpaZd9vLvYNRfYN5tdc4F9\ns9k1F9g3m11zQfmyRUREuLSfcSWBrpTWmjlz5tCwYcMShSIzM9P59YYNG2jcuLEV8YQQQvzK0j6L\n3bt3s3r1apo0acIzzzwDOG6TXbt2LYcOHUIpRVhYGKNGjbIyphBC1HiWFotrr72WRYsWldpe2WMq\nhBBCXJqlzVBCCCGqBikWQgghyiTFQgghRJmkWAghhCiTFAshhBBlsnxQnhBCCPuTK4tfTZo0yeoI\nF2TXXGDfbHbNBfbNZtdcYN9sds0F7skmxUIIIUSZpFgIIYQok8dLL730ktUh7CIyMtLqCBdk11xg\n32x2zQX2zWbXXGDfbHbNBRWfTTq4hRBClEmaoYQQQpTJNivlWWXLli28//77mKZJnz59GDhwoGVZ\nZs+eTUpKCgEBAc71O3Jzc5kxYwanTp0iLCyMCRMmuG/VwItIS0sjISGBrKwslFLExMTQr18/W2Q7\nd+4cL774IkVFRRQXF9OlSxcGDx5MamoqM2fOJCcnh8jISMaNG4enZ+V/3E3TZNKkSQQHBzNp0iTb\n5BozZgy1a9fGMAw8PDyIi4uzxc/zzJkzzJkzhyNHjqCU4oknniAiIsLyXMeOHWPGjBnOx6mpqQwe\nPJjo6GjLs3311VcsX74cpRSNGzcmNjaWrKysiv+c6RqsuLhYjx07Vp84cUIXFhbqp59+Wh85csSy\nPNu3b9f79+/XEydOdG6bP3++XrJkidZa6yVLluj58+dXeq6MjAy9f/9+rbXWeXl5evz48frIkSO2\nyGaaps7Pz9daa11YWKj/8pe/6N27d+v4+Hi9Zs0arbXWb7/9tl66dGmlZ9Na6y+//FLPnDlTv/ba\na1prbZtcsbGxOjs7u8Q2O/w833zzTZ2UlKS1dvw8c3NzbZHrfMXFxfqxxx7TqamplmdLT0/XsbGx\n+uzZs1prx+drxYoVbvmc1ehmqH379hEeHk79+vXx9PSka9euJCcnW5andevWpf4qSU5OJjo6GoDo\n6GhL8gUFBTk7y+rUqUPDhg3JyMiwRTalFLVr1waguLiY4uJilFJs376dLl26ANCrVy9LsqWnp5OS\nkkKfPn0Ax2Jfdsh1MVb/PPPy8ti5cyc333wz4Fga1NfX1/Jcf7Rt2zbCw8MJCwuzRTbTNDl37hzF\nxcWcO3eOwMBAt3zOanQzVEZGBiEhIc7HISEh7N2718JEpWVnZxMUFARAYGAg2dnZluZJTU3l4MGD\nNG/e3DbZTNPkueee48SJE9x6663Ur18fHx8fPDw8AAgODiYjI6PSc33wwQcMGzaM/Px8AHJycmyR\n6zdTpkwBoG/fvsTExFj+80xNTcXf35/Zs2dz+PBhIiMjGTFihOW5/mjt2rV069YNsP7fZ3BwMHfc\ncQdPPPEE3t7etG/fnsjISLd8zmp0sahqlFIopSw7f0FBAfHx8YwYMQIfH58Sz1mZzTAMpk2bxpkz\nZ5g+ffoVrcVeUTZt2kRAQACRkZFs377d6jilTJ48meDgYLKzs3nllVdKrcNsxc+zuLiYgwcP8sgj\nj9CiRQvef/99EhMTLc91vqKiIjZt2sT9999f6jkrsuXm5pKcnExCQgI+Pj68/vrrbNmyxS3nqtHF\nIjg4mPT0dOfj9PR0goODLUxUWkBAAJmZmQQFBZGZmYm/v78lOYqKioiPj6dHjx507tzZVtl+4+vr\nS5s2bdizZw95eXkUFxfj4eFBRkZGpf9cd+/ezcaNG9m8eTPnzp0jPz+fDz74wPJcv/ntvAEBAXTq\n1Il9+/ZZ/vMMCQkhJCSEFi1aANClSxcSExMtz3W+zZs307RpUwIDAwHr/w1s27aNevXqOc/buXNn\ndu/e7ZbPWY3us2jWrBnHjx8nNTWVoqIi1q1bR8eOHa2OVULHjh1ZtWoVAKtWraJTp06VnkFrzZw5\nc2jYsCEDBgywVbbTp09z5swZwHFn1NatW2nYsCFt2rRh/fr1AKxcubLSf673338/c+bMISEhgSef\nfJLrrruO8ePHW54LHFeIvzWNFRQUsHXrVpo0aWL5zzMwMJCQkBDnleG2bdto1KiR5bnOd34TFFj/\nbyA0NJS9e/dy9uxZtNbO75k7Pmc1flBeSkoK//rXvzBNk969ezNo0CDLssycOZMdO3aQk5NDQEAA\ngwcPplOnTsyYMYO0tDTLbs3btWsXL7zwAk2aNHFeZg8dOpQWLVpYnu3w4cMkJCRgmiZaa6Kiorjn\nnns4efIkM2fOJDc3l6ZNmzJu3Di8vLwqNdtvtm/fzpdffsmkSZNskevkyZNMnz4dcDT9dO/enUGD\nBpGTk2P5z/PQoUPMmTOHoqIi6tWrR2xsLFpry3OBo7DGxsby1ltvOZth7fA9W7RoEevWrcPDw4Or\nr76a0aNHk5GRUeGfsxpfLIQQQpStRjdDCSGEcI0UCyGEEGWSYiGEEKJMUiyEEEKUSYqFEEKIMkmx\nEDXSxIkTLRtZnZaWxoMPPohpmpacX4jLIbfOihpt0aJFnDhxgvHjx7vtHGPGjOHxxx+nXbt2bjuH\nEO4mVxZCXIHi4mKrIwhRKeTKQtRIY8aM4ZFHHnGOZPb09CQ8PJxp06aRl5fHv/71LzZv3oxSit69\nezN48GAMw2DlypUsW7aMZs2asXr1am655RZ69erF22+/zeHDh1FK0b59ex599FF8fX158803WbNm\nDZ6enhiGwT333ENUVBRjx47lk08+cc7dM3fuXHbt2oWfnx933XUXMTExgOPK5+jRo3h7e7NhwwZC\nQ0MZM2YMzZo1AyAxMZFvvvmG/Px8goKCeOyxx2jbtq1l31dRfdXoiQRFzebl5cXdd99dqhkqISGB\ngIAAZs2axdmzZ4mLiyMkJIS+ffsCsHfvXrp27crcuXMpLi4mIyODu+++m1atWpGfn098fDyLFy9m\nxIgRjBs3jl27dpVohkpNTS2R44033qBx48a8/fbbHDt2jMmTJxMeHs51110HOGawfeqpp4iNjWXB\nggW89957TJkyhWPHjrF06VJee+01goODSU1NlX4Q4TbSDCXEebKysti8eTMjRoygdu3aBAQE0L9/\nf9atW+fcJygoiNtvvx0PDw+8vb0JDw+nXbt2eHl54e/vT//+/dmxY4dL50tLS2PXrl088MADeHt7\nc/XVV9OnTx/n5HQA1157LR06dMAwDHr27MmhQ4cAx9TshYWFHD161DmXUnh4eIV+P4T4jVxZCHGe\ntLQ0iouLGTVqlHOb1rrEIlmhoaEljsnKyuKDDz5g586dFBQUYJqmy5PJZWZm4ufnR506dUq8/v79\n+52PAwICnF97e3tTWFhIcXEx4eHhjBgxgsWLF3P06FHat2/P8OHDbTfNvqgepFiIGu2Pi9WEhITg\n6enJu+++61xprCyffPIJAPHx8fj5+bFhwwbee+89l44NCgoiNzeX/Px8Z8FIS0tz+Rd+9+7d6d69\nO3l5efzzn//ko48+Yty4cS4dK0R5SDOUqNECAgI4deqUs60/KCiI9u3bM2/ePPLy8jBNkxMnTlyy\nWSk/P5/atWvj4+NDRkYGX375ZYnnAwMDS/VT/CY0NJRrrrmGjz/+mHPnznH48GFWrFhBjx49ysx+\n7NgxfvrpJwoLC/H29sbb29vSVeRE9SbFQtRoUVFRADz66KM899xzAIwdO5aioiImTpzIww8/zOuv\nv05mZuZFX+Pee+/l4MGDPPTQQ7z22mvcdNNNJZ4fOHAgn332GSNGjOCLL74odfyf//xnTp06xeOP\nP8706dO59957XRqTUVhYyEcffcSjjz7KyJEjOX369AWX+xSiIsits0IIIcokVxZCCCHKJMVCCCFE\nmaRYCCGEKJMUCyGEEGWSYiGEEKJMUiyEEEKUSYqFEEKIMkmxEEIIUSYpFkIIIcr0/wEdQehzvVrX\nmQAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107ba828>"
+       "<matplotlib.figure.Figure at 0x1208bce48>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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yyMjIAGDp0qXEx7u3nA4MDCQmIZFiIDI0hFA3r1NSWgxJA4g96/zqAYOpqq8l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\nrkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1208bccc0>"
       ]
      },
      "metadata": {},
@@ -397,7 +412,8 @@
    ],
    "source": [
     "util.plot_curve(loss_list, \"loss\")\n",
-    "util.plot_curve(avg_return_list, \"average return\")"
+    "util.plot_curve(avg_return_list, \"average return\")\n",
+    "util.plot_curve(avg_advantage_variance_list, \"average advantage variance\")"
    ]
   },
   {
@@ -425,7 +441,209 @@
     "\n",
     "can remove the baseline.\n",
     "\n",
-    "Modify the code to compare the variance and performance before and after adding baseline. And explain wht the baseline won't introduce bias. Then, write a report about your findings and explainations. "
+    "Modify the code to compare the variance and performance before and after adding baseline. And explain why the baseline won't introduce bias. Then, write a report about your findings and explainations. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 15.07 | Average Advantage Variance: 17.98873525729186\n",
+      "Iteration 2: Average Return = 17.27 | Average Advantage Variance: 24.259566651949285\n",
+      "Iteration 3: Average Return = 19.4 | Average Advantage Variance: 30.39233750543137\n",
+      "Iteration 4: Average Return = 20.87 | Average Advantage Variance: 34.60069318204511\n",
+      "Iteration 5: Average Return = 19.82 | Average Advantage Variance: 31.314898097805916\n",
+      "Iteration 6: Average Return = 22.94 | Average Advantage Variance: 40.7568094184233\n",
+      "Iteration 7: Average Return = 22.28 | Average Advantage Variance: 37.74998250285457\n",
+      "Iteration 8: Average Return = 22.94 | Average Advantage Variance: 38.78101747563966\n",
+      "Iteration 9: Average Return = 25.12 | Average Advantage Variance: 45.761837500421606\n",
+      "Iteration 10: Average Return = 27.19 | Average Advantage Variance: 52.82168922122262\n",
+      "Iteration 11: Average Return = 28.93 | Average Advantage Variance: 59.846480706886176\n",
+      "Iteration 12: Average Return = 28.39 | Average Advantage Variance: 56.644527151990275\n",
+      "Iteration 13: Average Return = 34.1 | Average Advantage Variance: 76.97377848497015\n",
+      "Iteration 14: Average Return = 32.65 | Average Advantage Variance: 70.55167723972754\n",
+      "Iteration 15: Average Return = 37.42 | Average Advantage Variance: 88.13425439000213\n",
+      "Iteration 16: Average Return = 35.18 | Average Advantage Variance: 79.30240705583327\n",
+      "Iteration 17: Average Return = 32.5 | Average Advantage Variance: 69.97039541707923\n",
+      "Iteration 18: Average Return = 39.19 | Average Advantage Variance: 94.2904341173091\n",
+      "Iteration 19: Average Return = 41.73 | Average Advantage Variance: 103.92601392727282\n",
+      "Iteration 20: Average Return = 42.05 | Average Advantage Variance: 103.99257977348967\n",
+      "Iteration 21: Average Return = 42.11 | Average Advantage Variance: 104.89584131423284\n",
+      "Iteration 22: Average Return = 45.93 | Average Advantage Variance: 118.66045468218458\n",
+      "Iteration 23: Average Return = 44.64 | Average Advantage Variance: 113.88206899584233\n",
+      "Iteration 24: Average Return = 45.75 | Average Advantage Variance: 118.51032952438266\n",
+      "Iteration 25: Average Return = 48.07 | Average Advantage Variance: 126.16384444022941\n",
+      "Iteration 26: Average Return = 50.03 | Average Advantage Variance: 134.5234890978518\n",
+      "Iteration 27: Average Return = 48.11 | Average Advantage Variance: 126.55897573954617\n",
+      "Iteration 28: Average Return = 49.45 | Average Advantage Variance: 131.74688877422443\n",
+      "Iteration 29: Average Return = 47.21 | Average Advantage Variance: 122.7608277162396\n",
+      "Iteration 30: Average Return = 50.56 | Average Advantage Variance: 135.83763136133996\n",
+      "Iteration 31: Average Return = 49.1 | Average Advantage Variance: 129.94562320002058\n",
+      "Iteration 32: Average Return = 54.49 | Average Advantage Variance: 151.0510482861703\n",
+      "Iteration 33: Average Return = 50.09 | Average Advantage Variance: 133.4490538033892\n",
+      "Iteration 34: Average Return = 49.64 | Average Advantage Variance: 132.64025183352587\n",
+      "Iteration 35: Average Return = 54.76 | Average Advantage Variance: 152.95771567447488\n",
+      "Iteration 36: Average Return = 56.61 | Average Advantage Variance: 158.71447656714705\n",
+      "Iteration 37: Average Return = 53.11 | Average Advantage Variance: 145.4200272660054\n",
+      "Iteration 38: Average Return = 57.82 | Average Advantage Variance: 163.68843848051407\n",
+      "Iteration 39: Average Return = 57.76 | Average Advantage Variance: 163.1967543818422\n",
+      "Iteration 40: Average Return = 55.12 | Average Advantage Variance: 153.0471693865027\n",
+      "Iteration 41: Average Return = 54.56 | Average Advantage Variance: 150.83696743769914\n",
+      "Iteration 42: Average Return = 60.15 | Average Advantage Variance: 172.4882976604602\n",
+      "Iteration 43: Average Return = 56.96 | Average Advantage Variance: 159.13974513624925\n",
+      "Iteration 44: Average Return = 56.71 | Average Advantage Variance: 159.0288286001276\n",
+      "Iteration 45: Average Return = 62.12 | Average Advantage Variance: 179.0243915544896\n",
+      "Iteration 46: Average Return = 61.46 | Average Advantage Variance: 176.85944016248106\n",
+      "Iteration 47: Average Return = 61.64 | Average Advantage Variance: 178.1822465379232\n",
+      "Iteration 48: Average Return = 62.54 | Average Advantage Variance: 180.48829735947496\n",
+      "Iteration 49: Average Return = 63.13 | Average Advantage Variance: 185.0033715857327\n",
+      "Iteration 50: Average Return = 57.41 | Average Advantage Variance: 162.58400523457303\n",
+      "Iteration 51: Average Return = 66.28 | Average Advantage Variance: 196.20115813447293\n",
+      "Iteration 52: Average Return = 60.79 | Average Advantage Variance: 175.35972648933014\n",
+      "Iteration 53: Average Return = 64.15 | Average Advantage Variance: 186.35501600348726\n",
+      "Iteration 54: Average Return = 62.55 | Average Advantage Variance: 180.64528544736172\n",
+      "Iteration 55: Average Return = 61.48 | Average Advantage Variance: 177.38064297854646\n",
+      "Iteration 56: Average Return = 70.65 | Average Advantage Variance: 212.41116672973388\n",
+      "Iteration 57: Average Return = 68.17 | Average Advantage Variance: 202.70380876828568\n",
+      "Iteration 58: Average Return = 65.08 | Average Advantage Variance: 191.84987149082335\n",
+      "Iteration 59: Average Return = 69.83 | Average Advantage Variance: 209.2672366722662\n",
+      "Iteration 60: Average Return = 77.01 | Average Advantage Variance: 236.62523402722152\n",
+      "Iteration 61: Average Return = 77.55 | Average Advantage Variance: 239.07744235445833\n",
+      "Iteration 62: Average Return = 79.43 | Average Advantage Variance: 245.0812624759146\n",
+      "Iteration 63: Average Return = 75.95 | Average Advantage Variance: 233.73103679982214\n",
+      "Iteration 64: Average Return = 79.47 | Average Advantage Variance: 245.21732948979385\n",
+      "Iteration 65: Average Return = 73.09 | Average Advantage Variance: 221.7741435321774\n",
+      "Iteration 66: Average Return = 80.21 | Average Advantage Variance: 248.86657222663212\n",
+      "Iteration 67: Average Return = 85.3 | Average Advantage Variance: 264.08645777997776\n",
+      "Iteration 68: Average Return = 80.84 | Average Advantage Variance: 250.83204418102667\n",
+      "Iteration 69: Average Return = 82.06 | Average Advantage Variance: 254.40793448872319\n",
+      "Iteration 70: Average Return = 89.24 | Average Advantage Variance: 277.8516626113031\n",
+      "Iteration 71: Average Return = 91.81 | Average Advantage Variance: 288.17092436324623\n",
+      "Iteration 72: Average Return = 94.63 | Average Advantage Variance: 300.1178249906723\n",
+      "Iteration 73: Average Return = 99.04 | Average Advantage Variance: 314.18512101162617\n",
+      "Iteration 74: Average Return = 105.22 | Average Advantage Variance: 332.3944809299041\n",
+      "Iteration 75: Average Return = 118.31 | Average Advantage Variance: 378.5654374226116\n",
+      "Iteration 76: Average Return = 121.46 | Average Advantage Variance: 385.60203499634395\n",
+      "Iteration 77: Average Return = 119.73 | Average Advantage Variance: 381.91600148350255\n",
+      "Iteration 78: Average Return = 119.72 | Average Advantage Variance: 382.1346147848214\n",
+      "Iteration 79: Average Return = 138.14 | Average Advantage Variance: 444.825602089336\n",
+      "Iteration 80: Average Return = 127.85 | Average Advantage Variance: 407.6044104774574\n",
+      "Iteration 81: Average Return = 137.89 | Average Advantage Variance: 441.71671559445605\n",
+      "Iteration 82: Average Return = 129.0 | Average Advantage Variance: 414.35461732857965\n",
+      "Iteration 83: Average Return = 139.75 | Average Advantage Variance: 448.80049076254386\n",
+      "Iteration 84: Average Return = 139.74 | Average Advantage Variance: 446.13348336138995\n",
+      "Iteration 85: Average Return = 137.64 | Average Advantage Variance: 442.4209762418483\n",
+      "Iteration 86: Average Return = 137.1 | Average Advantage Variance: 440.69758027219154\n",
+      "Iteration 87: Average Return = 139.93 | Average Advantage Variance: 446.0127710256396\n",
+      "Iteration 88: Average Return = 140.26 | Average Advantage Variance: 446.43292476636225\n",
+      "Iteration 89: Average Return = 143.18 | Average Advantage Variance: 455.1543973648255\n",
+      "Iteration 90: Average Return = 151.18 | Average Advantage Variance: 478.02890536608567\n",
+      "Iteration 91: Average Return = 149.82 | Average Advantage Variance: 474.8489712994313\n",
+      "Iteration 92: Average Return = 153.43 | Average Advantage Variance: 484.3441318615481\n",
+      "Iteration 93: Average Return = 157.22 | Average Advantage Variance: 495.13761951511435\n",
+      "Iteration 94: Average Return = 163.58 | Average Advantage Variance: 509.84860387406474\n",
+      "Iteration 95: Average Return = 165.33 | Average Advantage Variance: 511.91289314584435\n",
+      "Iteration 96: Average Return = 169.97 | Average Advantage Variance: 524.4769097030922\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 97: Average Return = 169.86 | Average Advantage Variance: 524.5263287282062\n",
+      "Iteration 98: Average Return = 176.71 | Average Advantage Variance: 539.9921097000191\n",
+      "Iteration 99: Average Return = 174.43 | Average Advantage Variance: 535.058614025152\n",
+      "Iteration 100: Average Return = 176.2 | Average Advantage Variance: 539.0051666387105\n",
+      "Iteration 101: Average Return = 185.43 | Average Advantage Variance: 560.1852420366822\n",
+      "Iteration 102: Average Return = 187.21 | Average Advantage Variance: 563.3867450825511\n",
+      "Iteration 103: Average Return = 185.87 | Average Advantage Variance: 563.1198251073577\n",
+      "Iteration 104: Average Return = 190.54 | Average Advantage Variance: 573.1258449778474\n",
+      "Iteration 105: Average Return = 190.25 | Average Advantage Variance: 572.3870107768262\n",
+      "Iteration 106: Average Return = 190.91 | Average Advantage Variance: 573.6210221642276\n",
+      "Iteration 107: Average Return = 186.53 | Average Advantage Variance: 562.7784407716526\n",
+      "Iteration 108: Average Return = 187.37 | Average Advantage Variance: 565.9406941649773\n",
+      "Iteration 109: Average Return = 189.42 | Average Advantage Variance: 570.2138834245601\n",
+      "Iteration 110: Average Return = 189.11 | Average Advantage Variance: 569.3320141979549\n",
+      "Iteration 111: Average Return = 186.09 | Average Advantage Variance: 561.2649158417557\n",
+      "Iteration 112: Average Return = 189.12 | Average Advantage Variance: 568.0836558974601\n",
+      "Iteration 113: Average Return = 187.45 | Average Advantage Variance: 566.0837000315038\n",
+      "Iteration 114: Average Return = 188.14 | Average Advantage Variance: 567.428133700983\n",
+      "Iteration 115: Average Return = 188.17 | Average Advantage Variance: 564.6584741109092\n",
+      "Iteration 116: Average Return = 186.31 | Average Advantage Variance: 563.5194788980236\n",
+      "Iteration 117: Average Return = 188.07 | Average Advantage Variance: 566.3828262406358\n",
+      "Iteration 118: Average Return = 190.58 | Average Advantage Variance: 573.2912512744505\n",
+      "Iteration 119: Average Return = 189.88 | Average Advantage Variance: 572.1843825386998\n",
+      "Iteration 120: Average Return = 189.97 | Average Advantage Variance: 570.5475639506664\n",
+      "Iteration 121: Average Return = 186.23 | Average Advantage Variance: 561.5233957040315\n",
+      "Iteration 122: Average Return = 194.57 | Average Advantage Variance: 581.7911166226448\n",
+      "Iteration 123: Average Return = 193.33 | Average Advantage Variance: 578.0868415350511\n",
+      "Iteration 124: Average Return = 193.38 | Average Advantage Variance: 577.7394444326355\n",
+      "Iteration 125: Average Return = 195.18 | Average Advantage Variance: 583.0868744607587\n",
+      "Solve at 125 iterations, which equals 12500 episodes.\n"
+     ]
+    }
+   ],
+   "source": [
+    "sess.run(tf.global_variables_initializer())\n",
+    "\n",
+    "n_iter = 200\n",
+    "n_episode = 100\n",
+    "path_length = 200\n",
+    "discount_rate = 0.99\n",
+    "baseline = None\n",
+    "\n",
+    "po = PolicyOptimizer(env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "                     discount_rate)\n",
+    "\n",
+    "# Train the policy optimizer\n",
+    "loss_list_without_baseline, avg_return_list_without_baseline, avg_advantage_variance_list_without_baseline = po.train()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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CIAhAZbZYdXU1li5dCsZEiSBjDDfddBNqamoCKlxYodNRbzGCIAgZVcrlqquuQnFxsdu2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\ntGtnT3FmZsYnit9ObSVw6ijQ0yPcZZ8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xYwZeeuklzJgxA++++26/fdra2rBz5048/fTT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\nRQghRMj9Bzm5BmZmGM8aAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122d57240>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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euwKCw0D6K4SDmEoWjpKVlUVQUBBgWx8jKysLgIyMDEJDQ+37hYSEkJGR4ZQY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\nTMo0bNgwvLy8sFgsuLm5MX7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fHebOncvGjRtxd3enbt26xMfHU7t2bQAWLFjAsmXLsFgs\nPPjgg7Rt27bqgtU1WElJiR4+fLg+fvy4Lioq0qNHj9YpKSnODqtMGRkZev/+/VprrXNzc/XIkSN1\nSkqKnjt3rl6wYIHWWusFCxbouXPnOjNMUxYtWqQnT56s//3vf2uttU5ISNCrVq3SWms9c+ZMvWTJ\nEmeGV6apU6fqpKQkrbXWRUVFOicnp1p9Dunp6To+Pl4XFBRorW3v//Lly6vF57B9+3a9f/9+/eST\nT9rLLvTeb9y4UY8bN04bhqF3796tn3vuOafE/Hfnq8OWLVt0cXGx1tpWnzN1SElJ0aNHj9aFhYX6\nxIkTevjw4bqkpKTKYq3Rl6H27dtHeHg4devWxd3dnS5durB+/Xpnh1WmoKAg+68ib29v6tevT0ZG\nBuvXryc2NhawrZXu6nVJT09n06ZN9OzZEwCtNdu3b6dTp04A9OjRw6XrkJuby86dO7nuuusAcHd3\np3bt2tXuczAMg8LCQkpKSigsLCQwMLBafA4tWrQ4p8V2ofd+w4YNdO/eHaUUUVFRnD59GqvVWuUx\n/9356hAdHY2bmxsAUVFRZGRkALa6denSBQ8PD+rUqUN4eDj79u2rslhdq11ZxTIyMggJCbE/DwkJ\nYe/evU6M6OKlpqZy8OBBmjRpQlZWFkFBQQAEBgaSlZXl5Oj+2SeffMLAgQPJy8sDIDs7Gx8fH/sf\nSnBwsP0PxRWlpqbi7+/P9OnTOXz4MJGRkQwePLhafQ7BwcHcfPPNPP7443h6ehIdHU1kZGS1+hzO\ndqH3PiMjg9DQUPt+ISEhZGRk2Pd1VcuWLaNLly6ArQ5Nmza1b6vqz6VGtyyqu/z8fBISEhg8eDA+\nPj6ltimlUEo5KbKybdy4kYCAAJe4blxeJSUlHDx4kOuvv54333yTWrVqkZiYWGofV/8ccnJyWL9+\nPdOmTWPmzJnk5+ezZcsWZ4dVKVz9vS/L119/jZubG926dXN2KEANb1kEBweTnp5uf56enk5wcLAT\nIzKvuLiYhIQEunXrRseOHQEICAjAarUSFBSE1WrF39/fyVFe2O7du9mwYQObN2+msLCQvLw8Pvnk\nE3JzcykpKcHNzY2MjAyX/jxCQkIICQmx/9rr1KkTiYmJ1epz2Lp1K3Xq1LHH2LFjR3bv3l2tPoez\nXei9Dw4OJi0tzb6fq/+tr1ixgo0bN/Lyyy/bE97fv6+q+nOp0S2Lxo0bc+zYMVJTUykuLmbNmjV0\n6NDB2WGVSWvNjBkzqF+/PjfddJO9vEOHDqxcuRKAlStXEhMT46wQy3TvvfcyY8YMpk2bxhNPPEGr\nVq0YOXIkLVu2ZO3atYDtD8aVP4/AwEBCQkI4evQoYPviveyyy6rV5xAaGsrevXspKChAa22vQ3X6\nHM52ofe+Q4cOJCcno7Vmz549+Pj4uOwlqC1btrBw4UKeffZZatWqZS/v0KEDa9asoaioiNTUVI4d\nO0aTJk2qLK4aPyhv06ZNzJ49G8MwuPbaa7n99tudHVKZdu3axcsvv0zDhg3tvzoGDBhA06ZNmTRp\nEmlpadXils0ztm/fzqJFixgzZgwnTpxg8uTJ5OTk0KhRI0aMGIGHh4ezQ7ygQ4cOMWPGDIqLi6lT\npw7x8fForavV5zB//nzWrFmDm5sbV1xxBUOHDiUjI8PlP4fJkyezY8cOsrOzCQgIoH///sTExJz3\nvddaM2vWLH799Vc8PT2Jj4+ncePGzq7CeeuwYMECiouL7f/PNG3alCFDhgC2S1PLly/HYrEwePBg\n2rVrV2Wx1vhkIYQQomw1+jKUEEIIcyRZCCGEKJMkCyGEEGWSZCGEEKJMkiyEEEKUSZKFqJGefPJJ\ntm/f7pRzp6Wlcf/992MYhlPOL0R5yK2zokabP38+x48fZ+TIkQ47x7Bhw3jsscdo06aNw84hhKNJ\ny0KICigpKXF2CEJUCWlZiBpp2LBhPPTQQ7z11luAbXrx8PBwJk6cSG5uLrNnz2bz5s0opbj22mvp\n378/FouFFStWsHTpUho3bkxycjLXX389PXr0YObMmRw+fBilFNHR0Tz88MPUrl2bqVOnsmrVKtzd\n3bFYLNx555107tyZ4cOH8/nnn9vnXvrggw/YtWsXvr6+3HrrrcTFxQG2ls+RI0fw9PRk3bp1hIaG\nMmzYMPvo48TERL777jvy8vIICgrikUceoXXr1k57X8Wlq0ZPJChqNg8PD2677bZzLkNNmzaNgIAA\npkyZQkFBAePHjyckJIRevXoBsHfvXrp06cIHH3xASUkJGRkZ3HbbbTRv3py8vDwSEhL48ssvGTx4\nMCNGjGDXrl2lLkOlpqaWiuOdd96hQYMGzJw5k6NHj/Laa68RHh5Oq1atANsMvU899RTx8fF88cUX\nfPTRR4wbN46jR4+yZMkS/v3vfxMcHExqaqr0gwiHkctQQpwlMzOTzZs3M3jwYLy8vAgICKBv376s\nWbPGvk9QUBA33ngjbm5ueHp6Eh4eTps2bfDw8MDf35++ffuyY8cOU+dLS0tj165d3HfffXh6enLF\nFVfQs2dP+2R4AM2aNY2U6aMAAAIYSURBVKN9+/ZYLBa6d+/OoUOHALBYLBQVFXHkyBH73FTh4eGV\n+n4IcYa0LIQ4S1paGiUlJfaJ28A2y+/Zi2SdvYgO2BLMJ598ws6dO8nPz8cwDNMTB1qtVnx9ffH2\n9i71+vv377c/DwgIsD/29PSkqKiIkpISwsPDGTx4MF9++SVHjhwhOjqaQYMGufTU26L6kmQharS/\nL44TEhKCu7s7s2bNsq8UV5bPP/8cgISEBHx9fVm3bh0fffSRqWODgoLIyckhLy/PnjDS0tJMf+F3\n7dqVrl27kpuby/vvv89nn33GiBEjTB0rxMWQy1CiRgsICODkyZP2a/1BQUFER0czZ84ccnNzMQyD\n48eP/+Nlpby8PLy8vPDx8SEjI4NFixaV2h4YGHhOP8UZoaGhXHnllfznP/+hsLCQw4cPs3z5clOr\nox09epRt27ZRVFSEp6cnnp6e1XplOOHaJFmIGq1z584APPzw/7dvxygQwlAURd+qXIdNGhuVEGwE\nwcYl2Ii7sLTJhrKAFIKtFlMPw/C1v6cN+ZDqEki8pmmSJPV9r/u+NY6j2rbVuq46juPvDOecUkqq\n61rzPKsoiq/1siy177uaplGM8Wf/MAzKOavrOi3LIufcoz8Z13Vp2zZ57xVC0HmeqqrqzfGBx3g6\nCwAwcbMAAJiIBQDARCwAACZiAQAwEQsAgIlYAABMxAIAYCIWAAATsQAAmD7RB4HLQp6xnwAAAABJ\nRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122d6e358>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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APz8/Tp06RUFBAcXFxXYNJ4S4Op2TBQd2ofoNRbm4ODqOqKdM9Vn07t2b3bt3\nM2DAAAYPHsy0adNwcXGhTx8Zzy2Eo+ltX4M2UP2jHR1F1GOmisWoUaNsr++66y5uvPFGiouL6dKl\ni71yCSFM0GWl6E1fwE2dUI2bOTqOqMdMD539tfbt29d0DiFENegt6yE3C8tjzzg6iqjnLlssXnnl\nFf72t78BMGXKlMtOIjht2rSrnqS0tJSpU6dSXl5ORUUFffr04f777yc9PZ3Zs2eTn59PaGgo48eP\nx9XVlbKyMubNm8fx48fx9vbmmWeeoXHjxtVsohD1ky4rQ6/9H7SLgPDOjo4j6rnLFouoqCjb6yFD\nhlzTSdzc3Jg6dSqenp6Ul5czZcoUunbtymeffcbw4cPp378/b7/9Nhs2bODWW29lw4YNNGzYkLlz\n57J161bef/99Jk6ceE0ZhKhvbFcVo5+WGaGF3V22WAwYMACwroaXlpbGPffcg5ubW7VOopTC09MT\ngIqKCioqKlBKcfDgQZ5++mkABg0axIoVK7j11lvZsWOHbYqRPn368O6776K1lr8QQpyjy8rQX/wP\n2rWH9tJ3KOzvqn0WFouFr7766prnhzIMgxdeeIHU1FRuu+02mjRpgpeXFy7nhvoFBASQnZ0NQHZ2\nNoGBgQC4uLjg5eVFfn4+Pj4+lT4zPj6e+Ph4AGbMmEFQUFC1srm6ulb7WGchbXAetdGOwo+XUZCT\nid8zU/AIDq7xz68PPwtpQ80y1cE9cOBA1q9fz2233VbtE1ksFl599VUKCwt57bXXOH36dLU/67zo\n6Giioy8MF8zMzKzW5wQFBVX7WGchbXAe9m6HzsnC+GgxdO1Nfkgb8u1wrvrws5A2mBMSEmJqP1PF\nIjk5mXXr1rFmzRoCAwMr3Q4y08H9aw0bNqRDhw4cPXqUoqIiKioqcHFxITs7m4CAAMB6lZGVlUVg\nYCAVFRUUFRXh7e1dpfMIUV/plUugogLL/X9ydBRxHTFVLIYOHcrQoUOrfZIzZ87g4uJCw4YNKS0t\nZd++fdx999106NCB7du3079/fzZt2kTPnj0B6NGjB5s2bSIsLIzt27fToUMH6a8QAtDHktDfJaCG\n348KburoOOI6YqpYDBo06JpOkpOTw/z58zEMA601ffv2pUePHrRo0YLZs2fz4YcfcsMNN9hGXQ0Z\nMoR58+Yxfvx4GjVqxDPPyBhyIXRZKcay+eAfhLrjPkfHEdcZpbXWZnbMzc0lOTmZ/Px8fn3ItQ6r\nrUnV7QeRe5vOoT60AezXDmPFYvRXq7A8/RKqY/ca//xfqw8/C2mDOTXaZ/H9998zd+5cmjVrRkpK\nCi1btiQlJYXw8HCnKhZC1FeqhLtqAAAgAElEQVT6WBJ6/WrUwNvtXiiEuBRTxWL58uXExsbSt29f\nRo8ezb/+9S82btxISkqKvfMJcd3T5WUYi2dDYGPUH0Y5Oo64TpmaojwzM5O+fftW2hYVFcXmzZvt\nEkoI8StHDkBGKpY/jEZ5ejk6jbhOmSoWPj4+5ObmAhAcHMzRo0dJS0vDMAy7hhNCgN77Pbi7Q8ce\njo4irmOmh84ePnyYPn36MHz4cKZNm4ZSijvvvNPe+YS4rmmt0fsSoX1XlLuHo+OI65ipYhETE2N7\nHRUVRYcOHSguLqZFixZ2CyaEAE7/BFnpqGEyVFY4lqnbUJ9//rntNhRYh3NJoRCi5uhd31IxfRL6\nbFHl7Xu/B0B1jnRELCFsTF1ZHDx4kA8++ICbbrqJAQMG0Lt3b7y8pKNNiJqgDQNj1TJIPYVe/wnq\nrgcuvLcvEVq3Q/kFOjChECaLxV/+8hcKCwvZvn07mzdv5t1336VLly7cfPPN9O7d294Zhajf9iVC\n6inwD0KvX40ePAzl7YvOz4PjR1B3jnB0QiHM3YYC6wSAQ4cOZerUqcTFxVFcXMy///1ve2YT4rpg\nfPkxBDbG8vRUKClBr/2ftWP72w2gNapLL0dHFKJqa3AfPnyYLVu28N1339GoUSPuv/9+e+US4rqg\nk5Mg+RDqj0+gmrdG9RuC3vQ5+uRRSD4ErUKhVVtHxxTCXLFYtmwZ3377LUop+vbty9/+9jfatGlj\n52hC1H/Gl6ugkTdqgHVdFvW7B9CJmyEzDfXgk6gBt8iMy8IpmCoWJSUljB8/nvbt29s7jxD1gs7P\ns95C8vG7sC0jFdw9UL7+1q+Li2D/DlT0XSgP67LDKjAYyytvQ8NGKDd3h2QX4lJMFYvHH3/c3jmE\nqDdKk/ZgTH8BPBtgmTYP5eGJLjiDMf05aNUOl4nnFgw7dggqKlAdKk8MqPwCHJBaiCsz3cEthLgy\nrTXGtg3kTJ0Ang0gKx396YfW9z7+DxTkw5F9tmcp9OG94OoKbcMdGVsIU6rUwS2EuJguOIPe8Lm1\nryH1Z9w6dqfi8UnoFe+i4z/BaNwU/c1XENYRjh6Ag7ug5wD04X3Qtr1M4yHqBLmyEOIa6fffRH/2\nIfgGoB4Zh/+UOFTDRqh7R0EDL/SyBeAfhOWpv4FXI/S+RHTBGUg5gQrv7Oj4QphiuliUl5dz6NAh\ntm3bBkBxcTHFxcV2CyZEXaCNCnTSHlS/obhMegXLzbei3NwAUN4+qD/8CZQFyx//jPJqiOrUA71/\nJ/rQPmsHuBQLUUeYug31008/MXPmTNzc3MjKyqJfv34kJSWRkJDAxIkT7Z1RCOeVchKKCuAyv/Qt\n/YagO/dENfKxbujSC75LQK/7H3g0gDY31l5WIa6BqSuLd955hxEjRjB79mxcXa31JSIigsOHD9s1\nnBDOTh/ZB4AK73TZfWyFAlAduoGLC/x0HMI6oFyl21DUDaaKxalTp7j55psrbfP09KS0tNQuoYSo\nK/Th/dC0uemJ/pRXI2gXYX19hQIjhLMxVSyCg4M5fvx4pW3Jyck0bdrULqGEqAt0eTkcPVjlfgfV\n1Tr5pmrf1R6xhLALU9fAI0aMYMaMGdxyyy2Ul5ezatUq1q9fz5gxY+ydTwjn9WMylJyterEYdId1\nHqiWN9gpmBA1z9SVRY8ePXjxxRc5c+YMERERZGRkMGnSJLp06WLvfEI4LX3Y2l9BWNVuJylXN1R7\n+bsj6hbTvWs33HCDTPshriv6yH6ML1dhefw5lFfDS75PizYob59LHC1E/WKqWCxfvvyS293c3AgI\nCKBr1674+fldch8h6ir9/Tewfwf6/Tfg8ecqzf6qy0qtU4tH3e7AhELUHlPF4pdffuH777+nXbt2\nBAYGkpWVRXJyMj169GDnzp0sWrSI5557jq5dL91hl5mZyfz588nNzUUpRXR0NMOGDaOgoIC4uDgy\nMjIIDg5m4sSJNGrUCK01ixcvZvfu3Xh4eBAbG0toaGiNNlyIq9E/JoOrG/r7zdChG6rf0Avv7dwG\nZaWyNra4bpgqFoZh8Mwzz9Cr14UVuxITE9myZQuvvPIKmzZt4v33379ssXBxceHhhx8mNDSUs2fP\nMnnyZDp37symTZvo1KkTMTExrF69mtWrVzNy5Eh2795Namoqc+bM4dixYyxcuJDp06fXTIuFMEGX\nl8HPJ1GDh6N//AH937fQbdujmoRY39+8DoKbwk0y/FVcH0x1cO/du5eePXtW2tajRw/27NkDwMCB\nA0lPT7/s8f7+/rYrgwYNGtC8eXOys7NJTEwkKioKgKioKBITEwHYsWMHAwcORClFWFgYhYWF5OTk\nVL11QlTXzz9BeTncEIblT8+CiyvGkjlow0Cf/gmOJaEG3oayyPRq4vpg6sqiadOmfPXVV9x++4X7\ns1999RVNmjQB4MyZM7i7m1uoJT09nRMnTtCuXTvy8vLw97cuBOPn50deXh4A2dnZBAUF2Y4JDAwk\nOzvbtu958fHxxMfHAzBjxoxKx1SFq6trtY91FtKGq9MlJaANlGeDq+5btGsr+UBA10hcm7Xg7J+e\n5szcV2i48xsqTqdQ5OpK0J1/wHKJtSfkZ+EcpA01y1SxGDNmDLNmzeKTTz4hICCA7OxsLBYLzz33\nHACnT59mxIgRV/2c4uJiZs2axahRo/Dy8qr0nlKqystHRkdHEx0dbfs6MzOzSsefFxQUVO1jnYW0\n4eoq5k+HogJcnr/6LU3j4B7wakiOqwcqMxPdqRdEdCV/6QKwWFDd+pJdbsAl8srPwjlIG8wJCQkx\ntZ+pYhEaGsrrr7/O0aNHyc3Nxc/Pj7CwsErzREVERFzxM8rLy5k1axY333wzvXtbn2D19fUlJycH\nf39/cnJy8PGxDkEMCAio9A3KysoiIEBWDxPVpw0DjuyHs4XozDRUUJMr7//jD9Cqre0fMEopLA8/\nhTF1HJw9ixp4W23EFsJpmL7h6urqSkREBP369SMiIsJWKMzQWvPmm2/SvHlz7rzzTtv2nj17kpCQ\nAEBCQgKRkZG27Zs3b0ZrzdGjR/Hy8rroFpQQVZJ+Gs4WAqB3br3irrqsDE6dRLVuV2m7CmqCemgs\nqkd/6dgW1x1Tv/GLiopYsWIFSUlJ5Ofno7W2vffGG29c9fgjR46wefNmWrVqxfPPPw/AAw88QExM\nDHFxcWzYsME2dBagW7du7Nq1iwkTJuDu7k5sbGx12iauY7qoAMrKUL7Wf2Tok8esb3j7ohO3wG33\nAGB8sRLcXFFD77pwG/T0j1BRDr8pFmCdcpx+Q2qlDUI4E1PFYuHChWRnZ3Pfffcxd+5cxo8fz5o1\na2y3k64mPDycjz766JLvTZky5aJtSil5WlxUi9YavX0TevlC8GyAZfrb1hFLJ5PB3QN1Swz646Xo\n9F8gIxX98VLrgcmHYfTTKA9P6/MVgGrd1oEtEcK5mCoW+/btIy4uDm9vbywWC5GRkbRt25aZM2dW\nuq0khL1pw4CCMyifyjMG6OKz6P070Ju/hMP7wC8QstKtk/3dEIY+cRRat0X1utlaLLZ9jf4uAZo0\nR/Ufil71Hjr1FJZ7H7UWFq+G1ucohBCAyWKhtbaNXvL09KSoqAg/Pz9SU1PtGk6I39Lxa9Ar3oVm\nLa1PT5eXoVOOw4ljUFYKPn6oB55A9RqI8dwj6N3boWWodb3rQXegAhtD6E3otStAayzPT0eFdUS3\nvAFj2XyMOf+wnqh9lyqPzhOiPjNVLFq3bk1SUhKdOnUiPDychQsX4unpSbNmzeydT4hK9LavoXEI\n+Pih168GVzdoeYP1AbnufaFde5TFxbrzTZ3Qe75D9exvLSQ3hAGgeg5AHz9iPSaso3Vbxx5YXnkb\nnfgNOuELVK+BjmqiEE7J9HMW5zu1R48ezQcffEBhYSHjxo2zazhxfTL++xb4+mMZfn+l7frUSfj5\nR9SDT2IZPMz6kJ2b64Xi8Buqa2/0B2+jt2+yfn1uvWvVf6j1Vta5Tm7b/q6uqL6Doe/gmm6SEHWe\nqWJx5swZbrzR+hfN19eXJ598ErCulidETdL5eehNX4BFoXsNRP2q30B/n2B9IK5nfwCUh8cVP8tW\nLDauhUbecO7ZCuXVCPX7h+3XCCHqIVPPWbz88suX3P7KK6/UaBgh9J7vQBugNXrNBxe2G4Z1yvCI\nrihvX1OfpQKCrcNfy8ugzY3SByHENbjilYVhGMC54Yjn/pyXlpaGi8ulL/+FuBRjy3r0lvXg1Qjl\nF4C660HUb+ZW0ru2QVATVPd+6PWr0bffi2reCo4fhqx01N0PVemcqmtv9I/JnL8FJYSonisWiwce\neMD2+o9//GOl9ywWC7///e/tk0rUC9owbLOy6ooK9CfvAwrKy9GH9qIz07A8M822j1GYD4f2oYb+\nDnXHvehvvsRYuQTL3Q+hE74EN3dUN3PP9pyneg5Af7ECFdGtppsnxHXlisVi3rx5aK156aWXmDZt\nmm27UgofHx/TM82K64s+W4Txbhz8/COWKa9bZ3lN2g252VjGTkZ174exeR162QL0xs9RQ38HQEni\nFqgoR3Xvi2rkg7rtHvTq9zD27wBARd6M8vS60qkvopo2xzJ3+WU7wYUQ5lyxWAQHBwOwYMGCWgkj\n6j6dfhpj3iuQ9jMYBvrrT1HD78fYEg/evnBuZTl1823oPd+jVy5FR3RFNWtJyfYE68N054e4DvsD\nqm04FBdBhQHnhrlWlRQKIa6dqdFQBQUFrFmzhh9//JHi4uJK7/36ikPUf7qsDJKTUO27XPxeaQnG\nv/4K5eVYJv4DI34N+stV6B79Ye/3qCHDUa5uwLlZXB8dj/HSOIzpk1CdelKy9zvUgFttt6WUUhDe\nuVbbJ4S4NFPF4vXXX6e8vJy+ffvKrafrnN74GXrFYtuTz5Xs3wl5OViefgkV3hlLIx+MfzyNMXuq\n9fZS/1sq7a58/bFM/D/0xs/Re7+H0lJ5GE4IJ2WqWBw9epSFCxfi5uZm7zzCyekd1um99eYvLyoW\nRuJm8PGDCOtVh2rRBtVroHUOphvCrKOafkO1CkU9Oh5tVBBggRzklpEQzsjUcxatWrUiKyvL3lmE\nk9NZ6XDiKHg1Qu/chi44c+G9s0WwbweqR/9KfQTq7ofAowFqyJUnnFQWF1yusiCREMJxTF1ZdOzY\nkenTpzNo0CD8/CrP9jlkiMztf704v2iQZdQEjAXT0ds3oqLvtr639zsoK0X1urnSMSq4KZbZ79n6\nKoQQdZOpYnH48GECAwPZv3//Re9JsajfKj0rsWOrdanRbn2sM7du/gp9btEg/f03EBAMoeEXfYYU\nCiHqPlPFYurUqfbOIWqRLi9Dr/8E1aMfqvHlF2vXh/ZivPFP1N0Pobr2hhNHUfc8AoAaeBt6yRzY\n8x26dTtI2o2KvstWWIQQ9UuV/2ZrrTEMw/ZH1C1aa/R7C9Af/wfj31PQeTnW7TlZGCuXonOsfVPa\nMDBWvAslxegP38F43TpEWvU4N4lfzwHQ0BtjwXSMFx6DigpUpIxkEqK+MnVlkZ2dzaJFizh06BCF\nhYWV3lu+fLldggn70F+tQm/9GtV3MHrnNow5/8Byx70Y778BBfnoI/uxPP9P6xxNKSdQj02En39E\nf/kxtApFNbauYaI8PLH8PQ597CBkZ4K7B7QKdXDrhBD2YqpYvP3223h4eDBlyhSmTp3KtGnTWLFi\nBd26yXw7dYnevR29cimq5wDUqKdRPQdgzHsF461/QYs2qGH3oz9ahP7gLfThfdDiBlTvKJTFgg7v\nBL+Z9E8FNrauPCeEqPdMP2exYMECPD09UUrRpk0bxo4dy//7f/+P6Ohoe2cUNUAfPYDx9qvWqbpH\nP23tW+gcieWJSehTJ1HD70e5uWOcyUWvWwmA5empF56m7tjDkfGFEA5mqlhYLBbbdOQNGzbkzJkz\nNGjQgOzsbLuGE1Wntb5o3QadcgJj3ssQ1ATL+Cko9wuLBqmeA6z9D+e/jhmJTvsZlIIO3WsttxDC\nuZkqFu3atWP37t306tWLLl26EBcXh7u7O23btrV3PlEFuqwM4+WJ4O2L5dHxqOCm1n6J9xaApxeW\nidNQ3j5X/Azl4oJL7IuXLDpCiOuXqWIxfvx428JHo0aN4tNPP+Xs2bMMHz7cruFE1egt6+H0T+Du\njjHtaWh7EyTtgVZtsfx5knXlOJOkUAghfs1UsaioqMDHx/ovUnd3d+699167hhJVp0tL0Gs/gnYR\nWB5/FmPJHDh6ABUzEnXbPShXUz9qIYS4JFO/QWJjY+nQoQP9+/enV69eeHp62juXqKKzX662Li70\np2dRgY2xPPt/UHK2yosFCSHEpZgqFgsWLODbb79l/fr1LFy4kO7duzNgwAC6detmah3uBQsWsGvX\nLnx9fZk1axZgXSMjLi6OjIwMgoODmThxIo0aNUJrzeLFi9m9ezceHh7ExsYSGirj9y9HV1RAVjqF\nHy+Dmzqhzq3/oJQCKRRCiBpiqlj4+Phw2223cdttt5GRkcHWrVv58MMPeeONN1i0aNFVjx80aBC3\n33478+fPt21bvXo1nTp1IiYmhtWrV7N69WpGjhzJ7t27SU1NZc6cORw7doyFCxcyffr06rewntEn\njlqXLC0qBMOAogLrf5XCMuYvjo4nhKinqjzdR15eHrm5ueTn59OwYUNTx0RERNCoUaNK2xITE4mK\nigIgKiqKxMREAHbs2MHAgQNRShEWFkZhYSE5OTlVjVkv6aJC6wN0JSWorn1QPfujbr8P9cg4Al57\nF9UuwtERhRD1lKkri1OnTrFlyxa2bt1KaWkpffv25fnnn6ddu3bVPnFeXh7+/v4A+Pn5kZeXB1in\nFgkKCrLtFxgYSHZ2tm3fX4uPjyc+Ph6AGTNmVDquKlxdXat9bG3RWpO39HVKcrLwf2UB7uGdKr3v\n6uqKW3m5g9LVjLrwczCjPrRD2uAcnKkNporF3//+d3r37s0TTzxBhw4dsNTwzKJKqWoN1YyOjq70\nBHlmZma1zh8UFFTtY2uLsfVr9JavUTEjORPUDH6Tty604WrqQxugfrRD2uAcaqMNISGXn3n610wV\ni3feeQfXGh566evrS05ODv7+/uTk5NiG5gYEBFT65mRlZREQEHC5j7lu6HUrrUuT3iHDloUQte+y\nFWDDhg2mPqC6ix/17NmThIQEYmJiSEhIIDIy0rZ93bp19O/fn2PHjuHl5XXJW1D1kT5xFEJaozw8\nKm/PSIXUU6g//rnSkqVCCFFbLlssvvnmG9trrTVHjhzBz8+PwMBAsrKyyM3NJTw83FSxmD17NklJ\nSeTn5/Pkk09y//33ExMTQ1xcHBs2bLANnQXo1q0bu3btYsKECbi7uxMbG1sDzXR++sdkjOmTrJP7\nPfW3SosI6QM7AVCdZDI/IYRjXLZY/Hp1vHfffZfIyMhK03usXbuW1NRUUyd55plnLrl9ypQpF21T\nSvH444+b+tz6RCesA2WBfYnozz5E3fXghff274TGza64qp0QQtiTqZ7qb775hjvuuKPStttvv73S\n1YeoPl1chP5+M6rvYFT/oehPP0Tv+c76XmkJHN6H6tTTwSmFENczU8XCz8+PHTt2VNq2Y8cOW6e0\nqDp9YCc6K8P6+vvNUFKMGngb6qGx0Lodxrtx1r6KIwegrFTWkxBCOJSpIU6jR49m1qxZrFmzhsDA\nQDIzMzl16hTPPvusvfPVSzozzbqmtY8flqenohO+hOatIfQmlFJYxk7G+MfTGG/9C9UqFNzd4aaO\njo4thLiOmSoWnTt3Zt68eezevZvs7Gy6d+9O9+7d8fb2tne+ekknnrt9Z7FgzJwMpSWoB8fYnjVR\ngY2xjH4GY/4r6B+ToXMkys3dgYmFENc70w9PeHt7M3DgQHtmuW7o77+B0JuwjHkBY/ZUyM5E9Y6q\ntI/q2ht1y93o9Z/ILSghhMOZXs/iyy+/tA1//bVp06bZJVh9pX9JgVMnUCMeRwUEYfnbLCg4g/Jq\ndNG+6p5HIKQVKlKKtBDCsUx1cC9dupT4+HgiIiI4fvw4vXv3Ji8vjw4dOtg7X72jE78BpWzrXisP\nT1Rg40vuq1zdsAy45aKH9IQQoraZKhbfffcdL774IsOGDcPFxYVhw4bx/PPPc/DgQXvnqxf0nu3o\nIwfQWltvQYV1RPnJFCZCiLrD1G2o0tJSAgMDAeuyqiUlJTRv3pyTJ0/aM1u9YHy1Cr1isfWLkFaQ\n9jPq1hjHhhJCiCoyVSyaN2/ODz/8QLt27QgNDWXFihU0aNBAJvi7ivOFQvUcAOGd0V+thgZeqO59\nHR1NCCGqxFSxGDVqlG1a8kcffZSFCxdy9uxZnnjiCbuGq8uMr1bbCoV6/DmUiwv65lusw2RluVMh\nRB1jqlj8epGjZs2a8fe//91ugeoDY/0n6BXvonr0txUKwDpjrBQKIUQdVLOrGAmM+E/QHy2CHv0q\nFQohhKjLanZFo+ucsf5coejeD8vjk1A1vGCUEEI4ilxZVJHOzqDi9WkYX6xEF5yxbjMMa2f2uSsK\ny5+lUAgh6hf5jVYFuqIC453X4MRR66yxn34AQU0gIxXKyy70UUihEELUM6Z+q2mt+frrr9m6dSv5\n+fm89tprJCUlkZubS79+/eyd0WF0Vjp60xeo1m2he1/0mv9C8iFrQWjRBr1pLTony7rWRPPWqF4D\npVAIIeolU7/Zli9fzv79+xk2bBjvvPMOAIGBgSxdurReFgtdVob+ahV67UdQWooG6xVEVjrq5lux\nnJv0Tz001qE5hRCitpgqFgkJCcycORMfHx8WLlwIQOPGjUlPT7drOEfQ+XkY816G40esHdV/GA0/\nJmOs+xi8fVEj/uzoiEIIUetMFQvDMPD09Ky0rbi4+KJtdZ1OO43x+kuQm41lzF9sk/0R1ASXHv0d\nmk0IIRzJ1Giobt268Z///IeysjLA2oexfPlyevSoP+ss6ONHMGb8Bc4WYnnu5QuFQgghhLli8cgj\nj5CTk8OoUaMoKirikUceISMjg4ceesje+WpFSeJWjFl/gwZeWCa/imob7uhIQgjhVEzdhvLy8uL5\n558nNzeXzMxMgoKC8PPzs3e2WmFs20Du0rnQ8gYsE/6O8vF3dCQhhHA6pvssAHx8fPDx8bFtOz+5\nYF2mGjfDPbI/ZSOfQnk2cHQcIYRwSqaKxQMPPHDJ7S4uLvj7+9O7d2/uv//+Otnhrdq1x6/PzWRm\nZjo6ihBCOC1TxWL06NEkJiYSExNDYGAgmZmZrFmzhu7duxMSEsKKFStYsmQJTz75pL3zCiGEcABT\nxeLzzz9n5syZeHlZp9cOCQmhbdu2TJ48mblz59KqVSteeOGFGg22Z88eFi9ejGEYDB06lJgYWV1O\nCCEcxVSnQ1FRESUlJZW2lZSUUFRUBICfnx+lpaU1FsowDBYtWsSLL75IXFwcW7du5dSpUzX2+UII\nIarG1JVFVFQUL7/8MnfccQdBQUFkZWWxdu1aoqKs017s3buXkJCQGguVnJxM06ZNadKkCQD9+vUj\nMTGRFi1a1Ng5hBBCmKe01vpqOxmGQXx8PNu3bycnJwc/Pz/69u1LdHQ0FovFdlXh7u5eI6G2b9/O\nnj17bH0gmzdv5tixY/zpT3+qtF98fDzx8fEAzJgxo9pXN66urpSXl19baAeTNjiP+tAOaYNzqI02\nmP29berKwmKxcOutt3Lrrbde08lqWnR0NNHR0bavqzuiKSgoqM6PhpI2OI/60A5pg3OojTaYvStk\nej7t3NxckpOTyc/P59cXI0OGDKl6uqsICAggKyvL9nVWVhYBAQE1fh4hhBDmmCoW33//PXPnzqVZ\ns2akpKTQsmVLUlJSCA8Pt0uxaNu2Lb/88gvp6ekEBASwbds2JkyYUOPnEUIIYY6pPovnnnuO++67\nj759+zJ69GgWL17Mxo0bSUlJ4ZFHHrFLsF27drF06VIMw2Dw4MHcc889djmPEEKIqzM1dDYzM5O+\nfftW2hYVFcXmzZvtEgqge/fuvP7668ydO9fuhWLy5Ml2/fzaIG1wHvWhHdIG5+BMbTBVLHx8fMjN\nzQUgODiYo0ePkpaWZpszSgghRP1mqs9i6NChHD58mD59+jB8+HCmTZuGUoo777zT3vmEEEI4AZeX\nXnrppavtFBYWRsuWLQFo06YNUVFRDBo0qF6tvx0aGuroCNdM2uA86kM7pA3OwVnacNUObsMwePjh\nh1myZAlubm61lUsIIYQTuWqfhcViISQkhPz8/NrII4QQwgmZGjr7ySefsG3bNu644w4CAwNRStne\n69ixo10DCiGEcDxTxeKpp5669MFKMW/evBoPVZvq4lTomZmZzJ8/n9zcXJRSREdHM2zYMAoKCoiL\niyMjI4Pg4GAmTpxIo0aNHB33igzDYPLkyQQEBDB58mTS09OZPXs2+fn5hIaGMn78eFxdTU80UOsK\nCwt58803SUlJQSnF2LFjCQkJqVM/h88++4wNGzaglKJly5bExsaSm5vr1D+HBQsWsGvXLnx9fZk1\naxbAZf//11qzePFidu/ejYeHB7GxsU7RD3CpNixbtoydO3fi6upKkyZNiI2NpWHDhgCsWrWKDRs2\nYLFYGD16NF27dq3dwPo6VlFRoceNG6dTU1N1WVmZnjRpkk5JSXF0rKvKzs7WP/zwg9Za66KiIj1h\nwgSdkpKily1bpletWqW11nrVqlV62bJljoxpyqeffqpnz56t//nPf2qttZ41a5besmWL1lrrt956\nS3/55ZeOjHdVc+fO1fHx8VprrcvKynRBQUGd+jlkZWXp2NhYXVJSorW2fv83btzo9D+HgwcP6h9+\n+EE/++yztm2X+77v3LlTv/LKK9owDH3kyBH917/+1SGZf+tSbdizZ48uLy/XWlvbc74NKSkpetKk\nSbq0tFSnpaXpcePG6YqKilrNa3oR7fLycg4dOsS2bdsAKC4upri42G5FrDb8eip0V1dX21Tozs7f\n39/2L6MGDRrQvHlzsjMGFz0AAAoJSURBVLOzSUxMtE0bHxUV5fRtycrKYteuXQwdOhQArTUHDx6k\nT58+AAwaNMip21BUVMShQ4dsU964urrSsGHDOvdzMAyD0tJSKioqKC0txc/Pz+l/DhERERddrV3u\n+75jxw4GDhyIUoqwsDAKCwvJycmp9cy/dak2dOnSBRcXF8A6CjU7Oxuwtq1fv364ubnRuHFjmjZt\nSnJycq3mNXVd+dNPPzFz5kzc3NzIysqiX79+JCUlkZCQwMSJE+2d0W6ys7MJDAy0fR0YGMixY8cc\nmKjq0tPTOXHiBO3atSMvLw9/f3/AuiBVXl6eg9Nd2ZIlSxg5ciRnz56F/9/evcc0db4BHP/Sau0Q\nKVDEGi9RGVHXzUYDQbTeopIYYrxkarzE1bHABuKmy7L9ZWKMUVEim2LABqJGxEuiLGQxxnhHNDiC\ni5uruk2JHXPQFBRCkVK6PwgnMuc4/n4CrXs+f5W2p+fpeTl9zvuec54XaGpqIjQ0VNlZoqKilJ0l\nENXV1REeHs7+/fupqalh3Lhx2Gy2oGqHqKgoFi5cyCeffIJOp8NisTBu3LigaocuL9vubreb6Oho\n5X1GoxG32628N1BduHBBuT3B7XYTFxenvNYfbaKqZ2G321mxYgW5ubnKuOU777yDw+Ho1eDEv2tt\nbSUnJwebzaZMedslJCSk24UIgaaqqgqDwRAQY8f/K5/Px4MHD0hOTiY7O5tBgwZRWlra7T2B3g7N\nzc3cvHmTvLw8CgoKaG1t5datW/0d1v8t0Ld7T06dOoVWq2XGjBn9HYpCVc/C6XS+ELRer3+tU6n2\nh2Auhd7e3k5OTg4zZswgMTERAIPBQENDA5GRkTQ0NBAeHt7PUb7c3bt3+f7776murqatrQ2Px8PB\ngwdpaWnB5/Oh1Wpxu90B3R5GoxGj0agc8U2dOpXS0tKgaofbt28TExOjxJiYmMjdu3eDqh26vGy7\nR0VFdZsTItD380uXLlFVVcXmzZuVhPf336r+aBNVPYuhQ4fy22+/dXuua7w/mD1fCr29vZ2Kigri\n4+P7O6we+f1+8vPzGTFiRLeSK/Hx8Vy+fBmAy5cvk5CQ0F8h9mjVqlXk5+eTl5fHZ599xrvvvsuG\nDRswm83cuHED6NxpArk9IiIiMBqN1NbWAp0/vCNHjgyqdoiOjub+/fs8e/YMv9+vfIdgaocuL9vu\n8fHxXLlyBb/fz7179wgNDQ3YIahbt27x7bff8uWXXzJo0CDl+fj4eCoqKvB6vdTV1fHHH3/w9ttv\n92lsqi6draqqIj8/n/nz51NWVsbSpUs5d+4c6enpWCyWvoiz1wRjKXSHw8HmzZsZPXq0cuSxcuVK\n4uLi2LNnDy6XKygu2ezy008/UVZWxldffcWff/5Jbm4uzc3NjB07lqysrICuHPDw4UPy8/Npb28n\nJiaGjIwM/H5/ULXDiRMnqKioQKvVMmbMGD7++GPcbndAt0Nubi537tyhqakJg8HA8uXLSUhI+Mft\n7vf7KSws5IcffkCn05GRkUFsbGx/f4V//A6nT5+mvb1d+X+Ji4sjLS0N6ByaunjxIhqNBpvNxuTJ\nk/s0XlXJAuDBgwecP3+e+vp6jEYj8+bNC+rxZiGEEOqpShZPnz4N6HFXIYQQvUtVslizZg1msxmr\n1UpCQgJ6vb4vYhNCCBEgVPcsrl+/Tnl5OTU1NUyZMgWr1crkyZOVa7GFEEK8uVSfs+hSX1/PtWvX\nKC8vp6GhgcLCwt6KTQghRIBQXe6jy5MnT2hsbKSpqUkpcCWEEOLNpqpn4XQ6KS8v59q1a7S1tZGU\nlITVau3z63yFeF02bdpEamoqZrO5z9ftcrnYuHEjhw4dQqN55eM1IfqFqmSxbt06EhMTmT59Omaz\nWf7BxRvjxIkTPH78mA0bNvTaOjIzM0lPT2fSpEm9tg4hepuqch92uz2gatkLESi6SmII8aZTfYK7\nsbGRX375haamJp5fpKs8sxDBJDMzkw8//JDdu3cDneXFTSYTu3btoqWlhUOHDlFdXU1ISAhz5sxh\n+fLlaDQaLl26xPnz54mNjeXKlSskJycze/ZsCgoKqKmpISQkBIvFQmpqKoMHD2bv3r2Ul5czYMAA\nNBoN77//PklJSaxfv56SkhKl9pLdbsfhcBAWFsaiRYuYN28e0NnzcTqd6HQ6KisriY6OJjMzU7kD\nubS0lDNnzuDxeIiMjOSjjz7ivffe67ftKt5cqroLlZWV7N27l+HDh/Po0SNGjRrFo0ePmDBhgiQL\nEbQGDhzIkiVLXhiGysvLw2Aw8M033/Ds2TN27NiB0Whk/vz5ANy/f59p06Zht9vx+Xy43W6WLFnC\nxIkT8Xg85OTkcPLkSWw2G1lZWTgcjm7DUHV1dd3i+Prrrxk1ahQFBQXU1taydetWTCaTMmVxVVUV\nn3/+ORkZGRw7doyioiK2bdtGbW0tZ8+eZfv27URFRVFXV0dHR0cfbT3xX6Pq5MPx48fJyMggOzsb\nvV5PdnY2aWlpjB07trfjE6JPNTY2Ul1djc1mQ6/XYzAYSElJUSb9gs7JpxYsWIBWq0Wn02EymZg0\naRIDBw4kPDyclJQU7ty5o2p9LpcLh8PB6tWr0el0jBkzhrlz5yoF8QAmTJjAlClT0Gg0zJw5k4cP\nHwKg0Wjwer04nU6lNlWwF/cUgUtVz8LlcpGUlNTtuVmzZpGWlsbatWt7JTAh+oPL5cLn8ynF26Cz\nyu/zk2Q9P5EOdCaYgwcP8vPPP9Pa2kpHR4fqwoENDQ2EhYXx1ltvdfv8X3/9VfnbYDAoj3U6HV6v\nF5/Ph8lkwmazcfLkSZxOJxaLhbVr1wZ0+W0RvFQli/DwcBobG4mIiGDo0KHcu3ePIUOGSJdXBL2/\nT5BjNBoZMGAAhYWFqk9cl5SUAJCTk0NYWBiVlZUUFRWpWjYyMpLm5mY8Ho+SMFwul+offKvVitVq\npaWlhQMHDlBcXExWVpaqZYV4FaqGoebOnavMipeSksKWLVv44osvSE5O7tXghOhtBoOB+vp65cAn\nMjISi8XC4cOHaWlpoaOjg8ePH//rsJLH40Gv1xMaGorb7aasrKzb6xERES+cp+gSHR3N+PHjOXr0\nKG1tbdTU1HDx4kVVM6TV1tby448/4vV60el06HS6oJ4dTgQ2VT2LxYsXK49nzZqF2WymtbWVkSNH\n9lpgQvSFpKQkrl69SmpqKjExMezcuZP169dTXFzMpk2b8Hg8DBs2jEWLFr30M5YtW8a+ffv44IMP\nMJlMzJw5k++++055ffHixRQVFXHkyBGWLl3K1KlTuy3/6aefYrfbSU9PJywsjGXLlqm6J8Pr9VJc\nXMzvv/+OVqtl/Pjx3YbPhHidXrk2lBBCiP8euRVbCCFEjyRZCCGE6JEkCyGEED2SZCGEEKJHkiyE\nEEL0SJKFEEKIHkmyEEII0SNJFkIIIXr0Fy+JjF314FN6AAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x113a7a588>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "util.plot_curve(loss_list_without_baseline, \"loss without baseline\")\n",
+    "util.plot_curve(avg_return_list_without_baseline, \"average return without baseline\")\n",
+    "util.plot_curve(avg_advantage_variance_list_without_baseline, \"average advantage variance without baseline\")"
    ]
   },
   {
@@ -453,6 +671,341 @@
     "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# set the hyperparameter for generalized advantage estimation (GAE)\n",
+    "LAMBDA = 0.98 # \\lambda\n",
+    "class PolicyOptimizer_actor_critic(PolicyOptimizer):\n",
+    "    def __init__(self, env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "        discount_rate=.99):\n",
+    "        PolicyOptimizer.__init__(self, env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "            discount_rate=.99)\n",
+    "    \n",
+    "    def process_paths(self, paths):\n",
+    "        for p in paths:\n",
+    "            if self.baseline != None:\n",
+    "                b = self.baseline.predict(p)\n",
+    "                b[-1] = 0 # terminal state\n",
+    "            else:\n",
+    "                b = 0\n",
+    "            \n",
+    "            \"\"\"\n",
+    "            1. Variable `b` is the reward predicted by our baseline\n",
+    "            2. Calculate the advantage function via one-step bootstrap\n",
+    "                    A(s, a) = [r(s,a,s') + \\gamma*v(s')] - v(s)\n",
+    "            3. `target_v` specifies the target of the baseline function\n",
+    "            \"\"\"\n",
+    "            r = util.discount_bootstrap(p[\"rewards\"], self.discount_rate, b)\n",
+    "            target_v = util.discount_cumsum(p[\"rewards\"], self.discount_rate)\n",
+    "            a = r - b\n",
+    "                        \n",
+    "            p[\"returns\"] = target_v\n",
+    "            p[\"baselines\"] = b\n",
+    "            p[\"advantages\"] = (a - a.mean()) / (a.std() + 1e-8) # normalize\n",
+    "            p[\"advantage_variance\"] = np.var(a) # My additional code for plotting advantage variance.\n",
+    "\n",
+    "        obs = np.concatenate([ p[\"observations\"] for p in paths ])\n",
+    "        actions = np.concatenate([ p[\"actions\"] for p in paths ])\n",
+    "        rewards = np.concatenate([ p[\"rewards\"] for p in paths ])\n",
+    "        advantages = np.concatenate([ p[\"advantages\"] for p in paths ])\n",
+    "        advantage_variances = np.array([ p[\"advantage_variance\"] for p in paths ])\n",
+    "\n",
+    "        return dict(\n",
+    "            observations=obs,\n",
+    "            actions=actions,\n",
+    "            rewards=rewards,\n",
+    "            advantages=advantages,\n",
+    "            advantage_variances=advantage_variances\n",
+    "        )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 22.2 | Average Advantage Variance: 0.0\n",
+      "Iteration 2: Average Return = 21.61 | Average Advantage Variance: 2.618711848254234\n",
+      "Iteration 3: Average Return = 23.1 | Average Advantage Variance: 1.6063604018694964\n",
+      "Iteration 4: Average Return = 23.73 | Average Advantage Variance: 1.6772316325092151\n",
+      "Iteration 5: Average Return = 25.26 | Average Advantage Variance: 1.974914730986716\n",
+      "Iteration 6: Average Return = 27.16 | Average Advantage Variance: 1.9638738826857867\n",
+      "Iteration 7: Average Return = 29.46 | Average Advantage Variance: 2.752185232343\n",
+      "Iteration 8: Average Return = 31.67 | Average Advantage Variance: 2.629188374708864\n",
+      "Iteration 9: Average Return = 31.46 | Average Advantage Variance: 2.9513828524634333\n",
+      "Iteration 10: Average Return = 35.63 | Average Advantage Variance: 2.033179000863392\n",
+      "Iteration 11: Average Return = 38.5 | Average Advantage Variance: 2.8707111426854315\n",
+      "Iteration 12: Average Return = 32.51 | Average Advantage Variance: 4.274929735704571\n",
+      "Iteration 13: Average Return = 41.42 | Average Advantage Variance: 1.8315472218041209\n",
+      "Iteration 14: Average Return = 42.57 | Average Advantage Variance: 1.955783426353485\n",
+      "Iteration 15: Average Return = 43.11 | Average Advantage Variance: 1.8658563437673097\n",
+      "Iteration 16: Average Return = 44.83 | Average Advantage Variance: 1.7473483790314435\n",
+      "Iteration 17: Average Return = 46.88 | Average Advantage Variance: 2.106799944891474\n",
+      "Iteration 18: Average Return = 43.77 | Average Advantage Variance: 1.5194944765792555\n",
+      "Iteration 19: Average Return = 44.45 | Average Advantage Variance: 1.2141827451708258\n",
+      "Iteration 20: Average Return = 47.32 | Average Advantage Variance: 1.8099085342257455\n",
+      "Iteration 21: Average Return = 49.28 | Average Advantage Variance: 2.2192375391553707\n",
+      "Iteration 22: Average Return = 54.02 | Average Advantage Variance: 1.6319310799430438\n",
+      "Iteration 23: Average Return = 48.88 | Average Advantage Variance: 1.5496540494114912\n",
+      "Iteration 24: Average Return = 48.74 | Average Advantage Variance: 1.6239565244819028\n",
+      "Iteration 25: Average Return = 54.36 | Average Advantage Variance: 1.1978108330452915\n",
+      "Iteration 26: Average Return = 49.49 | Average Advantage Variance: 1.6782422983063028\n",
+      "Iteration 27: Average Return = 51.34 | Average Advantage Variance: 1.2313562619874323\n",
+      "Iteration 28: Average Return = 57.35 | Average Advantage Variance: 1.4294406253303642\n",
+      "Iteration 29: Average Return = 58.83 | Average Advantage Variance: 1.1913636062614104\n",
+      "Iteration 30: Average Return = 56.69 | Average Advantage Variance: 1.2219937151829687\n",
+      "Iteration 31: Average Return = 55.69 | Average Advantage Variance: 1.421956092736856\n",
+      "Iteration 32: Average Return = 59.72 | Average Advantage Variance: 1.051743620877975\n",
+      "Iteration 33: Average Return = 59.54 | Average Advantage Variance: 1.2373861018340848\n",
+      "Iteration 34: Average Return = 59.1 | Average Advantage Variance: 1.4226768926799587\n",
+      "Iteration 35: Average Return = 62.81 | Average Advantage Variance: 1.1535522682342747\n",
+      "Iteration 36: Average Return = 59.03 | Average Advantage Variance: 1.2822561787338882\n",
+      "Iteration 37: Average Return = 63.48 | Average Advantage Variance: 1.4728389988006851\n",
+      "Iteration 38: Average Return = 71.23 | Average Advantage Variance: 1.374428174922424\n",
+      "Iteration 39: Average Return = 72.4 | Average Advantage Variance: 1.2048704671380506\n",
+      "Iteration 40: Average Return = 69.25 | Average Advantage Variance: 1.7760063270860524\n",
+      "Iteration 41: Average Return = 72.4 | Average Advantage Variance: 1.2322784278657506\n",
+      "Iteration 42: Average Return = 67.4 | Average Advantage Variance: 1.3099197707716028\n",
+      "Iteration 43: Average Return = 70.46 | Average Advantage Variance: 1.5135125211987688\n",
+      "Iteration 44: Average Return = 73.0 | Average Advantage Variance: 1.1910475208944094\n",
+      "Iteration 45: Average Return = 77.91 | Average Advantage Variance: 1.1220510591925463\n",
+      "Iteration 46: Average Return = 74.39 | Average Advantage Variance: 1.3415130481043016\n",
+      "Iteration 47: Average Return = 80.87 | Average Advantage Variance: 1.3414752845955136\n",
+      "Iteration 48: Average Return = 89.58 | Average Advantage Variance: 2.0035944243499086\n",
+      "Iteration 49: Average Return = 90.87 | Average Advantage Variance: 1.5454279382205494\n",
+      "Iteration 50: Average Return = 95.23 | Average Advantage Variance: 1.5349575543528546\n",
+      "Iteration 51: Average Return = 100.3 | Average Advantage Variance: 1.9620685037342693\n",
+      "Iteration 52: Average Return = 110.5 | Average Advantage Variance: 1.972112497055272\n",
+      "Iteration 53: Average Return = 117.66 | Average Advantage Variance: 1.5754476356397804\n",
+      "Iteration 54: Average Return = 121.0 | Average Advantage Variance: 0.9747368814393738\n",
+      "Iteration 55: Average Return = 128.16 | Average Advantage Variance: 1.0525259839006103\n",
+      "Iteration 56: Average Return = 124.59 | Average Advantage Variance: 1.1647503483115063\n",
+      "Iteration 57: Average Return = 121.33 | Average Advantage Variance: 1.1417377782772933\n",
+      "Iteration 58: Average Return = 127.83 | Average Advantage Variance: 0.7981933912859183\n",
+      "Iteration 59: Average Return = 125.66 | Average Advantage Variance: 1.3983114330700905\n",
+      "Iteration 60: Average Return = 127.39 | Average Advantage Variance: 1.2834272765846502\n",
+      "Iteration 61: Average Return = 131.23 | Average Advantage Variance: 0.8663537653116978\n",
+      "Iteration 62: Average Return = 134.27 | Average Advantage Variance: 0.632562390658519\n",
+      "Iteration 63: Average Return = 131.09 | Average Advantage Variance: 1.4796075148558734\n",
+      "Iteration 64: Average Return = 136.26 | Average Advantage Variance: 0.8212163557241312\n",
+      "Iteration 65: Average Return = 131.25 | Average Advantage Variance: 1.0785313154517895\n",
+      "Iteration 66: Average Return = 134.23 | Average Advantage Variance: 1.21557946905642\n",
+      "Iteration 67: Average Return = 137.9 | Average Advantage Variance: 1.456212814053223\n",
+      "Iteration 68: Average Return = 134.23 | Average Advantage Variance: 1.0428060784560123\n",
+      "Iteration 69: Average Return = 137.62 | Average Advantage Variance: 1.1523876226276624\n",
+      "Iteration 70: Average Return = 129.83 | Average Advantage Variance: 1.0669030813148008\n",
+      "Iteration 71: Average Return = 128.04 | Average Advantage Variance: 1.235354755657983\n",
+      "Iteration 72: Average Return = 128.84 | Average Advantage Variance: 1.267212306877897\n",
+      "Iteration 73: Average Return = 134.32 | Average Advantage Variance: 1.2198946578166363\n",
+      "Iteration 74: Average Return = 133.14 | Average Advantage Variance: 0.9603402687981378\n",
+      "Iteration 75: Average Return = 137.94 | Average Advantage Variance: 1.1631231890715796\n",
+      "Iteration 76: Average Return = 133.1 | Average Advantage Variance: 1.1121362927780853\n",
+      "Iteration 77: Average Return = 139.86 | Average Advantage Variance: 1.2310431668518336\n",
+      "Iteration 78: Average Return = 135.66 | Average Advantage Variance: 1.1680614602207675\n",
+      "Iteration 79: Average Return = 147.45 | Average Advantage Variance: 0.9828707477899856\n",
+      "Iteration 80: Average Return = 150.57 | Average Advantage Variance: 0.6843394546289409\n",
+      "Iteration 81: Average Return = 158.78 | Average Advantage Variance: 0.6272488790590012\n",
+      "Iteration 82: Average Return = 158.36 | Average Advantage Variance: 0.45672131811462435\n",
+      "Iteration 83: Average Return = 159.56 | Average Advantage Variance: 0.46968466271899234\n",
+      "Iteration 84: Average Return = 152.86 | Average Advantage Variance: 0.6873588158338724\n",
+      "Iteration 85: Average Return = 153.1 | Average Advantage Variance: 0.604007217470471\n",
+      "Iteration 86: Average Return = 150.9 | Average Advantage Variance: 0.6157551980678242\n",
+      "Iteration 87: Average Return = 143.22 | Average Advantage Variance: 0.7804170470043517\n",
+      "Iteration 88: Average Return = 147.32 | Average Advantage Variance: 1.102859585202047\n",
+      "Iteration 89: Average Return = 156.67 | Average Advantage Variance: 0.7110400090625277\n",
+      "Iteration 90: Average Return = 149.9 | Average Advantage Variance: 0.8075188490363938\n",
+      "Iteration 91: Average Return = 160.0 | Average Advantage Variance: 0.5343356536146188\n",
+      "Iteration 92: Average Return = 163.01 | Average Advantage Variance: 0.5614915022985459\n",
+      "Iteration 93: Average Return = 163.07 | Average Advantage Variance: 0.4859600697462536\n",
+      "Iteration 94: Average Return = 155.56 | Average Advantage Variance: 0.6427236044338821\n",
+      "Iteration 95: Average Return = 151.8 | Average Advantage Variance: 0.49612595587004404\n",
+      "Iteration 96: Average Return = 146.86 | Average Advantage Variance: 0.7278669050307421\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 97: Average Return = 144.54 | Average Advantage Variance: 0.7622247405890629\n",
+      "Iteration 98: Average Return = 137.01 | Average Advantage Variance: 0.7156952549156059\n",
+      "Iteration 99: Average Return = 138.43 | Average Advantage Variance: 0.7426439940438947\n",
+      "Iteration 100: Average Return = 151.15 | Average Advantage Variance: 1.0073336471407874\n",
+      "Iteration 101: Average Return = 161.88 | Average Advantage Variance: 0.6208734443790099\n",
+      "Iteration 102: Average Return = 167.13 | Average Advantage Variance: 0.5069164085843254\n",
+      "Iteration 103: Average Return = 166.72 | Average Advantage Variance: 0.4812595651801905\n",
+      "Iteration 104: Average Return = 165.26 | Average Advantage Variance: 0.5982363819871821\n",
+      "Iteration 105: Average Return = 160.76 | Average Advantage Variance: 0.5328720201851901\n",
+      "Iteration 106: Average Return = 161.03 | Average Advantage Variance: 0.6354634235509983\n",
+      "Iteration 107: Average Return = 152.72 | Average Advantage Variance: 0.6312697928647074\n",
+      "Iteration 108: Average Return = 144.88 | Average Advantage Variance: 0.8073272645956786\n",
+      "Iteration 109: Average Return = 147.77 | Average Advantage Variance: 0.8261131774218611\n",
+      "Iteration 110: Average Return = 150.2 | Average Advantage Variance: 1.0174551003310466\n",
+      "Iteration 111: Average Return = 155.17 | Average Advantage Variance: 0.8305768063599963\n",
+      "Iteration 112: Average Return = 162.21 | Average Advantage Variance: 0.7100680089660294\n",
+      "Iteration 113: Average Return = 169.29 | Average Advantage Variance: 0.5112088875851885\n",
+      "Iteration 114: Average Return = 163.94 | Average Advantage Variance: 0.7542355056059245\n",
+      "Iteration 115: Average Return = 167.45 | Average Advantage Variance: 0.5312420371663541\n",
+      "Iteration 116: Average Return = 164.38 | Average Advantage Variance: 0.5616659550789885\n",
+      "Iteration 117: Average Return = 161.74 | Average Advantage Variance: 0.6943714157162019\n",
+      "Iteration 118: Average Return = 153.4 | Average Advantage Variance: 0.693319407611283\n",
+      "Iteration 119: Average Return = 163.5 | Average Advantage Variance: 0.6427182721528508\n",
+      "Iteration 120: Average Return = 152.46 | Average Advantage Variance: 0.6670032225551854\n",
+      "Iteration 121: Average Return = 154.75 | Average Advantage Variance: 0.8271243707273764\n",
+      "Iteration 122: Average Return = 162.87 | Average Advantage Variance: 0.6022595609981034\n",
+      "Iteration 123: Average Return = 165.55 | Average Advantage Variance: 0.4952388630358368\n",
+      "Iteration 124: Average Return = 175.8 | Average Advantage Variance: 0.417058805372984\n",
+      "Iteration 125: Average Return = 179.2 | Average Advantage Variance: 0.5082330224968594\n",
+      "Iteration 126: Average Return = 179.61 | Average Advantage Variance: 0.3413316861189067\n",
+      "Iteration 127: Average Return = 183.65 | Average Advantage Variance: 0.6249603942343005\n",
+      "Iteration 128: Average Return = 181.0 | Average Advantage Variance: 0.43443150617250154\n",
+      "Iteration 129: Average Return = 174.36 | Average Advantage Variance: 0.47529196424970005\n",
+      "Iteration 130: Average Return = 170.24 | Average Advantage Variance: 0.5481818693197641\n",
+      "Iteration 131: Average Return = 162.22 | Average Advantage Variance: 0.6699927206707567\n",
+      "Iteration 132: Average Return = 158.41 | Average Advantage Variance: 0.5055151909768815\n",
+      "Iteration 133: Average Return = 160.93 | Average Advantage Variance: 0.5997417576724554\n",
+      "Iteration 134: Average Return = 160.03 | Average Advantage Variance: 0.6934194223882717\n",
+      "Iteration 135: Average Return = 159.7 | Average Advantage Variance: 0.5641904074455997\n",
+      "Iteration 136: Average Return = 158.1 | Average Advantage Variance: 0.5950847195736103\n",
+      "Iteration 137: Average Return = 166.83 | Average Advantage Variance: 0.458922793578491\n",
+      "Iteration 138: Average Return = 162.65 | Average Advantage Variance: 0.43796215163124386\n",
+      "Iteration 139: Average Return = 177.24 | Average Advantage Variance: 0.42542727286918675\n",
+      "Iteration 140: Average Return = 169.23 | Average Advantage Variance: 0.357635427493088\n",
+      "Iteration 141: Average Return = 173.01 | Average Advantage Variance: 0.3862795652255352\n",
+      "Iteration 142: Average Return = 181.62 | Average Advantage Variance: 0.44544831326144596\n",
+      "Iteration 143: Average Return = 179.41 | Average Advantage Variance: 0.3571544298944646\n",
+      "Iteration 144: Average Return = 180.47 | Average Advantage Variance: 0.39164152549599257\n",
+      "Iteration 145: Average Return = 175.67 | Average Advantage Variance: 0.5872865717334753\n",
+      "Iteration 146: Average Return = 181.69 | Average Advantage Variance: 0.4440724652594749\n",
+      "Iteration 147: Average Return = 186.16 | Average Advantage Variance: 0.45588128098025843\n",
+      "Iteration 148: Average Return = 182.13 | Average Advantage Variance: 0.3769393523749071\n",
+      "Iteration 149: Average Return = 184.34 | Average Advantage Variance: 0.3984993717896604\n",
+      "Iteration 150: Average Return = 182.48 | Average Advantage Variance: 0.43892768146626937\n",
+      "Iteration 151: Average Return = 182.2 | Average Advantage Variance: 0.6255471725880455\n",
+      "Iteration 152: Average Return = 183.28 | Average Advantage Variance: 0.3949747154362002\n",
+      "Iteration 153: Average Return = 179.01 | Average Advantage Variance: 0.4426888448939406\n",
+      "Iteration 154: Average Return = 175.48 | Average Advantage Variance: 0.5114608553781348\n",
+      "Iteration 155: Average Return = 169.82 | Average Advantage Variance: 0.43277049367405135\n",
+      "Iteration 156: Average Return = 172.78 | Average Advantage Variance: 0.550584656986368\n",
+      "Iteration 157: Average Return = 173.09 | Average Advantage Variance: 0.5543947119925517\n",
+      "Iteration 158: Average Return = 167.23 | Average Advantage Variance: 0.42735825506878267\n",
+      "Iteration 159: Average Return = 169.56 | Average Advantage Variance: 0.472411969516844\n",
+      "Iteration 160: Average Return = 168.98 | Average Advantage Variance: 0.4039837464946324\n",
+      "Iteration 161: Average Return = 166.76 | Average Advantage Variance: 0.48076327380790235\n",
+      "Iteration 162: Average Return = 171.22 | Average Advantage Variance: 0.4173885135459038\n",
+      "Iteration 163: Average Return = 174.69 | Average Advantage Variance: 0.3701853574566973\n",
+      "Iteration 164: Average Return = 175.65 | Average Advantage Variance: 0.3478973563767562\n",
+      "Iteration 165: Average Return = 179.56 | Average Advantage Variance: 0.3529044024578056\n",
+      "Iteration 166: Average Return = 182.09 | Average Advantage Variance: 0.43192536522108055\n",
+      "Iteration 167: Average Return = 182.73 | Average Advantage Variance: 0.3368232093949944\n",
+      "Iteration 168: Average Return = 186.84 | Average Advantage Variance: 0.45364047392213797\n",
+      "Iteration 169: Average Return = 185.76 | Average Advantage Variance: 0.4037368533037325\n",
+      "Iteration 170: Average Return = 188.49 | Average Advantage Variance: 0.4460219373726739\n",
+      "Iteration 171: Average Return = 186.03 | Average Advantage Variance: 0.5224019058033579\n",
+      "Iteration 172: Average Return = 183.8 | Average Advantage Variance: 0.558488897415905\n",
+      "Iteration 173: Average Return = 181.42 | Average Advantage Variance: 0.3713059388381771\n",
+      "Iteration 174: Average Return = 180.01 | Average Advantage Variance: 0.2988560269435438\n",
+      "Iteration 175: Average Return = 178.97 | Average Advantage Variance: 0.41949143778288045\n",
+      "Iteration 176: Average Return = 176.03 | Average Advantage Variance: 0.509069854199177\n",
+      "Iteration 177: Average Return = 175.91 | Average Advantage Variance: 0.4438047968253216\n",
+      "Iteration 178: Average Return = 172.65 | Average Advantage Variance: 0.4066252972683355\n",
+      "Iteration 179: Average Return = 172.06 | Average Advantage Variance: 0.3469279686434082\n",
+      "Iteration 180: Average Return = 178.09 | Average Advantage Variance: 0.4671773887722697\n",
+      "Iteration 181: Average Return = 176.46 | Average Advantage Variance: 0.4221562298505554\n",
+      "Iteration 182: Average Return = 171.18 | Average Advantage Variance: 0.3389583240414483\n",
+      "Iteration 183: Average Return = 172.76 | Average Advantage Variance: 0.44029185813282423\n",
+      "Iteration 184: Average Return = 175.45 | Average Advantage Variance: 0.3452279027568473\n",
+      "Iteration 185: Average Return = 172.97 | Average Advantage Variance: 0.39664798303552457\n",
+      "Iteration 186: Average Return = 176.49 | Average Advantage Variance: 0.37056479869686904\n",
+      "Iteration 187: Average Return = 176.37 | Average Advantage Variance: 0.3818859171403693\n",
+      "Iteration 188: Average Return = 176.04 | Average Advantage Variance: 0.3121444259287643\n",
+      "Iteration 189: Average Return = 174.8 | Average Advantage Variance: 0.32957777784207537\n",
+      "Iteration 190: Average Return = 174.89 | Average Advantage Variance: 0.34212199462264925\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 191: Average Return = 181.72 | Average Advantage Variance: 0.3973691078990239\n",
+      "Iteration 192: Average Return = 182.9 | Average Advantage Variance: 0.2939822335636896\n",
+      "Iteration 193: Average Return = 180.39 | Average Advantage Variance: 0.3127256627043685\n",
+      "Iteration 194: Average Return = 184.88 | Average Advantage Variance: 0.2979888181824994\n",
+      "Iteration 195: Average Return = 184.91 | Average Advantage Variance: 0.39057182841201565\n",
+      "Iteration 196: Average Return = 182.3 | Average Advantage Variance: 0.35510879795742\n",
+      "Iteration 197: Average Return = 186.67 | Average Advantage Variance: 0.34924674040547965\n",
+      "Iteration 198: Average Return = 188.83 | Average Advantage Variance: 0.39613644184273566\n",
+      "Iteration 199: Average Return = 181.39 | Average Advantage Variance: 0.40448112973191436\n",
+      "Iteration 200: Average Return = 180.25 | Average Advantage Variance: 0.4814011798512973\n"
+     ]
+    }
+   ],
+   "source": [
+    "sess.run(tf.global_variables_initializer())\n",
+    "\n",
+    "n_iter = 200\n",
+    "n_episode = 100\n",
+    "path_length = 200\n",
+    "discount_rate = 0.99\n",
+    "# reinitialize the baseline function\n",
+    "baseline = LinearFeatureBaseline(env.spec) \n",
+    "sess.run(tf.global_variables_initializer())\n",
+    "po = PolicyOptimizer_actor_critic(env, policy, baseline, n_iter, n_episode, path_length,\n",
+    "                     discount_rate)\n",
+    "\n",
+    "# Train the policy optimizer\n",
+    "loss_list, avg_return_list, avg_advantage_variance_list  = po.train()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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lIjNE7oiZByPOR/7eFgtAV691Gzu8hiKLMjRyMcyQjVwO7Ade+o1Z3UK+Prlp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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122adfc50>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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e9SNUTrmRdqLmgyRWLFh04jClRQXQoSvKvyV66/fuL1kAxuN/hhYtUS1dny5E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\nCwCA0QO0nHanufDRTwAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122adfba8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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LvsqTR3AoEBMPVFmmsIXb3cCVVFVfnkZGEESnoLqf/7fffoujR4+ipsZRvBYt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\nIi6k8BcRcSGFv4iICyn8RURc6AfHq3L4J6IQSgAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122b10240>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "util.plot_curve(loss_list, \"loss\")\n",
+    "util.plot_curve(avg_return_list, \"average return\")\n",
+    "util.plot_curve(avg_advantage_variance_list, \"average advantage variance\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -477,10 +1030,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 12,
+   "metadata": {},
    "outputs": [],
    "source": [
     "# set the hyperparameter for generalized advantage estimation (GAE)\n",
@@ -522,120 +1073,120 @@
     "                        (You're encouraged to try other \\lambda=[0,1])\n",
     "            Sample solution should be only 1 line. (you can use `util.discount` in policy_gradient/util.py)\n",
     "            \"\"\"\n",
+    "            \n",
     "            # YOUR CODE HERE >>>>>>>>\n",
+    "            a = util.discount(a, self.discount_rate * LAMBDA)\n",
     "            # <<<<<<<\n",
+    "            \n",
     "            p[\"returns\"] = target_v\n",
     "            p[\"baselines\"] = b\n",
     "            p[\"advantages\"] = (a - a.mean()) / (a.std() + 1e-8) # normalize\n",
+    "            p[\"advantage_variance\"] = np.var(a) # My additional code for plotting advantage variance.\n",
     "\n",
     "        obs = np.concatenate([ p[\"observations\"] for p in paths ])\n",
     "        actions = np.concatenate([ p[\"actions\"] for p in paths ])\n",
     "        rewards = np.concatenate([ p[\"rewards\"] for p in paths ])\n",
     "        advantages = np.concatenate([ p[\"advantages\"] for p in paths ])\n",
+    "        advantage_variances = np.array([ p[\"advantage_variance\"] for p in paths ])\n",
     "\n",
     "        return dict(\n",
     "            observations=obs,\n",
     "            actions=actions,\n",
     "            rewards=rewards,\n",
     "            advantages=advantages,\n",
+    "            advantage_variances=advantage_variances\n",
     "        )"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Iteration 1: Average Return = 25.12\n",
-      "Iteration 2: Average Return = 31.17\n",
-      "Iteration 3: Average Return = 30.07\n",
-      "Iteration 4: Average Return = 31.98\n",
-      "Iteration 5: Average Return = 36.77\n",
-      "Iteration 6: Average Return = 36.22\n",
-      "Iteration 7: Average Return = 43.52\n",
-      "Iteration 8: Average Return = 45.12\n",
-      "Iteration 9: Average Return = 50.86\n",
-      "Iteration 10: Average Return = 58.81\n",
-      "Iteration 11: Average Return = 58.87\n",
-      "Iteration 12: Average Return = 65.66\n",
-      "Iteration 13: Average Return = 69.72\n",
-      "Iteration 14: Average Return = 76.32\n",
-      "Iteration 15: Average Return = 77.74\n",
-      "Iteration 16: Average Return = 78.17\n",
-      "Iteration 17: Average Return = 94.97\n",
-      "Iteration 18: Average Return = 89.34\n",
-      "Iteration 19: Average Return = 98.15\n",
-      "Iteration 20: Average Return = 103.35\n",
-      "Iteration 21: Average Return = 106.54\n",
-      "Iteration 22: Average Return = 109.03\n",
-      "Iteration 23: Average Return = 113.63\n",
-      "Iteration 24: Average Return = 119.11\n",
-      "Iteration 25: Average Return = 115.67\n",
-      "Iteration 26: Average Return = 126.51\n",
-      "Iteration 27: Average Return = 131.33\n",
-      "Iteration 28: Average Return = 138.83\n",
-      "Iteration 29: Average Return = 143.7\n",
-      "Iteration 30: Average Return = 146.15\n",
-      "Iteration 31: Average Return = 146.41\n",
-      "Iteration 32: Average Return = 157.34\n",
-      "Iteration 33: Average Return = 160.51\n",
-      "Iteration 34: Average Return = 159.67\n",
-      "Iteration 35: Average Return = 169.42\n",
-      "Iteration 36: Average Return = 170.71\n",
-      "Iteration 37: Average Return = 174.41\n",
-      "Iteration 38: Average Return = 172.93\n",
-      "Iteration 39: Average Return = 173.29\n",
-      "Iteration 40: Average Return = 177.32\n",
-      "Iteration 41: Average Return = 177.14\n",
-      "Iteration 42: Average Return = 179.85\n",
-      "Iteration 43: Average Return = 181.82\n",
-      "Iteration 44: Average Return = 182.0\n",
-      "Iteration 45: Average Return = 181.89\n",
-      "Iteration 46: Average Return = 183.19\n",
-      "Iteration 47: Average Return = 183.87\n",
-      "Iteration 48: Average Return = 183.26\n",
-      "Iteration 49: Average Return = 183.27\n",
-      "Iteration 50: Average Return = 189.11\n",
-      "Iteration 51: Average Return = 181.45\n",
-      "Iteration 52: Average Return = 186.91\n",
-      "Iteration 53: Average Return = 188.84\n",
-      "Iteration 54: Average Return = 189.76\n",
-      "Iteration 55: Average Return = 189.51\n",
-      "Iteration 56: Average Return = 186.36\n",
-      "Iteration 57: Average Return = 190.55\n",
-      "Iteration 58: Average Return = 189.35\n",
-      "Iteration 59: Average Return = 189.84\n",
-      "Iteration 60: Average Return = 187.14\n",
-      "Iteration 61: Average Return = 191.82\n",
-      "Iteration 62: Average Return = 189.32\n",
-      "Iteration 63: Average Return = 190.74\n",
-      "Iteration 64: Average Return = 188.13\n",
-      "Iteration 65: Average Return = 190.99\n",
-      "Iteration 66: Average Return = 189.23\n",
-      "Iteration 67: Average Return = 186.98\n",
-      "Iteration 68: Average Return = 188.0\n",
-      "Iteration 69: Average Return = 191.68\n",
-      "Iteration 70: Average Return = 188.03\n",
-      "Iteration 71: Average Return = 193.07\n",
-      "Iteration 72: Average Return = 191.96\n",
-      "Iteration 73: Average Return = 189.53\n",
-      "Iteration 74: Average Return = 186.71\n",
-      "Iteration 75: Average Return = 190.05\n",
-      "Iteration 76: Average Return = 191.1\n",
-      "Iteration 77: Average Return = 193.49\n",
-      "Iteration 78: Average Return = 188.66\n",
-      "Iteration 79: Average Return = 191.49\n",
-      "Iteration 80: Average Return = 191.68\n",
-      "Iteration 81: Average Return = 193.19\n",
-      "Iteration 82: Average Return = 193.87\n",
-      "Iteration 83: Average Return = 195.04\n",
-      "Solve at 83 iterations, which equals 8300 episodes.\n"
+      "Iteration 1: Average Return = 29.49 | Average Advantage Variance: 28.872314758080293\n",
+      "Iteration 2: Average Return = 28.15 | Average Advantage Variance: 17.206342272832206\n",
+      "Iteration 3: Average Return = 27.0 | Average Advantage Variance: 12.806761327170523\n",
+      "Iteration 4: Average Return = 32.44 | Average Advantage Variance: 15.634516310988477\n",
+      "Iteration 5: Average Return = 34.46 | Average Advantage Variance: 20.01783041624987\n",
+      "Iteration 6: Average Return = 37.53 | Average Advantage Variance: 21.310244541815788\n",
+      "Iteration 7: Average Return = 38.8 | Average Advantage Variance: 17.76565792390446\n",
+      "Iteration 8: Average Return = 39.93 | Average Advantage Variance: 15.314962409840621\n",
+      "Iteration 9: Average Return = 44.31 | Average Advantage Variance: 17.46989303925956\n",
+      "Iteration 10: Average Return = 45.95 | Average Advantage Variance: 18.05843269318995\n",
+      "Iteration 11: Average Return = 53.0 | Average Advantage Variance: 17.74426220546417\n",
+      "Iteration 12: Average Return = 49.09 | Average Advantage Variance: 17.77919372061017\n",
+      "Iteration 13: Average Return = 48.67 | Average Advantage Variance: 14.776962417246967\n",
+      "Iteration 14: Average Return = 51.81 | Average Advantage Variance: 16.624198766364483\n",
+      "Iteration 15: Average Return = 51.97 | Average Advantage Variance: 20.04153164829221\n",
+      "Iteration 16: Average Return = 55.87 | Average Advantage Variance: 16.99985568064695\n",
+      "Iteration 17: Average Return = 53.47 | Average Advantage Variance: 19.72599719148008\n",
+      "Iteration 18: Average Return = 59.72 | Average Advantage Variance: 18.541893356444373\n",
+      "Iteration 19: Average Return = 63.67 | Average Advantage Variance: 17.050739084979295\n",
+      "Iteration 20: Average Return = 62.25 | Average Advantage Variance: 18.525438021561047\n",
+      "Iteration 21: Average Return = 66.61 | Average Advantage Variance: 19.28726074839487\n",
+      "Iteration 22: Average Return = 67.15 | Average Advantage Variance: 16.995452302811504\n",
+      "Iteration 23: Average Return = 66.98 | Average Advantage Variance: 24.757588333026966\n",
+      "Iteration 24: Average Return = 75.21 | Average Advantage Variance: 21.18360901150257\n",
+      "Iteration 25: Average Return = 70.0 | Average Advantage Variance: 21.301149461514694\n",
+      "Iteration 26: Average Return = 78.46 | Average Advantage Variance: 21.083082111278358\n",
+      "Iteration 27: Average Return = 96.7 | Average Advantage Variance: 26.353424788591227\n",
+      "Iteration 28: Average Return = 106.67 | Average Advantage Variance: 23.45533547478895\n",
+      "Iteration 29: Average Return = 101.16 | Average Advantage Variance: 29.264826073389617\n",
+      "Iteration 30: Average Return = 111.55 | Average Advantage Variance: 25.26743835870217\n",
+      "Iteration 31: Average Return = 115.91 | Average Advantage Variance: 31.85680625022796\n",
+      "Iteration 32: Average Return = 106.96 | Average Advantage Variance: 29.697064970832113\n",
+      "Iteration 33: Average Return = 119.25 | Average Advantage Variance: 34.714631945688765\n",
+      "Iteration 34: Average Return = 122.91 | Average Advantage Variance: 33.015112018018606\n",
+      "Iteration 35: Average Return = 119.12 | Average Advantage Variance: 36.70001894715965\n",
+      "Iteration 36: Average Return = 122.18 | Average Advantage Variance: 34.20717346138999\n",
+      "Iteration 37: Average Return = 136.47 | Average Advantage Variance: 34.733309609755715\n",
+      "Iteration 38: Average Return = 148.06 | Average Advantage Variance: 45.63779978755172\n",
+      "Iteration 39: Average Return = 150.39 | Average Advantage Variance: 49.24559131405508\n",
+      "Iteration 40: Average Return = 168.61 | Average Advantage Variance: 53.92765050703035\n",
+      "Iteration 41: Average Return = 159.2 | Average Advantage Variance: 55.81794386758404\n",
+      "Iteration 42: Average Return = 171.04 | Average Advantage Variance: 54.15680404395147\n",
+      "Iteration 43: Average Return = 170.13 | Average Advantage Variance: 61.198726682168115\n",
+      "Iteration 44: Average Return = 174.43 | Average Advantage Variance: 60.44522026528535\n",
+      "Iteration 45: Average Return = 169.38 | Average Advantage Variance: 63.872520021851244\n",
+      "Iteration 46: Average Return = 171.79 | Average Advantage Variance: 57.386026778772724\n",
+      "Iteration 47: Average Return = 168.56 | Average Advantage Variance: 62.52909614121163\n",
+      "Iteration 48: Average Return = 169.69 | Average Advantage Variance: 57.47088074792233\n",
+      "Iteration 49: Average Return = 168.36 | Average Advantage Variance: 60.72087431389055\n",
+      "Iteration 50: Average Return = 173.03 | Average Advantage Variance: 60.50950786907882\n",
+      "Iteration 51: Average Return = 172.58 | Average Advantage Variance: 63.92214355041393\n",
+      "Iteration 52: Average Return = 174.79 | Average Advantage Variance: 60.302795102723294\n",
+      "Iteration 53: Average Return = 178.41 | Average Advantage Variance: 67.4880031611061\n",
+      "Iteration 54: Average Return = 179.11 | Average Advantage Variance: 65.14119879633813\n",
+      "Iteration 55: Average Return = 175.09 | Average Advantage Variance: 65.21367449204124\n",
+      "Iteration 56: Average Return = 187.05 | Average Advantage Variance: 73.73217940642836\n",
+      "Iteration 57: Average Return = 181.6 | Average Advantage Variance: 70.44494600063697\n",
+      "Iteration 58: Average Return = 187.24 | Average Advantage Variance: 72.95514521207176\n",
+      "Iteration 59: Average Return = 186.1 | Average Advantage Variance: 71.36845834080641\n",
+      "Iteration 60: Average Return = 189.91 | Average Advantage Variance: 75.63274457559298\n",
+      "Iteration 61: Average Return = 187.05 | Average Advantage Variance: 73.7363350680365\n",
+      "Iteration 62: Average Return = 193.08 | Average Advantage Variance: 75.65042479520744\n",
+      "Iteration 63: Average Return = 193.68 | Average Advantage Variance: 77.58774989364953\n",
+      "Iteration 64: Average Return = 192.46 | Average Advantage Variance: 78.38194452881292\n",
+      "Iteration 65: Average Return = 191.46 | Average Advantage Variance: 74.49769174551977\n",
+      "Iteration 66: Average Return = 193.4 | Average Advantage Variance: 78.11108175525416\n",
+      "Iteration 67: Average Return = 194.03 | Average Advantage Variance: 78.69696023540335\n",
+      "Iteration 68: Average Return = 190.83 | Average Advantage Variance: 77.73340440641361\n",
+      "Iteration 69: Average Return = 190.9 | Average Advantage Variance: 75.55597520611458\n",
+      "Iteration 70: Average Return = 188.12 | Average Advantage Variance: 76.05893721294234\n",
+      "Iteration 71: Average Return = 190.92 | Average Advantage Variance: 74.98688264769811\n",
+      "Iteration 72: Average Return = 189.91 | Average Advantage Variance: 76.61094076669389\n",
+      "Iteration 73: Average Return = 189.28 | Average Advantage Variance: 72.69853971132002\n",
+      "Iteration 74: Average Return = 193.92 | Average Advantage Variance: 75.77114829746014\n",
+      "Iteration 75: Average Return = 186.94 | Average Advantage Variance: 73.99467465586848\n",
+      "Iteration 76: Average Return = 192.47 | Average Advantage Variance: 77.88797558969196\n",
+      "Iteration 77: Average Return = 196.41 | Average Advantage Variance: 79.98087979834315\n",
+      "Solve at 77 iterations, which equals 7700 episodes.\n"
      ]
     }
    ],
@@ -653,19 +1204,29 @@
     "                     discount_rate)\n",
     "\n",
     "# Train the policy optimizer\n",
-    "loss_list, avg_return_list = po.train()"
+    "loss_list, avg_return_list, avg_advantage_variance_list  = po.train()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w\nf3kU57Zc6DsAtEa1cU0vlXIu+l9vU7r4/1zHNBh/8SdPOnmsuhL98T8haSJqSMfKuiNMF1yG01pk\nDP2uroLZ81CBvdBZ70FIKOpHF7b5niosHHXVDeg3/wJ5X0Ld+9bWYjhyyGjWbMmI04zZ/xu/8Mqa\navLN2A6msAjjl8pyCPfOyAvRRe3ZZjRXJIxB5/wPPe2mNv81XU8fs+F8+WljPa/0WU2eo2L6o277\nDfqiq9CfvI+aeiWqLZ/RscnQbwAUHnbNj+gIFdMf0/89jH7/DfRHq0BrGDgE9YPhtq3eZ9BQTPc9\nTkRIMGU1xyEoGOdfHsX52gpMo5NQdYvI6k8/gopyTF5e6qQpatpNEBJqLL9yrBTTdbejv/kMdcEV\nqOD2LXqrUi9BZ3+E882/ogoOGkOXjxhzAlubZKlMAcb6cDn/c3s5mY7wi2axrsZUN8tX5rqI1ujd\n22DYKGPCXkkh7G/fHCxdZsP5+O+N5p5b70b1CmrxfDV0pHHesJYXpWx0nclU1/eCMTvcA1RgIKZr\nbsQ0/4/QLw419fL23WfYKILGn4EaMgI1YBCmG++AMis681WgbtHLjzNh3OmoumHFvqSUwnTZtaib\nfw07t+D8013g1O1+/1BXlrN+CdVVRtJ69XmjNhQVA3HNr6Lgun7SBagLLoMTnb8kv9Rc2kHV11wk\nuYgW6OoqOLgXdckMVPIkdMDz6K//1+YvfF1agnPZ78FWgmneQ53e3KNSLwWnA3XGOZ6972kTCFi8\n3HP3Gz4aNeUy9Kf/Qk+agt6VbwwhvqLx8GdfMp1zITo8EufyR1BnTO5QUyMYI8oCnnzNmKhaaYcK\nO5jDW11Fwbh2nGt1hs4myaUdXM1i0qkvWrJvpzE8dMRpqD5mGJuM/voz9IybXU1j2umg9tB+CDY3\neQttLTYSS5kN068fQo0c2+lhq969UZc0MVnQD6lrbkRv3IDz5WeMPZbGJKFGnObrsBpR48/E9PBf\noXdvz90zqLfR5BoZ3frJPiDNYu1Q3yym7bK+mGie3rMNlIKE0QDGUifWYqibj6Jra3GueIySudfj\nfO+NxiOADh/C+dgCOGbDNP8PXkksXY0KCcV0/e3w/QEjAftZreVUKizcSAg9hNRc2qF+ZVUq7b4N\nRPg1vXsbxA1G1S12qpLPRgf2Quf8D4Yk4PzLY7BxA71GjePE+29AVQVcewvKZELv2Izz+SUQEIjp\n7j+1uSmtJ1GnT0Kdd7Gxs+bo5pdHEd4lyaUdVHAoBARKn4tolnY6YO8O1MSTk/hUSCiMPwP9zefG\nvui5G1AzbyPq2p9R9PwjRsdsVQV6xFj0q3+GfgMwzV3Y4Tb6nsB0052+DkH8gCSXdlBKGXtcSJ+L\naE7Bd1BVacwtOIVKORed+6WRWK77BaapVxgjtH76cwg1o99/Az7/xNia9pf3umo9QnQ1klzaq0+Y\n9LmIZtVPnvxh57KacJaxodbZUzCdsr2uUgp11XU4o6Kh6DDqqus7PFNcCF+S5NJeUnMRLdm9DSKi\njAURT6GCQwj47dJmL+voirVC+AsZLdZesmGYaIHevQ0STmv3bHwhujpJLu2kzLIysmiaLjUWq/TH\n+RZCeIskl/aqq7l4ahl10Y00098iRE8iyaW9zGHgqIUad3apEz2J3pUPQUHGBk1C9FCSXNqrfoio\n9LuIH9A7NsOIsbIdg+jRJLm0kzLXzdKvkFn64iR9rBS+P4Bqxw6OQnQnklzaq0+Y8bNC5rqIk/SO\nLUD7d3AUoruQ5NJeZiO5aGkWE6fasQmCQ2DICF9HIoRPSXJpL3N9zUWSizhJ79gMI8e5va2wEN2V\nz3sc7XY7GRkZFBUV0bdvX+bPn4/Z3Hg9pbVr17J69WoApk2bxpQpUwB44403WLduHXa7nVdeecV7\ngYfWJRepufRIeucWY1fFSMvJY6UlcOR7Y4VeIXo4n9dcMjMzSUxM5OmnnyYxMZHMzMxG59jtdlat\nWsWSJUtYsmQJq1atwm43OtLPPPNMlixZ4u2wjZFAIaFSc+mBnOs/wfnYfThfeLzBcb19MwBqtPS3\nCOHz5JKTk0NqaioAqamp5OTkNDonNzeXpKQkzGYzZrOZpKQkcnNzARg1ahRRUVFejdmlT5ix+53o\nMfTGDeiXn4HwSNi5xdWBD8COzRDaB+KH+iw+IfyFz5NLWVmZKzlERkZSVlbW6Byr1Up09MmtPC0W\nC1ar1WsxNqtPGFpqLj2G3paH8y+PwpARmB4yEozzX2+dfH77Jhg1HmWS/hYhvNLnsmjRIkpLSxsd\nnzmz4ZakSqlOXegvKyuLrKwsAJYuXUpMTEy77hMYGEhMTAy2KAtOeznR7bxPd1dfTt3BiV352J5f\nQmDcYKL+8DSmsHAqpt2I/aVnCC8qICC6L8XFRwm7+jpC2/ieu1M5dTYpK/f4Qzl5JbksXLiw2eci\nIiKw2WxERUVhs9kIDw9vdI7FYiE/P9/12Gq1MnZs2/cTT0tLIy0tzfW4uLi4zfcAiImJobi4GGdQ\nMLrsu3bfp7urL6euTjudOJ/+E4Sacc59AGvNcagpRqecB+/+HdtrK1w7TlYMGk5lG99zdyknb5Cy\nck9nllNcXJxb5/m8WSwlJYXs7GwAsrOzmThxYqNzkpOTycvLw263Y7fbycvLIzk52duhNtZH9nTp\nETZ9BYf2o66+ocHoMNU7GHVxOmzdaGxRbA6HuME+DFQI/+Hz5JKens6mTZuYN28emzdvJj09HYA9\ne/awfPlyAMxmM9OnT2fBggUsWLCAGTNmuIYrv/rqq8yZM4fjx48zZ84c3n77be8Fbw6Dygq0w+G9\n1xRepbXG+cHb0DcWdXZqo+fVlEuNPzIO7UONTkSZfP5PSgi/4PN5LmFhYTzwwAONjickJJCQkOB6\nPHXqVKZOndrovFmzZjFr1qxOjbFZfeqa8CrtEBbhmxiER2it0Z99bCSIfgNOPrHlWziwG3XTnU1O\njFTBoaiLrkZnvgpjZD0xIer5PLl0aeZTJlJKcunS9Nefo//+LDrCguk3f0INGFRXa3kTLH1Rky9o\n9lp14ZVw/DjqrPO9GLEQ/k3q8B2gZPHKbkGfOI5+9yUYEA/aiXPZ/ejDB2FbHuzdgbp0OiqwV7PX\nq+AQTNfMQoU2XllCiJ5Kai4dYZYlYLoD/fE/oaQQ0z2Ljbkrj9+P8/H7ISIKIi2oH6W1fhMhRANS\nc+mIPvUrI0vNpavSpVb0h6vg9ElGf8uAeEz3LAGl4OA+1CXTUb2CfB2mEF2O1Fw6IjzS+FkuyaWr\n0pmvQu0JTDNudh1TAwZhumcJ+su1sgilEO0kyaUDVO9g6B0MxxqvPiD8nz6wB73+E9RF6Q1HiAEq\ndiDq6ht8FJkQXZ80i3VUWIQkly7K+d7r0CcMdflPfB2KEN2OJJeOCo9El0ty6Wq00wm7tqJSfoQK\n7ePrcITodiS5dJTUXLqmwsNQVSnbEQvRSSS5dJAKj4TyxtsECP+m9+8CQA0d6dtAhOimJLl0VHgk\nlB9DO2V9sS7lwG4ICjImTgohPE6SS0eFRYJ2ykTKLkbv3wXxw5tcL0wI0XGSXDrKNddFmsa6Cu1w\nwHd7kSYxITqPJJcOUvXJRTr1u47DB+F4DQyVznwhOoskl44KN1ZD1pJcugx9YDcgnflCdCZJLh3l\nahaT5NJl7N8FIaHQz73tWoUQbSfJpaNCzRAQIM1iXYjevxsGJ8iukUJ0IvnX1UFKKZlI2YXo2hPG\nlsTS3yJEp5Lk4gnhkehjMlqsS/j+ANTWwhDpbxGiM0ly8YTwSKm5dBF6f31nvtRchOhMPl9y3263\nk5GRQVFREX379mX+/PmYzY23i127di2rV68GYNq0aUyZMoWamhqeeOIJjh49islk4swzz+SGG7y/\nTLoKi0AXHPT664p22L/L2EE0pr+vIxGiW/N5zSUzM5PExESefvppEhMTyczMbHSO3W5n1apVLFmy\nhCVLlrBq1SrsdjsAV155JU8++SSPPvooO3bsYOPGjd5+C66ai9ba+68t2kTv3w1DRhh9ZUKITuPz\n5JKTk0NqaioAqamp5OTkNDonNzeXpKQkzGYzZrOZpKQkcnNz6d27N+PHjwcgMDCQYcOGUVJS4tX4\nAWMJmNoTxiq7wm/pmhooOICS/hYhOp3Pk0tZWRlRUVEAREZGUlbWuGPcarUSHR3temyxWLBarQ3O\nqaio4JtvviExMbFzA26KLAHTNRzaB04napj0twjR2bzS57Jo0SJKSxt3eM+cObPBY6VUu5orHA4H\nTz31FJdeein9+zfflp6VlUVWVhYAS5cuJSYmps2vBUYt6dRra+IHUwpEKE1QO+/ZHf2wnHytckMB\n5YDl9LMJiPafuPytnPyZlJV7/KGcvJJcFi5c2OxzERER2Gw2oqKisNlshIeHNzrHYrGQn5/vemy1\nWhk7dqzr8YoVK4iNjeXyyy9vMY60tDTS0tJcj4uLi9vyNlxiYmIaXKudRkIsO3gA1W9gu+7ZHf2w\nnDqDzvsKfXAvpitmtnquc2suRFiwOkF1clxt4Y1y6i6krNzTmeUUF+feyhY+bxZLSUkhOzsbgOzs\nbCZOnNjonOTkZPLy8rDb7djtdvLy8khOTgbgzTffpLKyktmzZ3sz7IbqmsVku2Pv0xvWoj9c5dZ+\nOnrfLhg2SjrzhfACnw9FTk9PJyMjgzVr1riGIgPs2bOHjz/+mDlz5mA2m5k+fToLFiwAYMaMGZjN\nZkpKSli9ejUDBw7kd7/7HQCXXHIJF154oXffRJixeKXMdfE+XV4GJ45DSRH0jW3+vAo7HP0edc5U\nL0YnRM/l8+QSFhbGAw880Oh4QkICCQkJrsdTp05l6tSGXwzR0dG8/fbbnR5ja1RAgDF3QpKL99mP\nGT+PHGoxuXCgblvjYaO8EJQQwufNYt1GWKTxV7Twrrrkog8favE0vc9ILgyRkWJCeIMkF0+RJWC8\nTmvdsObS0rn7dkLsIFRoHy9EJoSQ5OIhKjwSZPFK76qqAIfRkd9SzUVrDft2oobJ5EkhvEWSi6eE\nR8qGYd5WX2vpHdxyzcVWbNQqpb9FCK+R5OIpYRFQVYk+cdzXkfQc5XXJJWEM2I+h6x//UF1/ixoq\nyUUIb5Hk4in1S8BI05j31NVc1Ii6CbXN1F70vp0QGAiDhnopMCGEJBcPUa7kIk1j3qLrk8tII7no\nw01ve6D374L44ahevbwWmxA9nSQXT5GJlN5XP/R7yAjoFdRkzUU7HbB/N2qodOYL4U2SXDxFloDx\nPvsxCOwFwSHQfyD6yPeNzzn8PdRUSWe+EF4mycVTwqRZzOvsxyAswlhNe8AgaKJZTO/bASDDkIXw\nMkkuHqJ694beIbKnixfp8mPGsjsAsYOgpBB9vKbhSft2QUgf6OfeSq5CCM+Q5OJJ4RFSc/GmupoL\nAAMGgdZQWNDgFL1/JwwdgTLJR10Ib5J/cZ4UHomW5OI95WUos7H/jxowCGg4U18fr4FD+2WxSiF8\nQJKLJ4VFSrOYN9nLoS650C8OlIJTk0tejrGtccIYHwUoRM8lycWDlCxe6TW6ttZYWyysruYS1Bui\n+7mGI2uHA/3e6zAgHsaf4ctQheiR3E4uW7ZsobCwEACbzcazzz7L888/T2mpfJm6hEcay5A4Wt8V\nUXRQ/bpi5lO2xR4Q72oW0xvWwpFDmNJnoUwB3o9PiB7O7eSycuVKTHWdon//+99xOBwopVixYkWn\nBdflREQZncrWIl9H0v3Vz86v79AHVOxAOPo9+sRx9PtvGJMrT5/kqwiF6NHc3onSarUSExODw+Eg\nLy+P559/nsDAQG6//fbOjK9LUSPHogG9fROqpV0RRcfV922dWnOJHQQnjqMzX4WSQkw33oFSyjfx\nCdHDuV1zCQkJobS0lPz8fAYNGkRwcDAAtbW1nRZclxM3GCKj0Vu/9XUk3Z62lxu/mE+puQyIN577\n+J8wajyMTfZFaEII2lBzueSSS1iwYAG1tbXMnj0bgO3btzNw4MAOBWC328nIyKCoqIi+ffsyf/58\nzGZzo/PWrl3L6tWrAZg2bRpTpkwBYPHixZSWluJwOBgzZgw///nPXc133qaUQo1LRm/cgHY4UAHS\n1t9p7HWKgB70AAAgAElEQVQ1l7Cwk8dijeHIaI3pmllSaxHCh9xOLunp6Zx11lmYTCZiY40mH4vF\nwpw5czoUQGZmJomJiaSnp5OZmUlmZiazZs1qcI7dbmfVqlUsXboUgHvvvZeUlBTMZjPz588nNDQU\nrTXLli3jiy++4Ec/+lGHYuqQcWfC55/A/l3GPiOic9Tv3RJ6MrmosHCIjIb4YSeX4RdC+ESb/sSP\ni4tzJZYtW7ZQWlrK4MGDOxRATk4OqampAKSmppKTk9PonNzcXJKSkjCbzZjNZpKSksjNzQUgNDQU\nAIfDQW1trc//WlVjJ4AyobdI01insh+DUDMqsOHfR6bfLcX0i3t8FJQQop7byeXBBx9k+/btgFHb\neOqpp3jqqadcTVXtVVZWRlRUFACRkZGUlTWehGi1WomOjnY9tlgsWK1W1+PFixdz2223ERISwqRJ\nvh0dpPqEwdAR0u/S2ezHGnbm11Ex/VHBoT4ISAhxKrebxQ4ePMioUcYyGp988gkPPvggwcHBLFy4\nkGnTprV47aJFi5qcDzNz5swGj5VS7ap53H///Rw/fpynn36aLVu2kJSU1OR5WVlZZGVlAbB06VJi\nYmLa/FoAgYGBLV5rn3guFatewtI7CFNY4y/AnqK1cuoIW00V2hKNpZPu702dWU7djZSVe/yhnNxO\nLlprAI4cOQLAoEFG52lFRUWr1y5cuLDZ5yIiIrDZbERFRWGz2QgPb/xlbLFYyM/Pdz22Wq2MHduw\nTT0oKIiJEyeSk5PTbHJJS0sjLS3N9bi4uLjV2JsSExPT4rV62GhwOin+bA2miee26zW6g9bKqSMc\n1mKI7tdp9/emziyn7kbKyj2dWU5xce6tMO52s9jo0aP529/+xiuvvMLEiRMBI9GEnTpapx1SUlLI\nzs4GIDs723XvUyUnJ5OXl4fdbsdut5OXl0dycjLV1dXYbDbA6HP59ttvOzx6zSOGjTKWeZemsc5j\nP+ZatFII4X/crrnccccdvP/++4SHh3PVVVcBUFBQwGWXXdahANLT08nIyGDNmjWuocgAe/bs4eOP\nP2bOnDmYzWamT5/OggULAJgxYwZms5nS0lIeffRRTpw4gdaacePGcdFFF3UoHk9QAQEwdgJ660a0\n1j4fZNDdaK0bLrcvhPA7Ste3d/VABQUFrZ/UBHeqnM7//Rf992cxPfQMauCQdr1OV9dZVXNdVYlz\n3kzUjJsx/fgaj9/f26Spx31SVu7xh2Yxt2sutbW1rF69mnXr1rn6SM4//3ymTZtGYKDbt+kx1LjT\njaVgtn7bY5NLp6lftLIHD5YQwt+5nRVeffVV9uzZw2233Ubfvn0pKiri3XffpbKy0jVjX5ykLH2N\nVXq35sLFXf+va79St66Y9LkI4b/c7tDfsGEDv/3tb5kwYQJxcXFMmDCBe+65hy+++KIz4+vSVMIY\nOLjX12F0P66ai/S5COGv3E4uPbhrpv3iBkN5GVp2p/QoXd7EXi5CCL/idrPY5MmTeeSRR5gxY4ar\ns+jdd9/1+Yx4f6YGxKMBDh+Uv7I9qamNwoQQfsXt5DJr1izeffddVq5cic1mw2KxcM455zBjxozO\njK9ri6tbAr7gIGrUeB8H043Yj0FgIASH+DoSIUQzWkwuW7ZsafB43LhxjBs3rsHcje3btzN+vHxx\nNikqBnqHGDUX4TnlZWAOl/lDQvixFpPLn//85yaP1/+jrk8yzz77rOcj6waUUhAXjy74ztehdCva\nfqzBJmFCCP/TYnJ57rnnvBVHt6Xi4mX5fU+zH5M5LkL4Od9s2diTDBgMZTZ0RbmvI+k+ymVdMSH8\nnSSXTqbqOvWl38WDmtnLRQjhPyS5dLYBJ0eMiY7TtbVQaZfkIoSfk+TS2Sx9Iai31Fw8pbKueVHm\nDQnh1yS5dDJlMhlrjMmIMc+Q2flCdAmSXLxAxcWDNIt5Rt3sfCWjxYTwa5JcvGHAYCgtQVe2viW0\naJn+/oDxS4TFt4EIIVokycULZMSYZ2inA/3J+zB0JMT6wXbWQohmSXLxhvoRY5JcOmbjBig8jOmS\n6bL0ixB+TpKLN8T0g6Agqbl0gNYa50fvQr84OP1sX4cjhGiFJBcvUKYAiB3U7UeM6Zrqzrv59k1w\nYDfqx+lGeQoh/JrbS+53FrvdTkZGBkVFRfTt25f58+djNpsbnbd27VpWr14NwLRp05gyZUqD5x95\n5BEKCwtZtmyZN8JuMzUgHr0r39dhdBq9exvOR34HY5IwXXQ1jD/To/d3/ns1hEeiJk/16H2FEJ3D\n5zWXzMxMEhMTefrpp0lMTCQzM7PROXa7nVWrVrFkyRKWLFnCqlWrsNvtrue//PJLgoODvRl22w2I\nB2sRurrS15F0Cl1QN4rr+wM4n1mE88E7qP4syzP3/m4v5G9EpV2F6hXkkXsKITqXz5NLTk4Oqamp\nAKSmppKTk9PonNzcXJKSkjCbzZjNZpKSksjNzQWgurqaDz74gOnTp3s17rZScYONXw5/79tAOktZ\nKQCmh/+K+vlvoFcQZRkPob/b0+Fb6/+shuAQVOolHb6XEMI7fJ5cysrKiIqKAiAyMpKyssb7zVut\nVqKjo12PLRYLVqsVgDfffJMrr7ySoCA//4u2Lrnow9203+WYDcxhqN69MZ2diumexZjCInC++me0\n09nu2+rv9qJzPkOdfwkqtHFzqRDCP3mlz2XRokWUlpY2Oj5z5swGj5VSbRpiun//fo4ePcrs2bMp\nLCxs9fysrCyysoymmqVLlxITE+P2a50qMDCwzdfqqCgKAwMJOWYjrJ2v689KqyqpjYo5pVxiOH7r\nXdieeJA+uV8QevHVbb6ndjiwPvoXCI8getbtmLrprPz2fJ56Kikr9/hDOXkluSxcuLDZ5yIiIrDZ\nbERFRWGz2QgPb/wFYrFYyM8/2RlutVoZO3YsO3fuZO/evdxxxx04HA7Kysp46KGHeOihh5p8rbS0\nNNLS0lyPi4uL2/V+YmJi2ndthIWq7w9S087X9WeO4qNgDm9QLtHnpsEH71D+8nNUjByPauNik85P\n/4XelY/6+W+w1hyHmu5XbtCBz1MPJGXlns4sp7i4OLfO83mzWEpKCtnZ2QBkZ2czceLERuckJyeT\nl5eH3W7HbreTl5dHcnIyF198MStWrOC5557jj3/8I3Fxcc0mFr8QaUGXlvg6is5RZkNFRDU4pJTC\ndMMcqKlCv/tym26nS0vQq/8OY5NRZ53vyUiFEF7g8+SSnp7Opk2bmDdvHps3byY9PR2APXv2sHz5\ncgDMZjPTp09nwYIFLFiwgBkzZjQ5XNnvRVqgGyYXrbXR5xIe1eg5FTcYdVE6+vMs9G73h2I733wB\namsx3TBHZuML0QX5fJ5LWFgYDzzwQKPjCQkJJCQkuB5PnTqVqVObn+PQr18/v53jUk9FRqO3bPR1\nGJ5XXQXHj0NEZJNPqyt+aiSXNf9CjRjb6u30phz4Zj0qfRaqn3tVcCGEf/F5zaVHiYo2moiqutlc\nlzKb8bOJmguA6h0MI8eiD+xu9Vb68EGcLz4FA+JRP77Gk1EKIbxIkos3RdYNp+5uTWN1yeWHfS6n\nUoMToPBwi9sO6OKjOJ94AEwmTHfejwrs5fFQhRDeIcnFi1R9crF1r+Sij7VccwFQQ+qaOA/ubfoe\nZTacGQ/A8WpM8/8gzWFCdHGSXLwpytjgqtuNGKtvFmumzwWAwUZy0Qcaz9jXlXacTz4IpVZM8x5E\nDRrWGVEKIbxIkos3ddOaC8dsEBAILcygV+GREBUDTSWXj/8J33+H6Vf3oRLGdGakQggvkeTiRSqo\nt/EFXGr1dSieVVZqrFhsauXjNCShybXG9NaNMGwkatzpnRSgEMLbJLl4W1R0t2sW08dsEN5Ck1gd\nNTgBjn7fYGVoXWGH/btRY5M7M0QhhJdJcvG2SEv3axYrs0ELI8XqqcEJoDUc3H/y4PZNoJ2osVJr\nEaI7keTiZSoyuvs1ix0rbXEYssuQ+k79k/NddH4uBIfAsFGdFZ0QwgckuXhbVDQcK0U7HL6OxCO0\n0wHHytyruURajPNO6XfR23JhdCIq0OeLRQghPEiSi7dFRoN2nhy+29XZjxnvp4U5Lg0MTnANR9ZF\nR6DoCOo06W8RoruR5OJlqrvN0i+tn53feoc+1E2mPHwIXVNjNImBdOYL0Q1JcvG2uomU3Sa5uDE7\n/1RGp74TDu0zkktUDMQO7MQAhRC+IMnF2+pqLtrWPTr1dVndDqPudOjDyU79/btg+ybU2AmypL4Q\n3ZAkF28zhxuz2btdzcW9ZjGiYsAcjv7ff6HSDtLfIkS3JMnFy5TJ1L02DSuzQXCIsay+G5RSRu3l\n+wPG49MmdGZ0QggfkeTiC5EWdHeZSHms1P2RYnVU3SKWxA8z1hwTQnQ7klx8IdLSbSZS6jJby6sh\nN0ENGWH8lFFiQnRbklx8wJilX2LsPd/VHbOh2lhzYdQ4GDQUdVZq58QkhPA5mRbtC1HRUFMNVZUQ\n2sfX0XRMWSmMs7TpEhUWQcCDT3dSQEIIf+Dz5GK328nIyKCoqIi+ffsyf/58zObG+4KsXbuW1atX\nAzBt2jSmTJkCwEMPPYTNZiMoKAiA3//+90RERHgt/nY5dSJlF04u+ngNVFW4P1JMCNFj+Dy5ZGZm\nkpiYSHp6OpmZmWRmZjJr1qwG59jtdlatWsXSpUsBuPfee0lJSXEloXnz5pGQkOD12NtLRUajwUgu\ncYN9HU77uXagbGOzmBCi2/N5n0tOTg6pqUbbe2pqKjk5OY3Oyc3NJSkpCbPZjNlsJikpidzcXG+H\n6jn12x139YmUx4wJlG3ucxFCdHs+r7mUlZURFWV8OUVGRlJWVtboHKvVSnR0tOuxxWLBaj35xfz8\n889jMpk4++yzmT59erMzvrOyssjKygJg6dKlxMTEtCvmwMDAdl8LoMPCKARCj1dh7sB9fK16t4My\nIHLIUHo18T46Wk49hZST+6Ss3OMP5eSV5LJo0SJKS0sbHZ85c2aDx0qpNi8FMm/ePCwWC1VVVSxb\ntox169a5akI/lJaWRlpamutxcXFxm16rXkxMTLuvdQk1U1lwkOq6++hvv0Dv2orppz/v2H29yHnI\nmAhZ6lSoJsrDI+XUA0g5uU/Kyj2dWU5xcXFuneeV5LJw4cJmn4uIiMBmsxEVFYXNZiM8PLzRORaL\nhfz8fNdjq9XK2LFjXc8BhISEcO6557J79+5mk4tfiYp2TaTU1mKcLz0FVZXoK2eiQhsPaPBLZaWg\nFIT5+QAKIYTX+bzPJSUlhezsbACys7OZOHFio3OSk5PJy8vDbrdjt9vJy8sjOTkZh8PBsWPHAKit\nreWbb74hPj7eq/G3W91ESq01zlefN4YlAxzY0/J1/uSYDczhqIAAX0cihPAzPu9zSU9PJyMjgzVr\n1riGIgPs2bOHjz/+mDlz5mA2m5k+fToLFiwAYMaMGZjNZqqrq1m8eDEOhwOn00liYmKDZi9/piKj\n0Yf2o79cC5u/Rl32E/SHb6O/2+PR9bZ0dRX68yzUlMs8ngSM2fnSmS+EaMznySUsLIwHHnig0fGE\nhIQGw4unTp3K1KlTG5wTHBzMI4880ukxdor67Y7f/CskjEFdfR16w6cer7noT95HZ76KGhAPnl5u\npR3rigkhegafN4v1WJHRoDXUVGH62VyUKQCGJKAP7PbYS2iHA73u38bvhw+1/fq9O3C+8Dj6xImm\nTyizub0DpRCiZ5Hk4iMquq/x88rrjFoFdQs6Fh5GV1Z45kU25YC1bsTI4e/afLn+ap3xX87/Gj/n\ndBp9LhFtW/pFCNEzSHLxldOSMd25EHXJNNchVbdLI995pmnMufZDY3OuYaPaV3Opi0Nn/bPRIpv6\n68+gthY1dKQnQhVCdDOSXHxEBQSgJkw0msPq1S1Frz3Q76KPfA/5uajzf4waOAQOH2zb9U4nfLfP\nWDfs4D7YueWU5xzo9980lq45fVKHYxVCdD+SXPyICosASwx4oN9Fr/0QAgJR518MA+KhvAxdfsz9\nGxQehpoq1BU/BXM4zo//efLeX/0PjhzCdNX1xs6aQgjxA/LN4G8Gj+hwzUXXVKPXr0GdeQ4qPMrV\np9OW2os+uBcAlXAaKvUS2JSDLiwwBgm8/yYMGia1FiFEsyS5+Bk1JAEKCzrUqa+/zIaqCtSUy4wD\ncUZy0Ufa0DR2YA8EBkJcvHEfUwA6631jXk5hAaarr5NaixCiWfLt4GfqtwCmruYAoEsKcdx/O3p3\nfjNXNaTXfgiDhsKI04wDUTEQ1BsK2lBz+W4PxA1BBfZCRVpQZ52HXv8J+r03YHACTDjb7XsJIXoe\nSS7+pm7E2KnzXXTmq8YQ5c3ftHq5riiHg/tQZ6W6FgFVJhMMiHd7xJjWGg7uPTl6DVBpVxu7Z5YU\nGn0tbVxgVAjRs/h8hr5oSIVHGjWNun4X/d0e9Ia1rt9bdbTAuM+AQQ3vO2AQeseWpq5ozFoM9nKI\nH37y+sHDYfwZUF0NSSnu3UcI0WNJcvFHQxJcnfrOd1+GPmEwahzs3obWusVag65LLvT/wbLYA+Jh\nw1p0VSUqJLTl1z9ovLYaPLzBYdMdvwdafn0hhABpFvNLakgCHP0e/c16Y67K5T9BjUmC8jKwtbJH\nQ2EBKBPExDa8Z/2IsSOtN43pA3uNewwa1vAegYGowF5tei9CiJ5Jkosfqu/Ud/79GYjuZ6xoXN/R\n31rT2NECiO6L6vWDJFCXXLQbw5H1d3sgdiCqd+82xy6EECDJxT/Vd6RXVqDSZxmJYtAwUKZW58Do\nwsPQr4md4vrGGkOL3Rkx9l3DznwhhGgrSS5+SIVHQXQ/GDwcddb5xrHevWHAoBaTi9Yajn6P6j+g\n8T0DAqD/QHQrzWL6mA1KSxp05gshRFtJh76fMv36QQgJbTBRUQ1JQOfnNn9ReSlUV0H/gU0+rWIH\ntT7i7Lu9rtcSQoj2kpqLn1ID4lGR0Q0PDhkBZTZ0aUnTFx09bFzbVLMYGP0uxYXo4zXNvq6uSy7E\nD2v2HCGEaI0kly5EDa6rTRzY2+TzurB+GHLjZjHAWAZGO11zYZq8x3d7oG8sKtTckVCFED2cJJeu\nJH4YKNX8bpVHCyAgAKL7N/l0/cTKFkeMfbcXBkt/ixCiY3ze52K328nIyKCoqIi+ffsyf/58zObG\nfzWvXbuW1atXAzBt2jSmTJkCQG1tLStXriQ/Px+lFDNnzmTSpO65Wq8KDjE65ZvpN9FHCyC6v9F5\n35T+A435K80kF11ZAUVHUD9K81TIQogeyufJJTMzk8TERNLT08nMzCQzM5NZs2Y1OMdut7Nq1SqW\nLl0KwL333ktKSgpms5nVq1cTERHBU089hdPpxG63++JteI0aktD8Mi6FBY1n5p96ba8g6Nu/+ZrL\n/p3GebK7pBCig3zeLJaTk0NqaioAqamp5OTkNDonNzeXpKQkzGYzZrOZpKQkcnONUVOffvop6enp\nAJhMJsLDw70XvC8MGQGlJcaQ4VNoraHwMKqF5AIYnfrNzHXRu/KNmk3CaE9FK4TooXxecykrKyMq\nKgqAyMhIysrKGp1jtVqJjj45cspisWC1WqmoMPY8eeutt8jPz6d///7ccsstREZGeid4H1CDE9Bg\ndOonnnnyiVIrHK9pegLlqdfHD0dv+hpdYUf1adj8qHflQ/wwVHAra48JIUQrvJJcFi1aRGlpaaPj\nM2fObPBYKdWmRREdDgclJSWMHj2an/3sZ3zwwQe88sorzJ07t8nzs7KyyMrKAmDp0qXExMS04V2c\nFBgY2O5rO8oZOpEiIKS4AHPMj13Hjx/5DhsQMXIMvVuI7fjk87F98CZhBfsJnjzFdVzX1lK4bych\nF11FuIfemy/LqSuRcnKflJV7/KGcvJJcFi5c2OxzERER2Gw2oqKisNlsTTZrWSwW8vNPbpRltVoZ\nO3YsYWFh9O7dm7POOguASZMmsWbNmmZfKy0tjbS0k53VxcWtLALZjJiYmHZf6xH9B1KxbTPVp8Tg\n3GmUz7EQM6qF2LQlFnqHcOzLddhHjj95fN9OOF5DzaBhHntvPi+nLkLKyX1SVu7pzHKKi2ul6b2O\nz/tcUlJSyM7OBiA7O5uJEyc2Oic5OZm8vDzsdjt2u528vDySk5NRSnHmmWe6Es+WLVsYNGhQo+u7\nGzV4uGu/F5ejhyGwl7EXTEvXBgbC6PGNZvrrXXXJu373SiGE6ACfJ5f09HQ2bdrEvHnz2Lx5s6tz\nfs+ePSxfvhwAs9nM9OnTWbBgAQsWLGDGjBmu4co33HAD77zzDvfccw/r1q3jpptu8tl78ZqhI8Fa\n1GDUly4sMCY/urGvvRqbDEVH0EVHTl6/O9+4/oerAgghRDv4vEM/LCyMBx54oNHxhIQEEhJOrm81\ndepUpk6d2ui8vn378oc//KFTY/Q3avIF6PfeQP/zddSc3xkHj7Y8DLnB9WOT0YDelofqG2uMNNu9\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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WDfqy6ctfJaJ0D93xiYO+rrIuRmVdPJYR+o386e2tyN6E0tUZ3DiE8MTBMqivQV19g+sp\nFREJ6VPRFb7PGNNa4/j9zyE+0diUKicflZ2HWnSN8frRAwOPb6xz6xJzyZwO3d1udbc4cRS0HrAh\n1ninMqcZXWJ5gyd1NfcS4u/8YUjXDPOUJBdvRUUZ/8qMMRHidHcXjm0vgTnO7S9lNX02VBz1qvTK\nAHv3QPlB1FduQfVvwadMxhSfaKzj6O+cNS4DYsnonTF2TteYPn7Y+GK8jKl4QF1/I6Yfbg6dhZ1j\nSJKLl1z/kbokuYjQpbVGv/gEnCzH9M/fNTaR6m/6LGi3QX2N99fuOYvj1RchfSrqnL1QlFJMmHsJ\nul9y0WfPQosVhkguTJ4KyoQ+ZzqyPn7E2K43hKcXe0tFx4yLmV7+IMnFW85uMWm5iBCm//xbdMnf\nUTd+bdBxFecMK1+6xvSuv0J9DaaV3xgwRuI0YW4u1Negm3tnozU5S+0P3i2mIiNh0mT3Qf2Kw6gZ\n50+r5UIjycVbUZJcRGjTH7yN/sOvUQuvQd2wYvCD0qcZ+7p7mVx0u81YizH3Eph/2aDHRMztXa/i\nbL04Nwk7d41Lf5nTBkxH1tYGaLbC9PNnvOVCI8nFW73JRcuAvghB+kQ5jhceg6yLUf98x5ADwyo8\nHKbMQJ/wbqW+LvoVtNuMVssQ1w6fMQciIl1dY9q5On+oAX1AZUw3WjvO/1cVxniLminJZbyS5OKt\nSBnQF6FLv74NIiIx3b7OfZzlHGr6bDhRjnbYPbv2h++g3/xz72r5mUNfNzwcZszpG3dprDOq/CYO\nXUhSZUwzpvifPmnc6/gRCAs3aqGJcSno61xsNhtbtmyhvr6elJQU7r77bsxm9wG8nTt3sm3bNgCW\nL1/OkiVLAPjNb37DW2+9hc1m46WXXhr7gGVAX4QwXV0JMy4yVr6PZPpsePPPUF0FGcOXb9c1VThe\nfAJmXoRauWbES6vZ2eg//x7d2W7UFYtPRIVPGPqE/mVgZswxZopNmYGaMMw5IqQFveVSVFRETk4O\nTzzxBDk5ORQVFbkdY7PZ2Lp1Kxs3bmTjxo1s3boVm83YU+Xyyy9n48aNgQtYBvRFiNJaQ91pVGr6\nyAdjrNSHkQf1dVcnjmc3QXg4pm//+/BJwnntrLmgHXDscO8mYUN3iQGQnGr0ClSdMFpSFUdlMH+c\nC3pyKSkpoaCgAICCggJKSkrcjiktLSU3Nxez2YzZbCY3N5fS0lIA5syZQ2KiB3+l+YkKC4OICOiU\nMRcRYpqtRuUID5MLaRnGH0vDlN/XWqNf/imcPonptu8PuVbFTdbFxvTiowegsW7E85TJ2PxKV1YY\nLamuDphxkWf3EiEp6MmlpaXFlRwSEhJoaXHfIc9qtZKU1Ndfa7FYsFqtAYvxXCoqRrrFROjp3eVQ\npQ5RUfccyhQG07LQB8qM1sU5dGc7+tVfoN99E/WlVah5l3ocioqOgcxp6CMHjKnIHiQllTkdqirQ\nxw8Zj6XlMq4FZMxl/fr1NDc3uz2/atWqAY+VUmNa9qC4uJji4mIANm3aRHKyb8XfGqJjmKAdxPt4\n/lgLDw/3+b0FgsQ3OkPF1952hlbAMnc+YR7G3/HFlZx5cgOOH64l+rp/YOKKf8ZkjqP9L6/Stu0l\ndGsLUUtuIG7NHR4XanXGdybncjr++ho47JinzSBmhJjaL5pH69//RsSBfXTHmEnOzh2T4rDj9ec7\n3gQkudx///1DvhYfH09TUxOJiYk0NTURF+deFsFisXDgQF+tIqvVSnZ2ttdxFBYWUlhY6Hrc0NDg\n9TXAWKXf2dLCWR/PH2vJyck+v7dAkPhGZ6j4HOWHICICq0OhPI0/+zJM//Us+v9+R8ffiujY/r8Q\nM9HYgjf7UkzLbuHsjDk0etFT4IzPkTEdemeitUXG0D5CTDrB+EDt+nA3XJTj1T29MV5/vqEiPd2z\nbtegd4vl5+eza5dRsnvXrl0sWLDA7Zi8vDzKysqw2WzYbDbKysrIy8sLdKguKlq6xUTo0bWnIWWy\n13/tq6QUTF+7A9P6nxol3afPxvRvGwm7+/8bVdFINavfH4AjDegDOGuMORwoGW8Z94I+FXnZsmVs\n2bKFHTt2uKYiA5SXl7N9+3bWrl2L2WxmxYoVrFu3DoCVK1e6piu//PLLvP3223R3d7N27VqWLl3K\nTTfdNKYxq+gYaG4a03sI4bXa030f0D5QKWmor9/pt3CUJdlIKo11no25mOMgwQLNVhlvOQ8EPbnE\nxsbywAMPuD2flZVFVlbftqZLly5l6dKlbsetXr2a1atXj2mM51JR0dB5OqD3FGI4uqcHGmqG3Cck\nWNTseejuLs83+8qc3lv2RZLLeBf05DIeGd1iMhVZhJDGOrDbjc2oQoj6xzWown/w/Pi8hWhAJVjG\nLigREJJcfKCiYmQRpQgtdUZL2tMFlIGi4hLBk2oBvUwFN0DBDSMfKEJe0Af0xyPngL7PGy0J4We6\nd41LqLVcxIVLkosPTFHRRhdET0+wQxHCUHsaYsxgjg12JEIAklx84hqclK4xESJ07WlITT8v9l4X\n5wdJLj5wJRdZ6yJCRW2Vx2VfhAgESS4+ULIbpQghuqsLrA2eF6wUIgAkufigr+Ui05FFCKjvXXMl\nyUWEEEkuPlBRMuYiQkhtaE5DFhc2SS4+kAF9EUp0Te805EmSXETokOTiA+eYi5YBfREK6qohwdI3\nFihECJDk4gOTtFxECNG1VbJ4UoQcSS4+kAF9EVJqT8t4iwg5klx8MSECTCZpuYiAc2z7Jdb7/h+6\nqREA3dYKtjMyU0yEHEkuPlBKQVS0tFxEQOm6avTfXuPsof04HrkXXVPZb6aYdIuJ0CLJxVeR0dDZ\nHuwoxHlGHz+C/uDtwV/7428gLIyEHzwK3V04HrkP/f5bxovSchEhRpKLr6Ki0dItJvzMUfQSjv9+\nFL1/74Dn9emT6Pd2oa75IpH5V2K67xHjd/CNPxpdtMmpQYpYiMFJcvFVZJR0iwm/0lrDyXLQGsfz\nP0FbG1yvOf7wa4iMQt2wAgA1KR3TvY8YOzdOm4UKnxCkqIUYnCQXX0VFy4C+8C9rA9haUdd+Gc52\n4/jZj9F2O/pEOezdjSr8irHPfC+VYMF0/2OY/nVDEIMWYnCyE6WvoqKhoTXYUYjzyYmjAKjPXA0z\n5qD/ZzO66GV0ZQXEmFHXfcXtFGUyQWRkgAMVYmSSXHykIqNkhb7wK32y3Bg/yZyOaeZFOA5/gv7r\nqwCo5V9HxUwMcoRCeE66xXwl3WLCz/TJYzB5CirCaImoVbfB1JlGaZelXwxydEJ4R1ouvoqMls3C\nhH+dLEdlX+p6qCZEGIP2XZ2oyKggBiaE9yS5+CoqGrq70XY7Kiws2NGIcU43W6GlCaZlDXheRURC\nhIypiPEn6MnFZrOxZcsW6uvrSUlJ4e6778ZsNrsdt3PnTrZt2wbA8uXLWbJkCV1dXfzkJz+htrYW\nk8nE5Zdfzi233BKYwJ1/SXZ1gvSFi9E6UQ6Ampo1woFCjA9BH3MpKioiJyeHJ554gpycHIqKityO\nsdlsbN26lY0bN7Jx40a2bt2KzWYD4Mtf/jKPPfYYP/rRjzh06BD79u0LTOCy1bHwI32yHJSCKTOC\nHYoQfhH05FJSUkJBQQEABQUFlJSUuB1TWlpKbm4uZrMZs9lMbm4upaWlREZGMn/+fADCw8OZMWMG\njY2NgQncmVxkIaXwA32yHFIzZE8Wcd4IenJpaWkhMTERgISEBFpaWtyOsVqtJCUluR5bLBasVuuA\nY9ra2vjwww/JyckZ24B7qUhpuQg/OlkuXWLivBKQMZf169fT3Nzs9vyqVasGPFZKGRWHvWS323n8\n8cf5/Oc/T2rq0DWWiouLKS4uBmDTpk0kJyd7fS8wWknxqWk0AfFREUT4eJ2xEh4e7vN7CwSJbyBH\nSxP11gYmZucw0YP7yvdvdCS+wAhIcrn//vuHfC0+Pp6mpiYSExNpamoiLi7O7RiLxcKBAwdcj61W\nK9nZ2a7Hzz33HGlpaXzxi8OvBSgsLKSwsND1uKGhYZijh5acnExLVxcALbU1qMm+XWesJCcn+/ze\nAkHiG8hZpLI9KY0OD+4r37/RkfhGJz3dswrcQe8Wy8/PZ9euXQDs2rWLBQsWuB2Tl5dHWVkZNpsN\nm81GWVkZeXl5ALzyyiu0t7ezZs2aQIZtrHMBqYwsRk2fNGaKMXVmcAMRwo+CPhV52bJlbNmyhR07\ndrimIgOUl5ezfft21q5di9lsZsWKFaxbtw6AlStXYjabaWxsZNu2bWRkZHDvvfcCcMMNN3DttdeO\nfeBR/aYiCzEK+mQ5pKShYtyn4AsxXgU9ucTGxvLAAw+4PZ+VlUVWVt8A59KlS1m6dOmAY5KSkvjd\n73435jEOSqYiC385eUwG88V5J+jdYuNWhLPlIslF+E632aC+xm1lvhDjnSQXHxmlzqOk5SJG56Ss\nzBfnJ0kuoxEVLWMuYlT0yWPGF5JcxHlGkstoSMtFjNapY2BJRsW6T8EXYjyT5DIaUdEyFVmMiq6r\nhtSMYIchhN9JchmNyCjpFhOj01CLSh66qoQQ45Ukl9GIipFuMeEz3dkOrS2QkhbsUITwO0kuo6Ai\no2QqsvBdQ63xb7IkF3H+keQyGlHR0nIRvqs3kotKkW4xcf6R5DIaMhVZjIJ2tlykW0ychyS5jEZk\nFHR2orUOdiRiPKqvgeiJIDXFxHlIkstoREWDdkB3V7AjEeOQbqiFlFSf9jASItRJchkN526UMqgv\nfFFfI4P54rwlyWU0pDKy8JF2OIw1LjKYL85TklxGQUX2VkbulEF94aWWJug5Ky0Xcd7yeD+X/fv3\nM2nSJCZNmkRTUxO/+tWvMJlM3HzzzSQkJIxljKFLWi7CV/U1ACiZKSbOUx63XJ5//nlMJuPwX/7y\nl9jtdpRSPPfcc2MWXMhzJheZjiy8pBuM5IJ0i4nzlMctF6vVSnJyMna7nbKyMp555hnCw8P59re/\nPZbxhbbeAX3d2YHM9xFeqa8FpcCSEuxIhBgTHieX6OhompubOXXqFJmZmURFRdHT00NPT89Yxhfa\nXN1i7cGNQ4w/DTWQmIwKnxDsSIQYEx4nlxtuuIF169bR09PDmjVrADh48CAZGRdwufAo51bH0i0m\nvKPra2RlvjiveZxcli1bxmc+8xlMJhNpacZ/CovFwtq1a8csuJDnmi0mA/rCSw21qPmXBzsKIcaM\nx8kFID093fX1/v37MZlMZGdn+z2o8UKFT4DwcGm5CK/ori5jKrK0XMR5zOPZYg8++CAHDx4EoKio\niMcff5zHH3+cbdu2jVlw44JURhbeanSW2peZYuL85XFyOXXqFHPmzAHgjTfe4MEHH2TDhg1s3759\nzIIbFyKjpfyL8I6r1L60XMT5y+NuMWfl35oaY35+ZmYmAG1tbaMKwGazsWXLFurr60lJSeHuu+/G\nbHavErtz505XK2n58uUsWbIEgA0bNtDc3Izdbufiiy/mtttuc63HCYjoGHT76L4H4sLSt8ZFkos4\nf3mcXC666CJ+/vOf09TUxIIFCwAj0cTGxo4qgKKiInJycli2bBlFRUUUFRWxevXqAcfYbDa2bt3K\npk2bALjvvvvIz8/HbDZz9913ExMTg9aazZs3s2fPHq688spRxeSV2Hhjq1ohPFVfY7R4zXHBjkSI\nMePxn/h33HEHMTExTJs2jZtuugmA06dP84UvfGFUAZSUlFBQUABAQUEBJSUlbseUlpaSm5uL2WzG\nbDaTm5tLaWkpADExMQDY7XZ6enoCXr5cxSUYg7NCeEhK7YsLgcctl9jYWG6++eYBz1122WWjDqCl\npYXExEQAEhISaGlxbwVYrVaSkpJcjy0WC1ar1fV4w4YNHD16lLy8PBYuXDjqmLwSnwitzWit5cNC\neKa+Bialj3ycEOOYx8mlp6eHbdu28dZbb9HU1ERiYiJXX301y5cvJzx8+MusX7+e5uZmt+dXrVo1\n4LFSyqcP6B/84Ad0d3fzxBNPsH//fnJzcwc9rri4mOLiYgA2bdpEcnKy1/cCCA8Pd53blpaBrbub\nJHMMpuiJPl3P3/rHF4ou5Pi01tQ11BKTv5hYP/z+hSKJb3RCPT5PeZxcXn75ZcrLy/nWt75FSkoK\n9fX1vPrqq7S3t7tW7A/l/vvvH/K1+Ph4V7JqamoiLs69H9pisXDgwAHXY6vV6ra+JiIiggULFlBS\nUjJkciksLKSwsND1uKGhYdgV/fp9AAAgAElEQVS4h5KcnOw61xFmlO9oPF6OCpG/RvvHF4ou5Ph0\nSxN0d9ExMY4uP/z+hSKJb3RCPb7+6x2H4/GYy7vvvsu///u/c8kll5Cens4ll1zC97//ffbs2eNz\nkAD5+fns2rULgF27drkmC/SXl5dHWVkZNpsNm81GWVkZeXl5dHZ20tRkjHfY7Xb27t0b8HI0Kq53\nu4EW95aZEG6k1L64QHg9Fdnfli1bxpYtW9ixY4drKjJAeXk527dvZ+3atZjNZlasWMG6desAWLly\nJWazmebmZn70ox9x9uxZtNbMmzeP6667bkziHFK8MV7EGUkuYmSuaciySZg4z3mcXBYtWsQjjzzC\nypUrXc22V199ddQD6LGxsTzwwANuz2dlZZGVleV6vHTpUpYuXTrgmISEBB5++OFR3X/Uelsu+kyz\nlN0XI6t3rs6fFNw4hBhjHieX1atX8+qrr/L888/T1NSExWJh8eLFrFy5cizjC33mOGNfDmm5CE/U\n10CCBTUhItiRCDGmhk0u+/fvH/B43rx5zJs3b8C024MHDzJ//vyxizDEqbAwI8GckbUuYmS67jSk\nXsDbVIgLxrDJ5ac//emgzzsTizPJPPXUU/6PbDyJS0BLy0WMQGsN1ZWoBVcFOxQhxtywyeXpp58O\nVBzjW1yCdIuJkdnOQLsN0jKDHYkQYy6AFR7PX1ICRnikuhIAlSbdYuL8J8nFH/qVgBFiKLrGSC7S\nchEXAkku/hCXAN3dsq+LGF5NJUyIAEtKsCMRYsxJcvGH2N5V+jLuIoaha6ogNR0VyP2GhAgS+S33\nAykBIzxSU4mSLjFxgZDk4g9SAkaMQJ89Cw11Mt4iLhiSXPyhXwkYIQZVVw3aATJTTFwgJLn4g5SA\nESOpcU5DlpaLuDBIcvEDKQEjRuKahpwaGnv+CDHWJLn4i5SAEcOpqQRLMioqOtiRCBEQklz8RUrA\niGEY05BlvEVcOCS5+ImS5CKGoLWWacjigiPJxV/iE+FMk5SAEe5arNDZAZMluYgLhyQXf5ESMGIo\nNVWAzBQTFxZJLv4iJWDEEPpmismYi7hwSHLxEykBI4ZUUwWRUZCYFOxIhAgYSS7+IiVgxBB0dSWk\nZbp2cBXiQiDJxV+kBIwAdHub++9AbRVKusTEBUaSi79ICRgBOH7xJI4frkVXHAFAd3VBYx1MluQi\nLiySXPxESsCMDcdvn8fx0tPBDsMjuqcHPtkHHe04tjyIrjwOtTJTTFyYwoMdgM1mY8uWLdTX15OS\nksLdd9+N2Wx2O27nzp1s27YNgOXLl7NkyZIBrz/yyCPU1dWxefPmQIQ9uAuwBIzjL6+CSWH63PIx\nub7+6H0YL5trnTgKXR2oFV9Hv/EnHD95ALXk88ZrklzEBSbo/2uLiorIycnhiSeeICcnh6KiIrdj\nbDYbW7duZePGjWzcuJGtW7dis9lcr7/33ntERUUFMuzBXYCr9PXuYnTJ22Nz7bPdUF8LZ1rG5Pr+\npj8tA0BdeR2mf11vPPfHV4zu0kmTgxmaEAEX9ORSUlJCQUEBAAUFBZSUlLgdU1paSm5uLmazGbPZ\nTG5uLqWlpQB0dnbypz/9iRUrVgQ07sFcaCVgtMNufPi320Y+2Be1VcYeKO02o8spxOmDH8GUGajY\nOFRaJqZ71sPEWEhORUVEBjs8IQIq6N1iLS0tJCYa03gTEhJoaXH/K9VqtZKU1LdGwGKxYLVaAXjl\nlVf48pe/TERExIj3Ki4upri4GIBNmzaRnJzsU8zh4eGDntualk77vndJSkoK6rTToeLzN3tdNQ32\nHlR7m1f38zS+zk/34fxtsESEE2YZ+/cEvn3/dFcXdccOEfOFFcQ6z01OpufR59HtbUzw488jUD9f\nX0l8oxPq8XkqIMll/fr1NDe7/0W/atWqAY+VUl59KFdUVFBbW8uaNWuoq6sb8fjCwkIKCwtdjxsa\nGjy+V3/JycmDnuuYEAndXTRUnUJFxfh0bX8YKj5/04cOGP+2tVJfW2tMavCAp/E5Dh9wfW09cRzl\n8C1Ob/ny/dOflsHZbjqnzaar/7kToiA+Cvz48wjUz9dXEt/ohHp86eme7UkUkORy//33D/lafHw8\nTU1NJCYm0tTURFxcnNsxFouFAwf6fdBYrWRnZ3P48GGOHTvGHXfcgd1up6WlhYceeoiHHnpoLN7G\nyPqXgAlicgkUXV/d96C9DWLdf3ajun71qb4HrZ51N+ruLtAaFRnYMTj9aRmEhcHs7IDeV4hQFfQx\nl/z8fHbt2gXArl27WLBggdsxeXl5lJWVYbPZsNlslJWVkZeXx/XXX89zzz3H008/zX/+53+Snp4e\nvMTC+VkCRjvsaMcQTYa6fsmlrdX/Nz99yrXnvPZwUF+/9DSOJ9f7P5aR7nvwI5g+O6gtViFCSdCT\ny7Jly/joo4+46667+Pjjj1m2bBkA5eXlPPvsswCYzWZWrFjBunXrWLduHStXrhx0unLQnYclYBzP\nPIz+n8Gnd+sxTC66pwfqTqPm5BhP2DxMLrWnofzTgE4A0O1tUHEUNfeSgN1TiFAX9AH92NhYHnjg\nAbfns7KyyMrKcj1eunQpS5cuHfI6kyZNCu4aFxhQAuZ8qCKlzzTDRx+g4+IHP6C+BmLjobXF/y2X\n+hqw2yHrYnhnu+fTkdtaoacHqk/BlBn+jWkoh/eDdqAuluQihFPQWy7nlfOsBIwufdeYCtzS5LY4\nVGttdIvNmGM8bvNtOrLjnWIcO//P/YXqkwCojKlg7k1gnuiNQ5846lM8vtAHP4KICJh5UcDuKUSo\nk+TiR+dbCRi9d0/f6vjK4wNfbGmC7i7UjNnGYx9bLnr7H9CvvWysmen//Onewfy0TIiNQ3uQXLTD\n3rfm5mS5T/H4Qh/8CGZloyZMCNg9hQh1klz8LTkVffAjY3X5OKbbbHDwI9QioytSV1YMPKC+BgA1\nbZbRWvMhuWi73Vgo2W6DinNaGtWVkDTJmPUV62HLpb0NereZ1iePeR2PL/SZJqg6gbo4NyD3E2K8\nkOTiZ6Zlt0BdNfpPvwt2KKOiPyoBux1VcAMkWOBUxcDXnYP5qekQY/at5dJYa4yPAHr/3oHXrz4J\nk6cAoGITPEsuzq652Hg4dcxIXmNMH/wYQMZbhDhH0Af0zzcq+1LUoqXo119FL7gKlTk92CH5RO/d\nDYnJMG0WZE53b7nUVRtdZpZJMNHc98Hujere7X8jo9EH9sE/fNW4t8MONVV9s69i4zwb0LedAUDN\nvQT9/lvGDpAZU72Paxi69D0c7xRDRzt0dhjl9KMnwrSZfr2PEOOdtFzGgLrpVogx4/jlU25jCeOB\n7uyAT/ahLluEMplQmTOg+hS652zfQfXVRrdVeDhMjEX70i3Wu0hSXXktHDvcNymgsR7OdvdVEo6N\nh64OY4HkcJwxZOcZ1x+DQX3HX1+FQ/uNmWyx8ai5l6D+6TaUybPqBEJcKCS5jAFljkOt+hYcP4ze\n8edgh+O9/R/C2W7UpYuMx5nTwd5jtAR66bpqSOmt9DvRDDYfusWqKyE+EbXgKmNW2qdGMVJ6B/NV\nem+rw7k4tfXMsJdzJic182KIiPT7oL52OKDyBGrhEsLu3UTYvzyI6f/9G6Yrr/XrfYQ4H0hyGSNq\nwWchJx9d9DK6ceS6Z6FE791jtBZmzwUwWi5gbH7lVF+N6i0jrybG+lQZWdcYe8sz4yKInugad9G9\n05CZbLRcVGzvOpuRSsC09SafuHiYMgPt7xljjXXQ1WEkWyHEsCS5jBGlFKZbvgOAfvUXQY7Gc/ps\nN/qjD1B5V/R19aRlQHg49I676LZWY2ZWSprx+sRYrwf0tdZQXYmaPMWYwj33EvQn+1zPE29BxfRW\nYXAllxHGXdpsxsy16BhjFtvJ40OXrvFF7/tXgVqcKcQ4JsllDKmkFNTVn0Pv3TN+dqg8UGrspnjZ\nYtdTKiwM0qeinTPGemeKOVsuTDRDe5t3s7NamqCjzTWuouZfBs2NcPqkMRaTPqXv2N7kMuJaF1sr\nxJiNpDg1y2hl1J32PKYR6FPHjeSV7t9JAkKcjyS5jDF11XVg70G/+2awQ/GI3rvHmP10cc6A51Xm\nDKiqMI5xTkN2jbn0VkNub/P8Rs7BfGfX17xLjWvv3wvVpwbuOR/nacul1Uh0gOqdvaVP+K9rTFdV\nwKT0gFdcFmI8kuQyxlT6VMi6GP12sdHlE+L0sYNwUQ4q/JzV5lOm95WBcZbaT0k1/u39QPema0w7\nJwc417JYUmDyFPQ7xcYU3/4tl8homBAx4nRk3dZqdNEBTJ5qnOPPcZdTxyFzmv+uJ8R5TJJLAKgr\nC42/1I8dCnYow9I9PVBfg+r/wd5LZUw3vqg8bnSLJSa7tu5Vzg90b8Zdqk9BVLSxQNN5j3mX9WvR\n9HU9KaWMtS6edIuZjVaUCgsz1uf4qeWiOzuM740M5gvhEUkuAaAWXAWRUei//y3YoQzPWYm4f5eU\nk2vGWEXvNOS0vtd8arkYM8X67zyq5l/Wd8Dkc2KITRh5zKWtFTWxbysGNS0LTh7zT4ux6oRxzUwZ\nzBfCE5JcAkBFxaAWfBb9wdvozvZghzO0c8ZB+lOxcX1lYOpr+gbzAcxGy8WrysjVp9zvMzvb6Moy\nx/bNEHPypL5Y/24xMAb1O9pcddBGw1WhQFouQnhEkkuAqKuug65OdMnbwQ5lSLqmtxxL7+6PbjJn\noMs/NbYUGNBy8a5bzNFmg2ara7zFSUVEovKugFnzBrRooHetyzDrXHTPWWOsxtyXXNTU3v2AvBh3\n0R++Q/v/bXV/ofI4RMdA0iSPryXEhUySS6DMvMgYsH57e7AjGVpNJSQkDblVr8qc3lcNuX/LJTrG\nq8rI9qrevVoGayHddg+m79znflJsPLSeGbqLy7mIs3/LJWMqhIV7Ne7i+Os2Wl98ythdsh9dWQEZ\n092SnhBicJJcAkQpZbRejh1Cnz4Z7HAGpasr3cc6+uvfJdQvuShTmFeVkXucXUyDjO0oUxjKNMiv\nZVy8UW+sq2PwizrLz/RLLip8AmRMQ3/8gef7wZw+AWe70R++0/e81lBZgZoyfcRrCCEMklwCSC26\nxvhL+p3iYIfiRmsNNZUD15ecY8DK9JTJA1/0ojJyT2UFhIW7X2M4zjGYoaYj9yYX1a9bDEBdvwxq\nq3A8+F106XvD36OuGrqNfXj0e7v6nm+oNbrcZLxFCI9JcgkgFRsPM+egQ3FKcovV+AAdruWSmgHh\nE4xqwNHndJ15URnZXlkBkyYb04U9pGKdxSuHSC7t7i0XANMVBZh+uAUSLDie3oDjxSfQHUNMquht\nUUVeUQCHPkY31hvP9y4elZliQnhOkkuAqUmT/TJ7ye9691YZtuXSu3aE1HT3F72ojNxTddJtMH9E\nsb1VAIZILnqQbjEnlTEN03/8GPWFm9C7d+B49pHBr3GqAkwmzLd823j8/q6+55WCDFlAKYSnZLOw\nQEuZbKx07+oMqTIirpliw7VcANM3/sX4oD2HmhiLrh25jpfuOYujpgqVt9C7AHtbLrq1hUGH1J1d\ncmb35ALG+Iu6cTUO+1l08R/R3V2uRaCu2KoqIC2T8CnTjaoKe95E37DCGMxPmRxSPy8hQp20XALN\nOYU31Fov1ZXGivl4y7CHqfSpqMFaHZ5WRq6tBod9xCTmxtlyGaoAaNsZCAszSsUMQ82eZ+xNUzHI\nRmKnjrtW4KuF1xjrfk4dM6Yhy3iLEF6R5BJgrim8IZZcdE0lTJ7i+1RbTysj1zgXanrXLaYiIo3k\nZxtiwzCbsYByxPhnXgxgrNfpR7fbwFrvqkSg8q80Jl/s+quxaFRmignhlaB3i9lsNrZs2UJ9fT0p\nKSncfffdmM1mt+N27tzJtm3bAFi+fDlLliwB4KGHHqKpqYmIiAgAfvjDHxIfH+92fsjonSGl66sH\n794JlupK1Nxc38/vXxnZ2coYhK4eYaHmcGLjh5wtpttsg463nEvFxkFaBvrowOTi2qvF2XIxx0HO\n5ca6JK2lppgQXgp6cikqKiInJ4dly5ZRVFREUVERq1evHnCMzWZj69atbNq0CYD77ruP/Px8VxK6\n6667yMrKCnjsvlATzcaakBBquejOdmMvlWEG80fUv77YMMmF6kpMKam+jV/ExqOHWqV/bumXYais\nuejS99AOh2tNzWDlXUwLr8HhnL4sM8WE8ErQu8VKSkooKCgAoKCggJKSErdjSktLyc3NxWw2Yzab\nyc3NpbS0NNCh+k9KGroudJIL1Ub5e2+7qvrzpDKy1hp99BMmzJjj202Gqy9mOzPkYL6bWXONOGur\n+p6rrDDO71elmdx8Y28bKfsihNeC3nJpaWkhMTERgISEBFpa3D88rFYrSUlJrscWiwWr1ep6/Mwz\nz2AymbjiiitYsWLFkP3uxcXFFBcbCxg3bdpEcnKyTzGHh4f7fC5A85Rp9Bw96NE1zvz0EUzxFsw3\nf2vM4uvYX8IZIHHufMJ9fF9nMzKxAnFhisghrnH26KdYrQ1EL7pmyGOGcyYlla6TxwZ9b/Wd7UQk\npRDvwXV7Fiym8RdPYq6tJDrH2KSssaYSNX02lpSUAd+/thVfw9HSRGxKitfxjpXR/v6NNYlvdEI9\nPk8FJLmsX7+e5mb37oxVq1YNeKyU8npA+a677sJisdDR0cHmzZt56623XC2hcxUWFlJYWOh63NDQ\n4NW9nJKTk30+F8ARZ0HX11BfWzvsQkKtNY6/b4ekSXRef+OYxec4chDCwmgKj0L5+L50jzGQ31J9\nGtMQ13C8+VcwmZhw2SKfvn+OCZHoM03U19W5lYhxnGmhK2yCR9fVETFgjqW19H3a8hahHXYcJ46i\nrr6BhoaGgd+/gi8A0DWKn7e/jfb3b6xJfKMT6vGlpw+yzm0QAUku999//5CvxcfH09TURGJiIk1N\nTcTFuffXWywWDhw44HpstVrJzs52vQYQHR3NVVddxdGjR4dMLiEjJc3YN8VaP7C68LkaaqGjHWpP\nox12o4bXGNDVp4x1HOGj+HXwpFts7x6YMx9TXDz48p8nLt74vnW0DRhf0d1dRt0xD7vFlFKQNRd9\n9KDxRF2NUfZFBu2F8Jugj7nk5+eza5exEnrXrl0sWLDA7Zi8vDzKysqw2WzYbDbKysrIy8vDbrdz\n5owxNbWnp4cPP/yQKVN8HzcIFOWsqeXcLngozkHms93gLEUyFmqqRjeYDyNWRtbVlUbtsku9XDzZ\n31AlYFyr891nGQ5FZc2F2iqjoGXlceM5GbQXwm+CPuaybNkytmzZwo4dO1xTkQHKy8vZvn07a9eu\nxWw2s2LFCtatWwfAypUrMZvNdHZ2smHDBux2Ow6Hg5ycnAHdXiGrt7Wi62pQ2UMfpk8d73tQWzVo\nK8fxh19DdAym65f5FIru6YG6alTeZ3w632mkysh63x7jOG9X5ve/R2wcGozpyP2TYe891cRhZqmd\ne61Zc41rlX9qzBQzmWCQ7Z2FEL4JenKJjY3lgQcecHs+KytrwPTipUuXsnTp0gHHREVF8cgjg9eJ\nCmkJFqMA5AjTkXXlcdcMKV1TiZp/+cDXtUbv/D+IiEBf9xXfFkA21Bgr1tP88ME6TGVkvXcPzJiD\nsoxioHKoloszoXk6Wwxg+iwID0cf/RRdUwWpGagJEb7HJoQYIOjdYhciZTIZ05E96RabM88YX6iu\ncn+9xWpMwbU2+L5uprem2GAbd3ltiMrI2loPJ46OrksMXGX33da6tPnQLTYhAqbNQpcfNPZqkfEW\nIfxKkkuwpKQNmxB0R7tRdiRzhrGivHaQ5HKqou/4Qx/7FIZ2Jq1UH1bMn2ti7KCVkfU+YyGiunTR\n6K5vdlZGHlgCpq8isufdYgAq62I4fgQa62CKjLcI4U+SXIJE9SaXIbftde4hMmUGKi3D1cLoT/cO\nRBMzEXxMLlSfggQLKmaib+f3oyaa+7Yb7kfv22PULfOl5Ev/64eHG+M6fmi5QO+gvr3H+FpaLkL4\nlSSXYEmZDF2d7h+UvbSzVZI5wxi8bmly29edU8chaRJq3mXoQx8PnaiGoU+fHP1MMadBKiPr1jNw\n+BPUZaNstTjFDVJfrK0VIiLcSuiPaNbFfV/LTDEh/EqSS5CoSb0zv4YqA1N53GiRWJL7NvA6p2tM\nV1YYazPmzIdmq7FNrxd0z1moqkBN81NdtkEqI+uP3gftGH2XmNNg9cXaWr3uEgNQcYkwabKRFBOG\n32pACOEdSS7B4pyOPMS4iz51HDJnGDPAeruTXBWF6V04WFNldJtdnGM8d+gj72KoOgE9PTBttg9v\nYBD9KyM74/zgHaMu19SZfrmFSp8KJ44ZidF5D5vnRSvdrrf0S6gln/d9qwEhxKAkuQRLUqqx6HCQ\nGWPaYYeqEyjnIHNymrERVv+Wy+mTRos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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x122975940>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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mfxyPX1Qba74n5pA9/T546Sm8h43Co3k4RvOWmNlZnE1NwqNFBEGP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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1278b4d30>"
+       "<matplotlib.figure.Figure at 0x122975cf8>"
       ]
      },
      "metadata": {},
@@ -673,9 +1234,9 @@
     },
     {
      "data": {
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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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NN98kNjYWgLi4OHr06ME777xDjx49iIuLq/onEMJN6L0/gjZQPfpdeWch3JSl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\nFAoiImL6AwJDfc3HpVBYAAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x127a02390>"
+       "<matplotlib.figure.Figure at 0x122d96f98>"
       ]
      },
      "metadata": {},
@@ -684,15 +1245,14 @@
    ],
    "source": [
     "util.plot_curve(loss_list, \"loss\")\n",
-    "util.plot_curve(avg_return_list, \"average return\")"
+    "util.plot_curve(avg_return_list, \"average return\")\n",
+    "util.plot_curve(avg_advantage_variance_list, \"average advantage variance\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": []
   }
diff --git a/report.md b/report.md
index 1e5017e..63f16e3 100644
--- a/report.md
+++ b/report.md
@@ -1,3 +1,52 @@
-# Homework3-Policy-Gradient report
+# CEDL2017 HW3 Report
 
-TA: try to elaborate the algorithms that you implemented and any details worth mentioned.
+## Problem 1
+In problem 1, I use `tf.contrib.layers` to construct my 2-layer neural network, nothing special here.
+```python
+h1 = tf.contrib.layers.fully_connected(self._observations, num_outputs=hidden_dim, activation_fn=tf.tanh)
+h2 = tf.contrib.layers.fully_connected(h1, num_outputs=out_dim, activation_fn=None)
+probs = tf.nn.softmax(h2)
+```
+
+## Problem 2
+Here we calculate the surrogate loss:
+```python
+# 1. self._advantages is a vector containing Ri for all timestep.
+# 2. log_prob is a vector containing log(pi(a|s)) for all timestep.  
+# 3. Element-wise product of Ri and log_prob.
+# 4. Sum over time, divide by T to get surrogate loss.
+neg_log_prob = -log_prob # Minimizing negative log-likelihood is same as maximizing log-likelihood.
+surr_loss = tf.reduce_mean(neg_log_prob*self._advantages)
+```
+Note that the optimizer in TensorFlow minimizes loss, thus we simply maximizes the log-likelihood by adding negative sign, which is equivalent.
+
+## Problem 3
+In problem 3, we need to modify the reward to **advantage**, which is just reward subtracted by baseline:
+```python
+a = r - b
+```
+
+| Loss | Average Return | Average Advantage Variance |
+| ---- | ------ | -------- |
+|![](https://i.imgur.com/CI5SzP1.png) | ![](https://i.imgur.com/ecYw6FZ.png) | ![](https://i.imgur.com/3K5Hlp8.png)
+
+## Problem 4
+We found that after removing the baseline, the average advantage variance explodes, but the average return still can exceed 195 within about 80 iterations. The reason why the baseline won't introduce the bias can be proved as follows:
+
+| Loss | Average Return | Average Advantage Variance |
+| ---- | ------ | -------- |
+| ![](https://i.imgur.com/oRClDgo.png) |![](https://i.imgur.com/TVwJWpp.png) |![](https://i.imgur.com/ZVIds7Y.png)
+
+## Problem 5
+In problem 5, we modify the advantage from the original version to actor-critic algorithm whose advantage function is one-step bootstrap. But the return cannot achieve to 195 within 200 iterations, may need more iterations to learn. Moreover, as shown in the following figure, the loss is very unstable.
+
+| Loss | Average Return | Average Advantage Variance |
+| ---- | ------ | -------- |
+| ![](https://i.imgur.com/BYYoKv9.png) | ![](https://i.imgur.com/oZ2AaGT.png) | ![](https://i.imgur.com/yRGRWIY.png)
+
+## Problem 6
+In problem 6, we further modify the one-step bootstrap to the form of Generative Advantage Estimation (GAE). After this modification, the agent can achieve to 195 within about 80 iterations, but the average advantage variance is higher than the one in problem 3.
+
+| Loss | Average Return | Average Advantage Variance |
+| ---- | ------ | -------- |
+| ![](https://i.imgur.com/rFjgB4E.png) | ![](https://i.imgur.com/O0FqYC9.png) | ![](https://i.imgur.com/uFMMSvU.png)