diff --git a/Lab3-policy-gradient.ipynb b/Lab3-policy-gradient.ipynb
index 4529e50..e2870b5 100644
--- a/Lab3-policy-gradient.ipynb
+++ b/Lab3-policy-gradient.ipynb
@@ -28,14 +28,14 @@
   },
   {
    "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"
+      "[2017-11-09 21:06:04,796] Making new env: CartPole-v0\n"
      ]
     }
    ],
@@ -103,14 +103,14 @@
   },
   {
    "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",
+      "/data/VSLab/cindy/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",
       "  \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
      ]
     }
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "collapsed": true
    },
@@ -214,6 +214,7 @@
     "            Sample solution should be only 1 line.\n",
     "            \"\"\"\n",
     "            # YOUR CODE HERE >>>>>>\n",
+    "            a = r - b\n",
     "            # <<<<<<<<\n",
     "\n",
     "            p[\"returns\"] = r\n",
@@ -258,98 +259,101 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 36,
    "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 = 23.85\n",
+      "Iteration 2: Average Return = 23.57\n",
+      "Iteration 3: Average Return = 26.73\n",
+      "Iteration 4: Average Return = 23.72\n",
+      "Iteration 5: Average Return = 29.51\n",
+      "Iteration 6: Average Return = 29.11\n",
+      "Iteration 7: Average Return = 33.62\n",
+      "Iteration 8: Average Return = 33.97\n",
+      "Iteration 9: Average Return = 36.23\n",
+      "Iteration 10: Average Return = 38.44\n",
+      "Iteration 11: Average Return = 39.96\n",
+      "Iteration 12: Average Return = 39.45\n",
+      "Iteration 13: Average Return = 42.85\n",
+      "Iteration 14: Average Return = 43.61\n",
+      "Iteration 15: Average Return = 45.27\n",
+      "Iteration 16: Average Return = 43.89\n",
+      "Iteration 17: Average Return = 42.31\n",
+      "Iteration 18: Average Return = 43.78\n",
+      "Iteration 19: Average Return = 48.6\n",
+      "Iteration 20: Average Return = 46.76\n",
+      "Iteration 21: Average Return = 50.42\n",
+      "Iteration 22: Average Return = 52.99\n",
+      "Iteration 23: Average Return = 50.61\n",
+      "Iteration 24: Average Return = 51.63\n",
+      "Iteration 25: Average Return = 50.24\n",
+      "Iteration 26: Average Return = 54.49\n",
+      "Iteration 27: Average Return = 51.36\n",
+      "Iteration 28: Average Return = 55.87\n",
+      "Iteration 29: Average Return = 52.58\n",
+      "Iteration 30: Average Return = 55.4\n",
+      "Iteration 31: Average Return = 59.45\n",
+      "Iteration 32: Average Return = 59.11\n",
+      "Iteration 33: Average Return = 58.57\n",
+      "Iteration 34: Average Return = 59.13\n",
+      "Iteration 35: Average Return = 60.21\n",
+      "Iteration 36: Average Return = 60.96\n",
+      "Iteration 37: Average Return = 64.74\n",
+      "Iteration 38: Average Return = 64.05\n",
+      "Iteration 39: Average Return = 60.94\n",
+      "Iteration 40: Average Return = 64.21\n",
+      "Iteration 41: Average Return = 62.26\n",
+      "Iteration 42: Average Return = 62.89\n",
+      "Iteration 43: Average Return = 68.1\n",
+      "Iteration 44: Average Return = 68.12\n",
+      "Iteration 45: Average Return = 63.39\n",
+      "Iteration 46: Average Return = 67.38\n",
+      "Iteration 47: Average Return = 70.87\n",
+      "Iteration 48: Average Return = 72.09\n",
+      "Iteration 49: Average Return = 73.45\n",
+      "Iteration 50: Average Return = 77.83\n",
+      "Iteration 51: Average Return = 82.17\n",
+      "Iteration 52: Average Return = 82.36\n",
+      "Iteration 53: Average Return = 93.19\n",
+      "Iteration 54: Average Return = 96.17\n",
+      "Iteration 55: Average Return = 92.18\n",
+      "Iteration 56: Average Return = 102.75\n",
+      "Iteration 57: Average Return = 108.82\n",
+      "Iteration 58: Average Return = 116.45\n",
+      "Iteration 59: Average Return = 122.99\n",
+      "Iteration 60: Average Return = 129.69\n",
+      "Iteration 61: Average Return = 125.34\n",
+      "Iteration 62: Average Return = 129.97\n",
+      "Iteration 63: Average Return = 127.21\n",
+      "Iteration 64: Average Return = 128.79\n",
+      "Iteration 65: Average Return = 131.9\n",
+      "Iteration 66: Average Return = 138.26\n",
+      "Iteration 67: Average Return = 142.85\n",
+      "Iteration 68: Average Return = 134.08\n",
+      "Iteration 69: Average Return = 144.27\n",
+      "Iteration 70: Average Return = 158.98\n",
+      "Iteration 71: Average Return = 154.36\n",
+      "Iteration 72: Average Return = 166.53\n",
+      "Iteration 73: Average Return = 159.18\n",
+      "Iteration 74: Average Return = 172.68\n",
+      "Iteration 75: Average Return = 173.62\n",
+      "Iteration 76: Average Return = 172.15\n",
+      "Iteration 77: Average Return = 189.19\n",
+      "Iteration 78: Average Return = 188.13\n",
+      "Iteration 79: Average Return = 186.94\n",
+      "Iteration 80: Average Return = 187.69\n",
+      "Iteration 81: Average Return = 189.64\n",
+      "Iteration 82: Average Return = 194.26\n",
+      "Iteration 83: Average Return = 193.36\n",
+      "Iteration 84: Average Return = 194.6\n",
+      "Iteration 85: Average Return = 194.76\n",
+      "Iteration 86: Average Return = 193.97\n",
+      "Iteration 87: Average Return = 197.55\n",
+      "Solve at 87 iterations, which equals 8700 episodes.\n"
      ]
     }
    ],
@@ -361,6 +365,7 @@
     "path_length = 200\n",
     "discount_rate = 0.99\n",
     "baseline = LinearFeatureBaseline(env.spec)\n",
+    "#baseline = None\n",
     "\n",
     "po = PolicyOptimizer(env, policy, baseline, n_iter, n_episode, path_length,\n",
     "                     discount_rate)\n",
@@ -371,14 +376,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
      "data": {
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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w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\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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9HmAwgO/pBDt9Xv77cvUB1kaw2lpt26eOOu7vEXkY6WLP7E6R6M4ge8JDAeCj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\n3Ch5LgRRdjQ0AoNhIaw6EKZikzKCjEuZwyZOBZs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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107bac18>"
+       "<matplotlib.figure.Figure at 0x7fca746e8b70>"
       ]
      },
      "metadata": {},
@@ -386,9 +391,9 @@
     },
     {
      "data": {
-      "image/png": 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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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qRv+0E9p1QjWQ7Y5F1dn0ZPHLL78wd+5c3NzcOHv2LP369SM5OZnExETrEh1C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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107ba828>"
+       "<matplotlib.figure.Figure at 0x7fca746e8cf8>"
       ]
      },
      "metadata": {},
@@ -453,6 +458,315 @@
     "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "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",
+    "\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",
+    "\n",
+    "        return dict(\n",
+    "            observations=obs,\n",
+    "            actions=actions,\n",
+    "            rewards=rewards,\n",
+    "            advantages=advantages,\n",
+    "        )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 22.94\n",
+      "Iteration 2: Average Return = 23.9\n",
+      "Iteration 3: Average Return = 26.62\n",
+      "Iteration 4: Average Return = 26.77\n",
+      "Iteration 5: Average Return = 28.61\n",
+      "Iteration 6: Average Return = 29.24\n",
+      "Iteration 7: Average Return = 29.39\n",
+      "Iteration 8: Average Return = 34.7\n",
+      "Iteration 9: Average Return = 37.46\n",
+      "Iteration 10: Average Return = 41.37\n",
+      "Iteration 11: Average Return = 43.73\n",
+      "Iteration 12: Average Return = 41.94\n",
+      "Iteration 13: Average Return = 47.76\n",
+      "Iteration 14: Average Return = 49.99\n",
+      "Iteration 15: Average Return = 44.16\n",
+      "Iteration 16: Average Return = 48.46\n",
+      "Iteration 17: Average Return = 52.53\n",
+      "Iteration 18: Average Return = 50.79\n",
+      "Iteration 19: Average Return = 56.56\n",
+      "Iteration 20: Average Return = 54.66\n",
+      "Iteration 21: Average Return = 65.03\n",
+      "Iteration 22: Average Return = 59.23\n",
+      "Iteration 23: Average Return = 65.73\n",
+      "Iteration 24: Average Return = 70.38\n",
+      "Iteration 25: Average Return = 66.4\n",
+      "Iteration 26: Average Return = 65.68\n",
+      "Iteration 27: Average Return = 71.83\n",
+      "Iteration 28: Average Return = 79.67\n",
+      "Iteration 29: Average Return = 78.99\n",
+      "Iteration 30: Average Return = 78.95\n",
+      "Iteration 31: Average Return = 86.47\n",
+      "Iteration 32: Average Return = 81.24\n",
+      "Iteration 33: Average Return = 84.15\n",
+      "Iteration 34: Average Return = 94.35\n",
+      "Iteration 35: Average Return = 98.22\n",
+      "Iteration 36: Average Return = 94.28\n",
+      "Iteration 37: Average Return = 93.68\n",
+      "Iteration 38: Average Return = 105.48\n",
+      "Iteration 39: Average Return = 104.71\n",
+      "Iteration 40: Average Return = 105.42\n",
+      "Iteration 41: Average Return = 107.04\n",
+      "Iteration 42: Average Return = 116.34\n",
+      "Iteration 43: Average Return = 114.66\n",
+      "Iteration 44: Average Return = 118.14\n",
+      "Iteration 45: Average Return = 115.36\n",
+      "Iteration 46: Average Return = 117.33\n",
+      "Iteration 47: Average Return = 114.32\n",
+      "Iteration 48: Average Return = 108.95\n",
+      "Iteration 49: Average Return = 115.65\n",
+      "Iteration 50: Average Return = 122.03\n",
+      "Iteration 51: Average Return = 114.99\n",
+      "Iteration 52: Average Return = 119.97\n",
+      "Iteration 53: Average Return = 128.22\n",
+      "Iteration 54: Average Return = 126.47\n",
+      "Iteration 55: Average Return = 130.88\n",
+      "Iteration 56: Average Return = 128.5\n",
+      "Iteration 57: Average Return = 121.95\n",
+      "Iteration 58: Average Return = 126.64\n",
+      "Iteration 59: Average Return = 124.77\n",
+      "Iteration 60: Average Return = 137.17\n",
+      "Iteration 61: Average Return = 137.53\n",
+      "Iteration 62: Average Return = 140.29\n",
+      "Iteration 63: Average Return = 145.03\n",
+      "Iteration 64: Average Return = 139.62\n",
+      "Iteration 65: Average Return = 138.46\n",
+      "Iteration 66: Average Return = 146.39\n",
+      "Iteration 67: Average Return = 138.62\n",
+      "Iteration 68: Average Return = 133.26\n",
+      "Iteration 69: Average Return = 136.21\n",
+      "Iteration 70: Average Return = 144.76\n",
+      "Iteration 71: Average Return = 145.95\n",
+      "Iteration 72: Average Return = 154.51\n",
+      "Iteration 73: Average Return = 150.25\n",
+      "Iteration 74: Average Return = 148.1\n",
+      "Iteration 75: Average Return = 150.94\n",
+      "Iteration 76: Average Return = 136.67\n",
+      "Iteration 77: Average Return = 142.4\n",
+      "Iteration 78: Average Return = 140.58\n",
+      "Iteration 79: Average Return = 139.84\n",
+      "Iteration 80: Average Return = 147.7\n",
+      "Iteration 81: Average Return = 152.02\n",
+      "Iteration 82: Average Return = 153.34\n",
+      "Iteration 83: Average Return = 162.21\n",
+      "Iteration 84: Average Return = 158.12\n",
+      "Iteration 85: Average Return = 148.66\n",
+      "Iteration 86: Average Return = 152.34\n",
+      "Iteration 87: Average Return = 148.23\n",
+      "Iteration 88: Average Return = 142.87\n",
+      "Iteration 89: Average Return = 145.72\n",
+      "Iteration 90: Average Return = 151.07\n",
+      "Iteration 91: Average Return = 158.23\n",
+      "Iteration 92: Average Return = 162.57\n",
+      "Iteration 93: Average Return = 160.04\n",
+      "Iteration 94: Average Return = 169.14\n",
+      "Iteration 95: Average Return = 167.32\n",
+      "Iteration 96: Average Return = 164.28\n",
+      "Iteration 97: Average Return = 153.93\n",
+      "Iteration 98: Average Return = 158.54\n",
+      "Iteration 99: Average Return = 144.05\n",
+      "Iteration 100: Average Return = 135.54\n",
+      "Iteration 101: Average Return = 138.51\n",
+      "Iteration 102: Average Return = 148.48\n",
+      "Iteration 103: Average Return = 140.53\n",
+      "Iteration 104: Average Return = 139.38\n",
+      "Iteration 105: Average Return = 135.05\n",
+      "Iteration 106: Average Return = 143.64\n",
+      "Iteration 107: Average Return = 138.43\n",
+      "Iteration 108: Average Return = 152.02\n",
+      "Iteration 109: Average Return = 144.2\n",
+      "Iteration 110: Average Return = 158.02\n",
+      "Iteration 111: Average Return = 159.88\n",
+      "Iteration 112: Average Return = 163.54\n",
+      "Iteration 113: Average Return = 168.14\n",
+      "Iteration 114: Average Return = 171.32\n",
+      "Iteration 115: Average Return = 178.71\n",
+      "Iteration 116: Average Return = 178.04\n",
+      "Iteration 117: Average Return = 180.24\n",
+      "Iteration 118: Average Return = 182.85\n",
+      "Iteration 119: Average Return = 182.12\n",
+      "Iteration 120: Average Return = 186.04\n",
+      "Iteration 121: Average Return = 185.63\n",
+      "Iteration 122: Average Return = 182.71\n",
+      "Iteration 123: Average Return = 176.87\n",
+      "Iteration 124: Average Return = 171.52\n",
+      "Iteration 125: Average Return = 169.93\n",
+      "Iteration 126: Average Return = 158.71\n",
+      "Iteration 127: Average Return = 156.51\n",
+      "Iteration 128: Average Return = 153.18\n",
+      "Iteration 129: Average Return = 155.3\n",
+      "Iteration 130: Average Return = 146.95\n",
+      "Iteration 131: Average Return = 148.82\n",
+      "Iteration 132: Average Return = 152.21\n",
+      "Iteration 133: Average Return = 149.03\n",
+      "Iteration 134: Average Return = 150.53\n",
+      "Iteration 135: Average Return = 154.33\n",
+      "Iteration 136: Average Return = 154.49\n",
+      "Iteration 137: Average Return = 153.89\n",
+      "Iteration 138: Average Return = 150.47\n",
+      "Iteration 139: Average Return = 160.86\n",
+      "Iteration 140: Average Return = 163.6\n",
+      "Iteration 141: Average Return = 166.85\n",
+      "Iteration 142: Average Return = 175.23\n",
+      "Iteration 143: Average Return = 178.09\n",
+      "Iteration 144: Average Return = 180.45\n",
+      "Iteration 145: Average Return = 185.31\n",
+      "Iteration 146: Average Return = 188.67\n",
+      "Iteration 147: Average Return = 182.87\n",
+      "Iteration 148: Average Return = 188.51\n",
+      "Iteration 149: Average Return = 188.94\n",
+      "Iteration 150: Average Return = 189.6\n",
+      "Iteration 151: Average Return = 186.93\n",
+      "Iteration 152: Average Return = 184.95\n",
+      "Iteration 153: Average Return = 180.02\n",
+      "Iteration 154: Average Return = 179.71\n",
+      "Iteration 155: Average Return = 177.26\n",
+      "Iteration 156: Average Return = 176.67\n",
+      "Iteration 157: Average Return = 169.96\n",
+      "Iteration 158: Average Return = 165.06\n",
+      "Iteration 159: Average Return = 164.42\n",
+      "Iteration 160: Average Return = 165.6\n",
+      "Iteration 161: Average Return = 159.56\n",
+      "Iteration 162: Average Return = 156.3\n",
+      "Iteration 163: Average Return = 157.01\n",
+      "Iteration 164: Average Return = 157.3\n",
+      "Iteration 165: Average Return = 159.48\n",
+      "Iteration 166: Average Return = 162.55\n",
+      "Iteration 167: Average Return = 156.57\n",
+      "Iteration 168: Average Return = 165.83\n",
+      "Iteration 169: Average Return = 167.71\n",
+      "Iteration 170: Average Return = 165.84\n",
+      "Iteration 171: Average Return = 174.17\n",
+      "Iteration 172: Average Return = 169.89\n",
+      "Iteration 173: Average Return = 168.22\n",
+      "Iteration 174: Average Return = 172.54\n",
+      "Iteration 175: Average Return = 173.42\n",
+      "Iteration 176: Average Return = 175.52\n",
+      "Iteration 177: Average Return = 178.82\n",
+      "Iteration 178: Average Return = 178.88\n",
+      "Iteration 179: Average Return = 179.88\n",
+      "Iteration 180: Average Return = 178.69\n",
+      "Iteration 181: Average Return = 176.84\n",
+      "Iteration 182: Average Return = 176.58\n",
+      "Iteration 183: Average Return = 180.72\n",
+      "Iteration 184: Average Return = 179.4\n",
+      "Iteration 185: Average Return = 184.02\n",
+      "Iteration 186: Average Return = 180.37\n",
+      "Iteration 187: Average Return = 180.69\n",
+      "Iteration 188: Average Return = 177.86\n",
+      "Iteration 189: Average Return = 181.92\n",
+      "Iteration 190: Average Return = 176.18\n",
+      "Iteration 191: Average Return = 176.33\n",
+      "Iteration 192: Average Return = 173.94\n",
+      "Iteration 193: Average Return = 182.09\n",
+      "Iteration 194: Average Return = 181.12\n",
+      "Iteration 195: Average Return = 180.44\n",
+      "Iteration 196: Average Return = 181.09\n",
+      "Iteration 197: Average Return = 181.23\n",
+      "Iteration 198: Average Return = 174.55\n",
+      "Iteration 199: Average Return = 177.6\n",
+      "Iteration 200: Average Return = 180.68\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 = po.train()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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u9OQJSL/6MbD/DTUuxSvnnW7998uVP78Z4DeqHI1rjKZTsuWi6e6cSaty+LqY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\nAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fca987ef400>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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Ej54IZWftVVMAuvbbOZeohlJeXuAfSNXBfaAM1MSb0Ws/t14c4KZZiyN7wOlT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\nAMCIWAAAjIgFAMCIWAAAjL4AiTG+YW5x1ccAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fca7478e9e8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "util.plot_curve(loss_list, \"loss\")\n",
+    "util.plot_curve(avg_return_list, \"average return\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -477,7 +791,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 38,
    "metadata": {
     "collapsed": true
    },
@@ -523,6 +837,7 @@
     "            Sample solution should be only 1 line. (you can use `util.discount` in policy_gradient/util.py)\n",
     "            \"\"\"\n",
     "            # YOUR CODE HERE >>>>>>>>\n",
+    "            a = util.discount(a, self.discount_rate * LAMBDA)\n",
     "            # <<<<<<<\n",
     "            p[\"returns\"] = target_v\n",
     "            p[\"baselines\"] = b\n",
@@ -543,7 +858,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 41,
    "metadata": {
     "scrolled": true
    },
@@ -552,90 +867,84 @@
      "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 = 26.73\n",
+      "Iteration 2: Average Return = 29.58\n",
+      "Iteration 3: Average Return = 30.35\n",
+      "Iteration 4: Average Return = 31.41\n",
+      "Iteration 5: Average Return = 32.59\n",
+      "Iteration 6: Average Return = 34.69\n",
+      "Iteration 7: Average Return = 37.11\n",
+      "Iteration 8: Average Return = 38.33\n",
+      "Iteration 9: Average Return = 37.64\n",
+      "Iteration 10: Average Return = 38.12\n",
+      "Iteration 11: Average Return = 40.68\n",
+      "Iteration 12: Average Return = 40.16\n",
+      "Iteration 13: Average Return = 41.06\n",
+      "Iteration 14: Average Return = 45.88\n",
+      "Iteration 15: Average Return = 46.71\n",
+      "Iteration 16: Average Return = 48.98\n",
+      "Iteration 17: Average Return = 42.03\n",
+      "Iteration 18: Average Return = 43.09\n",
+      "Iteration 19: Average Return = 51.08\n",
+      "Iteration 20: Average Return = 42.84\n",
+      "Iteration 21: Average Return = 48.44\n",
+      "Iteration 22: Average Return = 52.36\n",
+      "Iteration 23: Average Return = 47.93\n",
+      "Iteration 24: Average Return = 52.08\n",
+      "Iteration 25: Average Return = 49.84\n",
+      "Iteration 26: Average Return = 51.89\n",
+      "Iteration 27: Average Return = 49.26\n",
+      "Iteration 28: Average Return = 50.71\n",
+      "Iteration 29: Average Return = 53.88\n",
+      "Iteration 30: Average Return = 55.18\n",
+      "Iteration 31: Average Return = 54.39\n",
+      "Iteration 32: Average Return = 56.3\n",
+      "Iteration 33: Average Return = 56.19\n",
+      "Iteration 34: Average Return = 55.11\n",
+      "Iteration 35: Average Return = 54.54\n",
+      "Iteration 36: Average Return = 55.6\n",
+      "Iteration 37: Average Return = 57.24\n",
+      "Iteration 38: Average Return = 59.34\n",
+      "Iteration 39: Average Return = 59.58\n",
+      "Iteration 40: Average Return = 63.38\n",
+      "Iteration 41: Average Return = 61.38\n",
+      "Iteration 42: Average Return = 62.72\n",
+      "Iteration 43: Average Return = 61.87\n",
+      "Iteration 44: Average Return = 64.68\n",
+      "Iteration 45: Average Return = 68.04\n",
+      "Iteration 46: Average Return = 68.8\n",
+      "Iteration 47: Average Return = 74.53\n",
+      "Iteration 48: Average Return = 75.49\n",
+      "Iteration 49: Average Return = 73.06\n",
+      "Iteration 50: Average Return = 82.74\n",
+      "Iteration 51: Average Return = 81.61\n",
+      "Iteration 52: Average Return = 83.54\n",
+      "Iteration 53: Average Return = 83.64\n",
+      "Iteration 54: Average Return = 91.18\n",
+      "Iteration 55: Average Return = 99.76\n",
+      "Iteration 56: Average Return = 102.8\n",
+      "Iteration 57: Average Return = 106.76\n",
+      "Iteration 58: Average Return = 125.01\n",
+      "Iteration 59: Average Return = 140.17\n",
+      "Iteration 60: Average Return = 150.5\n",
+      "Iteration 61: Average Return = 161.18\n",
+      "Iteration 62: Average Return = 164.11\n",
+      "Iteration 63: Average Return = 169.09\n",
+      "Iteration 64: Average Return = 165.04\n",
+      "Iteration 65: Average Return = 161.85\n",
+      "Iteration 66: Average Return = 173.47\n",
+      "Iteration 67: Average Return = 167.83\n",
+      "Iteration 68: Average Return = 166.76\n",
+      "Iteration 69: Average Return = 171.62\n",
+      "Iteration 70: Average Return = 181.6\n",
+      "Iteration 71: Average Return = 182.21\n",
+      "Iteration 72: Average Return = 183.27\n",
+      "Iteration 73: Average Return = 187.42\n",
+      "Iteration 74: Average Return = 186.45\n",
+      "Iteration 75: Average Return = 187.57\n",
+      "Iteration 76: Average Return = 186.98\n",
+      "Iteration 77: Average Return = 196.64\n",
+      "Solve at 77 iterations, which equals 7700 episodes.\n"
      ]
     }
    ],
@@ -658,14 +967,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 42,
    "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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Ya/U9F0VcpnJYLJYeFlNDKRX6XJxzccJWPBcge0WX1yP+RtlCH+5Ev4eSzAcA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\nAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1278b4d30>"
+       "<matplotlib.figure.Figure at 0x7fca98784630>"
       ]
      },
      "metadata": {},
@@ -673,9 +982,9 @@
     },
     {
      "data": {
-      "image/png": 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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x127a02390>"
+       "<matplotlib.figure.Figure at 0x7fca987840b8>"
       ]
      },
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diff --git a/policy_gradient/policy.py b/policy_gradient/policy.py
index 99fecf3..c22b0b6 100644
--- a/policy_gradient/policy.py
+++ b/policy_gradient/policy.py
@@ -30,6 +30,8 @@ def __init__(self, in_dim, out_dim, hidden_dim, optimizer, session):
         Sample solution is about 2~4 lines.
         """
         # YOUR CODE HERE >>>>>>
+        hidden1 = tf.layers.dense(inputs=self._observations, units=hidden_dim, activation=tf.nn.tanh)
+        probs = tf.layers.dense(inputs=hidden1, units=out_dim, activation=tf.nn.softmax)
         # <<<<<<<<
 
         # --------------------------------------------------
@@ -72,6 +74,7 @@ def __init__(self, in_dim, out_dim, hidden_dim, optimizer, session):
         Sample solution is about 1~3 lines.
         """
         # YOUR CODE HERE >>>>>>
+        surr_loss = -tf.reduce_mean(self._advantages * log_prob)
         # <<<<<<<<
 
         grads_and_vars = self._opt.compute_gradients(surr_loss)
diff --git a/policy_gradient/util.py b/policy_gradient/util.py
index 61ef302..dbe25b8 100644
--- a/policy_gradient/util.py
+++ b/policy_gradient/util.py
@@ -32,7 +32,9 @@ def discount_bootstrap(x, discount_rate, b):
     Sample code should be about 3 lines
     """
     # YOUR CODE >>>>>>>>>>>>>>>>>>>
-    # <<<<<<<<<<<<<<<<<<<<<<<<<<<<
+    b_sift = np.roll(b, -1)
+    b_sift[-1] = 0.0
+    return x + discount_rate * b_sift
  
 def plot_curve(data, key, filename=None):
     # plot the surrogate loss curve
diff --git a/report.md b/report.md
index 1e5017e..2006056 100644
--- a/report.md
+++ b/report.md
@@ -1,3 +1,145 @@
+# 105061525 許菀庭
 # Homework3-Policy-Gradient report
 
-TA: try to elaborate the algorithms that you implemented and any details worth mentioned.
+## Problem 1: Construct a Neural Network to Represent Policy
+
+```python
+hidden1 = tf.layers.dense(inputs=self._observations, units=hidden_dim, activation=tf.nn.tanh)
+probs = tf.layers.dense(inputs=hidden1, units=out_dim, activation=tf.nn.softmax)
+```
+我用tensorflow中的tf.layers.dense來實現一個2-layer neural network。tf.layers.dense代表的就是fully-connected layer，輸入inputs、output dimension 和 activation function 就可以。這個network代表的是policy，因此inputs是observations，outputs是對應此observation，各個action的probabilities。
+
+## Problem 2: Compute the Surrogate Loss
+
+```python
+surr_loss = -tf.reduce_mean(self._advantages * log_prob)
+```
+這裡實現了policy gradient的surrogate loss，計算每個episode的每個time step的 advantage * log pi(a|s)，然後取平均。因為advantage是越大越好，但optimizer是要minimize loss，所以這裡加一個負號。
+
+
+## Problem 3: Reduce Variance Using a Baseline
+
+```python
+a = r - b
+# a is advantages
+# r is rewards
+# b is baseline values
+```
+這個步驟把reward減掉baseline，baseline是用一個estimate的value function算出來的。這個的目的是要讓我們的model在採取一個action的reward會比baseline還高的時候，才去encourage 這個action。這麼做可以reduce variance，讓training過程更穩定。
+
+
+## Problem 4: Compare the Results Before and After Adding Baseline
+
+### 1. Why the baseline won't introduce bias
+
+加上baseline並不會改變原本的expectation: 
+
+<img src="images/surr_loss.PNG" width="300"/>
+
+把 r 換成 r - b 之後，增加的項就是負的 <img src="images/baseline.PNG" width="150"/>
+
+而這項的結果是0，推導如下:
+
+<img src="images/baseline_0.PNG" width="800"/>
+
+因此，加上baseline並不會造成bias。
+
+### 2. Compare with no baseline
+
+因為有sample的關係，每次實驗結果會有點不一樣，所以我有加baseline和沒加baseline的實驗各跑了六次，六次結果如下:
+
+#### with baseline
+<table>
+  <tr>
+    <td>Loss</td>
+    <td><img src="images/loss_withbase.PNG"/></td>
+    <td><img src="images/loss_withbase_2.PNG"/></td>
+    <td><img src="images/loss_withbase_3.PNG"/></td>
+    <td><img src="images/loss_withbase_4.PNG"/></td>
+    <td><img src="images/loss_withbase_5.PNG"/></td>
+    <td><img src="images/loss_withbase_6.PNG"/></td>
+  </tr>
+  <tr>
+    <td>Rewards</td>
+    <td><img src="images/return_withbase.PNG"/></td>
+    <td><img src="images/return_withbase_2.PNG"/></td>
+    <td><img src="images/return_withbase_3.PNG"/></td>
+    <td><img src="images/return_withbase_4.PNG"/></td>
+    <td><img src="images/return_withbase_5.PNG"/></td>
+    <td><img src="images/return_withbase_6.PNG"/></td>
+  </tr>
+  <tr>
+    <td>Iter</td>
+    <td>80</td>
+    <td>61</td>
+    <td>74</td>
+    <td>77</td>
+    <td>75</td>
+    <td>86</td>
+  </tr>
+</table>
+
+#### no baseline
+<table>
+  <tr>
+    <td>Loss</td>
+    <td><img src="images/loss_nobase.PNG"/></td>
+    <td><img src="images/loss_nobase_2.PNG"/></td>
+    <td><img src="images/loss_nobase_3.PNG"/></td>
+    <td><img src="images/loss_nobase_4.PNG"/></td>
+    <td><img src="images/loss_nobase_5.PNG"/></td>
+    <td><img src="images/loss_nobase_6.PNG"/></td>
+  </tr>
+  <tr>
+    <td>Rewards</td>
+    <td><img src="images/return_nobase.PNG"/></td>
+    <td><img src="images/return_nobase_2.PNG"/></td>
+    <td><img src="images/return_nobase_3.PNG"/></td>
+    <td><img src="images/return_nobase_4.PNG"/></td>
+    <td><img src="images/return_nobase_5.PNG"/></td>
+    <td><img src="images/return_nobase_6.PNG"/></td>
+  </tr>
+  <tr>
+    <td>Iter</td>
+    <td>55</td>
+    <td>132</td>
+    <td>92</td>
+    <td>57</td>
+    <td>73</td>
+    <td>109</td>
+  </tr>
+</table>
+
+從上面兩個表可以觀察出以下幾點:
+
+* no baseline的收斂速度不一定會比較慢，有的時候會很快就收斂 (e.g. no baseline的第2和第4個實驗)
+* with baseline大概都花60 ~ 90個iterations；no baseline的花50 ~ 150個iterations
+* with baseline收斂速度相較no baseline穩定很多，雖然no baseline在運氣好的時候可以收斂非常快，但在實驗需要很長的training time時，穩定的收斂速度會比較適合
+* no baseline的rewards，到後半會上升的比較慢，有可能是variance比較大，較難找到好的actions
+
+## Problem 5: Actor-Critic Algorithm (With Bootstrapping)
+
+```python
+b_sift = np.roll(b, -1)
+b_sift[-1] = 0.0
+return x + discount_rate * b_sift
+```
+原本在problem 1~3中，reward是計算從time step t到最後一個time step的immediate reward做discount並加總，這樣的算法bias小但variance高。
+而bootstrapping是將reward改成現在這個time step的immediate reward加上discount factor乘以下個time step的value，這樣的算法variance小但bias大。
+
+result如下:
+
+<img src="images/loss_bootstrap.PNG" width=300/> <img src="images/return_bootstrap.PNG"  width=300/>
+
+改成bootstrap的結果非常差，會一直無法收斂，我推測是因為bias高的關係。
+
+## Problem 6: Generalized Advantage Estimation
+
+```python
+a = util.discount(a, self.discount_rate * LAMBDA)
+```
+
+GAE的算法是將前面兩種reward方式(high variance, low bias和low variance, high bias)結合。
+最後結果如下:
+
+<img src="images/loss_GAE.PNG" width=300/> <img src="images/return_GAE.PNG" width=300/>