diff --git a/Lab3-policy-gradient.ipynb b/Lab3-policy-gradient.ipynb
index 4529e50..3fa987a 100644
--- a/Lab3-policy-gradient.ipynb
+++ b/Lab3-policy-gradient.ipynb
@@ -28,17 +28,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "[2017-09-12 22:50:43,560] Making new env: CartPole-v0\n"
-     ]
-    }
-   ],
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
    "source": [
     "import gym\n",
     "import tensorflow as tf\n",
@@ -103,14 +97,14 @@
   },
   {
    "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/vufg/miniconda3/envs/vufg_env/lib/python3.6/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 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "collapsed": true
    },
@@ -214,6 +208,7 @@
     "            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 +253,74 @@
   },
   {
    "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 = 23.94\n",
+      "Iteration 2: Average Return = 29.41\n",
+      "Iteration 3: Average Return = 29.07\n",
+      "Iteration 4: Average Return = 33.33\n",
+      "Iteration 5: Average Return = 36.63\n",
+      "Iteration 6: Average Return = 41.97\n",
+      "Iteration 7: Average Return = 42.01\n",
+      "Iteration 8: Average Return = 46.57\n",
+      "Iteration 9: Average Return = 50.73\n",
+      "Iteration 10: Average Return = 56.44\n",
+      "Iteration 11: Average Return = 55.85\n",
+      "Iteration 12: Average Return = 58.21\n",
+      "Iteration 13: Average Return = 60.61\n",
+      "Iteration 14: Average Return = 62.97\n",
+      "Iteration 15: Average Return = 73.2\n",
+      "Iteration 16: Average Return = 74.45\n",
+      "Iteration 17: Average Return = 75.49\n",
+      "Iteration 18: Average Return = 93.8\n",
+      "Iteration 19: Average Return = 80.37\n",
+      "Iteration 20: Average Return = 95.74\n",
+      "Iteration 21: Average Return = 94.82\n",
+      "Iteration 22: Average Return = 95.57\n",
+      "Iteration 23: Average Return = 115.67\n",
+      "Iteration 24: Average Return = 115.55\n",
+      "Iteration 25: Average Return = 129.97\n",
+      "Iteration 26: Average Return = 135.37\n",
+      "Iteration 27: Average Return = 142.41\n",
+      "Iteration 28: Average Return = 146.57\n",
+      "Iteration 29: Average Return = 153.47\n",
+      "Iteration 30: Average Return = 151.56\n",
+      "Iteration 31: Average Return = 153.89\n",
+      "Iteration 32: Average Return = 161.93\n",
+      "Iteration 33: Average Return = 160.61\n",
+      "Iteration 34: Average Return = 161.11\n",
+      "Iteration 35: Average Return = 166.7\n",
+      "Iteration 36: Average Return = 168.21\n",
+      "Iteration 37: Average Return = 166.36\n",
+      "Iteration 38: Average Return = 169.14\n",
+      "Iteration 39: Average Return = 172.67\n",
+      "Iteration 40: Average Return = 177.67\n",
+      "Iteration 41: Average Return = 179.71\n",
+      "Iteration 42: Average Return = 181.75\n",
+      "Iteration 43: Average Return = 175.76\n",
+      "Iteration 44: Average Return = 183.49\n",
+      "Iteration 45: Average Return = 185.19\n",
+      "Iteration 46: Average Return = 187.87\n",
+      "Iteration 47: Average Return = 185.34\n",
+      "Iteration 48: Average Return = 185.09\n",
+      "Iteration 49: Average Return = 194.09\n",
+      "Iteration 50: Average Return = 187.81\n",
+      "Iteration 51: Average Return = 180.4\n",
+      "Iteration 52: Average Return = 192.99\n",
+      "Iteration 53: Average Return = 193.37\n",
+      "Iteration 54: Average Return = 192.48\n",
+      "Iteration 55: Average Return = 192.81\n",
+      "Iteration 56: Average Return = 192.75\n",
+      "Iteration 57: Average Return = 193.78\n",
+      "Iteration 58: Average Return = 194.72\n",
+      "Iteration 59: Average Return = 192.91\n",
+      "Iteration 60: Average Return = 195.15\n",
+      "Solve at 60 iterations, which equals 6000 episodes.\n"
      ]
     }
    ],
@@ -371,14 +342,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "data": {
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NnnIp+h+voj98xxgdFmnB9It7UAHNf2mdyjTlMpx5X6H/9TZE90N1YIkjFR6J6Z7Fxl/w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\nDTX+jM4LWgjRo/i85iLaToVFoC66Cv3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B9c28Cpoumi97GLv0i8VoEjCWAZ/IOZfz58+zaJGxxL///e/59re/zWOPPcbv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\nAAAASUVORK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107bac18>"
+       "<matplotlib.figure.Figure at 0x7f06d460c5f8>"
       ]
      },
      "metadata": {},
@@ -386,9 +357,9 @@
     },
     {
      "data": {
-      "image/png": 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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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vb3kEJX4jg/GEcDi7isWOHTt4+eWXadOmDSdPnqRdu3acPHmSbt262V0sFi1a\nREpKCvn5+cycOZOYmBgmTZrEwoUL2bhxo63rLFjnotq9ezezZ8/G09OT2NjYy89QuBwZjCeE49lV\nLFatWkVsbCyDBw9m+vTp/Pvf/2bTpk2cPHnS7gs9/PDDF9z+5JNPVtumlOKee+6x+72F89PFReh3\nEsA3ADp0RnXoAq3a2NqxdGUlnDsN6SfQP3wng/GEcDC7ikVmZiaDBw+usi0qKooZM2YwderUBglM\nNC36++/QO7aCuztUVKABvFtAu3DOlxZjnDoOFeW249WkO02LVYimyK5i4evrS05ODv7+/oSEhHDo\n0CFatmxpmzNKiIvRWZlwPA119aBLH7hvJ/j6Y3n+DTh9Cn3sMBw7jD55FEtgCKprBLRtjwprD23a\nyV2FEA5mV7EYNWoUqampDBo0iPHjx/P000+jlGLChAkNHZ9wcvqz1egtX2CJewMVdOFurrqyEr1/\nN+rqQSh3D2jXEdWuIwy39r4LcLFeKkI4I7uKxcSJE20zzEZFRdGzZ09KSkq44oorGjQ44fz0of3W\nr7u2ocZMuvBBR1KhqBAVEenAyIQQtVHjdB+GYXDXXXfZVskDa/9dKRSiJjovB05bO0HoXdsuftyP\nO8HNDbr3dVRoQohaqrFYWCwWwsLCyM/Pd0Q8wpUcTrF+7XMN/HQQnXXugofpfbugcw+UdwsHBieE\nqA27JhIcNmwYzz//PJs3b2bfvn38+OOPtj9CXIw+9CN4NsMy2dpjTu/aXv2YrHNw6hgqQtZzF6Ix\ns6vN4ssvvwTgww8/rLJdKcUrr7xS/1EJl6AP7YdO3aw9mNp1tD6KGn1j1WN+tE5tL+0VQjRudhWL\nJUuWNHQcwsXowgL4+RhqonWVRdV/KDrxHXTWOVTgb72i9N6dENQK2rQzK1QhhB3sXkS7oqKCAwcO\nsH279VFCSUkJJSUlDRaYcHJpKaA1qksvAFTkMKDqoyhdXg4HfkBFRNZ6xmEhhGPZVSxOnDjBQw89\nxGuvvcarr74KQEpKiu17If5IH9pvHY0d3hUA1ToMruhYtVfUoR+hrFTaK4RwAnYVi9dff51bb72V\nRYsW4e5ufXLVo0cPUlNTGzQ44bz0oR+hY1eUx2/T16vIoXAk1dYrSu/bCR6ecFVvs8IUQtjJrmJx\n6tQphg8fXmWbl5dXjUupiqZJlxTBiSOorr2qbFf9h1r377Y+itL7dsJVEahmzRweoxCiduwqFiEh\nIfz000+a2V9CAAAW+UlEQVRVtqWlpREaKktaigtISwXDQHXtWWWzCm1rfRS1cxv6bDpknJZHUEI4\nCbt6Q916663ExcUxevRoKioqWLNmDV999RX33XdfQ8cnnJA+vN+63kR49cWJVOQvvaK2fmF9LV1m\nhXAKdt1Z9O/fn3/84x/k5eXRo0cPzp07x6OPPkqfPn0aOj7hhPShH+HKziiv5tX22R5FJa2D0CtQ\nIXJ3KoQzsOvOIi8vj44dO8qCRKJGuqwUjh5GRf/pgvutj6I6WEdt95a7CiGchV3FIjY2lp49ezJs\n2DAGDBiAl5esJSAu4ughqKyo1rj9eypyGPrUMVQvaa8QwlnYVSwSEhL45ptv+PLLL3n99dfp168f\nw4YN4+qrr8bNza2hYxRORB/8EZSCzt0veowaOQFa+sJVEQ6MTAhRF3avlHf99ddz/fXXc+7cObZt\n28YHH3zAq6++yhtvvNHQMQonog/vty5e5O1z0WNUc2/UtWMdGJUQoq7sKha/l5ubS05ODvn5+bRo\nUbcppdPT01m4cKHtdUZGBjExMRQWFrJhwwZ8fX0BmDJlCv369avTtUTD0xXl8FMqavj1ZocihKhn\ndhWLU6dO8fXXX7Nt2zbKysoYPHgwjz32GJ07d67TxcPCwliwYAFgXWTpvvvu45prrmHTpk2MHz+e\niRMn1un9hYMdS4Oysku2VwghnJNdxeKf//wnAwcOZMaMGfTs2dO2xGp92rdvH6GhoYSEXHidZtG4\n6fIy9J5vrC+69DA3GCFEvbOrWLz++uu2OaEayrZt2xg6dKjt9fr169m6dSvh4eFMnToVH5+LPwMX\njqcL8iAtBX34APrIATieBhUV0L4TqqWf2eEJIeqZ0lprew7MyckhLS2N/Px8fn/KyJEj6xxERUUF\n9913H/Hx8fj7+5OTk2Nrr1i1ahXZ2dnExsZWOy8pKYmkpCQA4uLi6jRXlbu7OxUVFZd9fmPSELno\nygrKDx+gbM93lO75loq0A6A1uHvg0bkbHt1749GtN549r8bSon4Lu/xsGi9XyseVcgH78/H09Kzx\nGLDzzmLHjh28/PLLtGnThpMnT9KuXTtOnjxJt27d6qVY7Nmzh44dO+Lv7w9g+wowatQonn/++Que\nFx0dTXR0tO11ZmbmZccQHBxcp/Mbk/rMRWuNXrUM/c1GKCoEZYHwrqg/TUF16w0dOmN4eFIKlAIU\nl1j/1CP52TRerpSPK+UC9ucTFhZm1/vZVSxWrVpFbGwsgwcPZvr06fz73/9m06ZNnDx50q6L1OSP\nj6Cys7MJCAgArIWqXTtZRc00B/ehN3wCVw/Ccs210L0vqp7vHIQQjZ9dxSIzM5PBgwdX2RYVFcWM\nGTOYOnVqnQIoKSlh7969zJgxw7btnXfe4dixYyilCAkJqbJPOJaRtA5a+mG599Eqa1MIIZoWuwfl\n5eTk4O/vT0hICIcOHaJly5YYhlHnALy8vHjzzTerbHvwwQfr/L6i7nRGOuxNRo2PkUIhRBNnV7EY\nNWoUqampDBo0iPHjx/P000+jlGLChAkNHZ8wkd74KVjcUFE3mB2KEMJkdhWLSZMm2b6PioqiZ8+e\nlJSUcMUVVzRYYMJcuqgQ/XUSasBwlH+g2eEIIUx2WYMngoOD6zsO0cjobUlQWnzRqcaFEE1L/Q/F\nFk5PG5Xojf8LnXugrqzblC5CCNcgxUJU90MyZJ7FEi1zcwkhrKRYiGqMpHUQ1Ar6DjQ7FCFEIyHF\nQlShTxyBQz+iRo5HycJWQohfSLEQVeikT6CZF2rYaLNDEUI0Ig07laxwGrqiHP3fr9DJW1HDx1xy\npTshRNMjxaKJ00YlesdW9Nr3IPMsdOmBGhdjdlhCiEZGikUTpbWGvckYa96Gn49Du45YZj8Fvfqh\nlDI7PCFEIyPFognSaSkYH70FaQegVRvUvY+iIoehGmAFRCGEa5Bi0YTon09grFkJP+wAv0DUnbGo\nodGoBl4FUQjh/OS3RBOgz59Df/Ieevsm8PJCTboTFT0R1czL7NCEEE5CioUL0/m56M8+RG/+DAA1\neiLqhptRPr4mRyaEcDZSLJyYzjwLP5+AkNYQ1BrVrBkARlEhxrr30F+uhbJS1JCR1mVQg0JMjlgI\n4aykWDgpnXEaY/5c67rYv/ILhJDWZJ5NR+fnQv8hWG68E9VGppIXQtSNFAsnpEtLMV6NAxSWh55C\nFxZYx0icO4POPItn996Uj56E6tDF7FCFEC5CioWT0Vqj30mAn49hmf0kqld//jgqwj84mMzMTFPi\nE0K4JulY72T05s/R325CTZyC6tXf7HCEEE1Eo7izmDVrFl5eXlgsFtzc3IiLi6OgoICFCxdy7tw5\nQkJCmDNnDj4+TXu+In0kFb1qGUREypQcQgiHahTFAuCpp57C1/e3Lp2JiYlEREQwadIkEhMTSUxM\n5M477zQxQnPpvGyMpXEQGIzl7rky2loI4VCN9jdOcnIyUVFRAERFRZGcnGxyRObRJcUYrz4PRQVY\n7v87qkXTvsMSQjheo7mzmD9/PgCjR48mOjqa3NxcAgICAPD39yc3N9fM8EyjC/MxFv8PHD2MuvcR\nVLuOZockhGiCGkWxmDdvHoGBgeTm5vLMM88QFhZWZb9S6oIzoSYlJZGUlARAXFwcwcHBlx2Du7t7\nnc5vCJVZmeS8+E+M9JP4/W0+XoOi7DqvMeZSF66UjyvlAq6VjyvlAvWfT6MoFoGBgQD4+fkxYMAA\n0tLS8PPzIzs7m4CAALKzs6u0Z/wqOjqa6Oho2+u6dBcNbmTdTfW5MxgLn4S8HCyzn6Sgc08K7Iyv\nseVSV66UjyvlAq6VjyvlAvbn88f/nF+M6W0WJSUlFBcX277fu3cv7du3JzIyki1btgCwZcsWBgwY\nYGaYDqV/Po7x/BNQWIBl7jxU9z5mhySEaOJMv7PIzc3lhRdeAKCyspJhw4bRt29fOnXqxMKFC9m4\ncaOt62xToE8cwYj/J3h4Yvnbc6i2V5odkhBCmF8sWrduzYIFC6ptb9myJU8++aQJEZlHnzqK8eKT\n4OWF5dFnUSGhZockhBBAI3gMJax0+glrofDwxPLIfCkUQohGRYpFI6BPn8KI/79gccPyyDOoVm3M\nDkkIIaqQYmEyfTbdWii0thaK0LZmhySEENWY3mbRVOifT6DXfwRlZWitwTBAG3DsMFRWYnl0vqw7\nIYRotKRYOIDOycJ46V9QXAj+QaAUWCygLNA6DMttM6TXkxCiUZNi0cB0WSlGwrNQmI/l8ThU+05m\nhySEELUmbRYNSGuNXrEYjh6yzhQrhUII4aSkWDQg/ekqdPJ/UZOnovoNNjscIYS4bFIsGoje+TV6\n7XuoQdehxv7Z7HCEEKJOpFg0AH0kFWP5IujUDTX1gQvOmCuEEM5EGrjrkdYaveET9P9bAQFBWGL/\ngfLwMDssIYSoMykW9UQX5mMsfwl+2AF9rsEybTbKp/q06kII4YykWNQDfTgFY9kLkJuDuvUe1Kg/\nyaMnIYRLkWJRR8aXieiPVkBQKyx//zfqys5mhySEEPVOisVl0lqjE99Bf/Yh9BtifezU3NvssIQQ\nokFIsbgMWmv0qmXoDZ+gho9B3Xk/yuJmdlhCCNFgpFjUkjYq0e+8iv7vl6joiaiYu6V9Qgjh8qRY\nXIQuKoDycmjREuVu/WvSFRXo5YvQO7aixsegbrxDCoUQokmQYnEB+kgqxov/F8rKrBuae0OLltbZ\nYs+dQU3+C5YbZFS2EKLpkGLxBzr7PMarz4FvAGrMTVCYBwX5UJCHLixAjY/BMjTa7DCFEMKhTC0W\nmZmZLFmyhJycHJRSREdHM27cOFavXs2GDRvw9bUOapsyZQr9+vVr8Hhs04mXlGCZ8z+yxoQQQvzC\n1GLh5ubGXXfdRXh4OMXFxTzxxBP07t0bgPHjxzNx4kSHxaK1Rr+9BI4dxjLrH1IohBDid0wtFgEB\nAQQEBADQvHlz2rZtS1ZWlimxFCW+h/52s7XRuu8gU2IQQojGqtHMOpuRkcHRo0fp3Nk6Anr9+vU8\n+uijJCQkUFBQ0KDX1vt2UfB2Aqr/UNT4mAa9lhBCOCOltdZmB1FSUsJTTz3F5MmTGThwIDk5Obb2\nilWrVpGdnU1sbGy185KSkkhKSgIgLi6Osl97L9VCxc/HyfrbvbiHhhEw/1WUV/O6JdMIuLu7U1FR\nYXYY9caV8nGlXMC18nGlXMD+fDw9Pe16P9OLRUVFBc8//zx9+vRhwoQJ1fZnZGTw/PPPEx8fX+N7\npaen1/r6+nwGxspXCH7on2RbXGM68eDgYDIzM80Oo964Uj6ulAu4Vj6ulAvYn09YWJhd72fqYyit\nNUuXLqVt27ZVCkV2drbt+x07dtCuXbsGi0EFtcJtzv/g1qpNg11DCCGcnakN3AcPHmTr1q20b9+e\nxx57DLB2k922bRvHjh1DKUVISAgzZswwM0whhGjyTC0W3bp1Y/Xq1dW2O2JMhRBCCPs1mt5QQggh\nGi8pFkIIIWokxUIIIUSNpFgIIYSokRQLIYQQNZJiIYQQokamj+AWQgjR+MmdxS+eeOIJs0OoN66U\nC7hWPq6UC7hWPq6UC9R/PlIshBBC1EiKhRBCiBq5/etf//qX2UE0FuHh4WaHUG9cKRdwrXxcKRdw\nrXxcKReo33ykgVsIIUSN5DGUEEKIGpk662xj8P3337N8+XIMw2DUqFFMmjTJ7JBqJSEhgd27d+Pn\n52dbIKqgoICFCxdy7tw5QkJCmDNnDj4+PiZHWrPMzEyWLFlCTk4OSimio6MZN26c0+ZTVlbGU089\nRUVFBZWVlQwaNIiYmBgyMjJYtGgR+fn5hIeH8+CDD+Lu7hz/FA3D4IknniAwMJAnnnjCqXOZNWsW\nXl5eWCwW3NzciIuLc9rPGkBhYSFLly7l5MmTKKW4//77CQsLq798dBNWWVmpH3jgAX3mzBldXl6u\nH330UX3y5Emzw6qV/fv36yNHjui5c+fatr399tt6zZo1Wmut16xZo99++22zwquVrKwsfeTIEa21\n1kVFRXr27Nn65MmTTpuPYRi6uLhYa611eXm5/vvf/64PHjyo4+Pj9ddff6211vq1117T69evNzPM\nWvnkk0/0okWL9HPPPae11k6dS2xsrM7Nza2yzVk/a1pr/fLLL+ukpCSttfXzVlBQUK/5NOnHUGlp\naYSGhtK6dWvc3d0ZMmQIycnJZodVKz169Kj2P4Xk5GSioqIAiIqKcpqcAgICbA1yzZs3p23btmRl\nZTltPkopvLy8AKisrKSyshKlFPv372fQoEEAjBgxwmnyOX/+PLt372bUqFGAdaVLZ83lYpz1s1ZU\nVMSBAwcYOXIkYF1/u0WLFvWaj3PcLzaQrKwsgoKCbK+DgoI4fPiwiRHVj9zcXAICAgDw9/cnNzfX\n5IhqLyMjg6NHj9K5c2enzscwDB5//HHOnDnD9ddfT+vWrfH29sbNzQ2AwMBAsrKyTI7SPitWrODO\nO++kuLgYgPz8fKfN5Vfz588HYPTo0URHRzvtZy0jIwNfX18SEhI4fvw44eHhTJs2rV7zadLFoilQ\nSqGUMjuMWikpKSE+Pp5p06bh7e1dZZ+z5WOxWFiwYAGFhYW88MILpKenmx3SZdm1axd+fn6Eh4ez\nf/9+s8OpF/PmzSMwMJDc3FyeeeYZwsLCqux3ps9aZWUlR48e5a9//StdunRh+fLlJCYmVjmmrvk0\n6WIRGBjI+fPnba/Pnz9PYGCgiRHVDz8/P7KzswkICCA7OxtfX1+zQ7JbRUUF8fHxDB8+nIEDBwLO\nnc+vWrRoQc+ePTl06BBFRUVUVlbi5uZGVlaWU3zmDh48yM6dO9mzZw9lZWUUFxezYsUKp8zlV7/G\n6ufnx4ABA0hLS3Paz1pQUBBBQUF06dIFgEGDBpGYmFiv+TTpNotOnTpx+vRpMjIyqKioYPv27URG\nRpodVp1FRkayZcsWALZs2cKAAQNMjsg+WmuWLl1K27ZtmTBhgm27s+aTl5dHYWEhYO0ZtXfvXtq2\nbUvPnj359ttvAdi8ebNTfOZuv/12li5dypIlS3j44Yfp1asXs2fPdspcwHr3+uvjtJKSEvbu3Uv7\n9u2d9rPm7+9PUFCQ7c513759XHHFFfWaT5MflLd7927eeustDMPguuuuY/LkyWaHVCuLFi0iJSWF\n/Px8/Pz8iImJYcCAASxcuJDMzEyn6v6XmprKk08+Sfv27W23y1OmTKFLly5Omc/x48dZsmQJhmGg\ntWbw4MHcfPPNnD17lkWLFlFQUEDHjh158MEH8fDwMDtcu+3fv59PPvmEJ554wmlzOXv2LC+88AJg\nfYQzbNgwJk+eTH5+vlN+1gCOHTvG0qVLqaiooFWrVsTGxqK1rrd8mnyxEEIIUbMm/RhKCCGEfaRY\nCCGEqJEUCyGEEDWSYiGEEKJGUiyEEELUSIqFaJLmzp1r2kjkzMxM7rrrLgzDMOX6QlwO6TormrTV\nq1dz5swZZs+e3WDXmDVrFvfddx+9e/dusGsI0dDkzkKIOqisrDQ7BCEcQu4sRJM0a9Ys/vrXv9pG\n8bq7uxMaGsqCBQsoKirirbfeYs+ePSiluO6664iJicFisbB582Y2bNhAp06d2Lp1K2PGjGHEiBG8\n9tprHD9+HKUUffr04e6776ZFixa8/PLLfP3117i7u2OxWLj55psZPHgwDzzwAO+//75tTqXXX3+d\n1NRUfHx8uPHGG4mOjgasdz6nTp3C09OTHTt2EBwczKxZs+jUqRMAiYmJfP755xQXFxMQEMA999xD\nRESEaX+vwnU16YkERdPm4eHBTTfdVO0x1JIlS/Dz82Px4sWUlpYSFxdHUFAQo0ePBuDw4cMMGTKE\n119/ncrKSrKysrjpppvo3r07xcXFxMfH8+GHHzJt2jQefPBBUlNTqzyGysjIqBLHSy+9RLt27Xjt\ntddIT09n3rx5hIaG0qtXL8A64+sjjzxCbGwsH3zwAW+++Sbz588nPT2d9evX89xzzxEYGEhGRoa0\ng4gGI4+hhPidnJwc9uzZw7Rp0/Dy8sLPz4/x48ezfft22zEBAQHccMMNuLm54enpSWhoKL1798bD\nwwNfX1/Gjx9PSkqKXdfLzMwkNTWVO+64A09PTzp06MCoUaNsk78BdOvWjX79+mGxWLj22ms5duwY\nYJ3+vLy8nFOnTtnmAwoNDa3Xvw8hfiV3FkL8TmZmJpWVlcyYMcO2TWtdZZGs4ODgKufk5OSwYsUK\nDhw4QElJCYZh2D1ZW3Z2Nj4+PjRv3rzK+x85csT22s/Pz/a9p6cn5eXlVFZWEhoayrRp0/jwww85\ndeoUffr0YerUqU41TbhwHlIsRJP2x8VggoKCcHd354033rCtAFeT999/H4D4+Hh8fHzYsWMHb775\npl3nBgQEUFBQQHFxsa1gZGZm2v0Lf9iwYQwbNoyioiL+85//8O677/Lggw/ada4QtSGPoUST5ufn\nx7lz52zP+gMCAujTpw8rV66kqKgIwzA4c+bMJR8rFRcX4+Xlhbe3N1lZWXzyySdV9vv7+1drp/hV\ncHAwV111Fe+99x5lZWUcP36cTZs2MXz48BpjT09P58cff6S8vBxPT088PT2dZmU34XykWIgmbfDg\nwQDcfffdPP744wA88MADVFRUMHfuXKZPn86LL75Idnb2Rd/jlltu4ejRo/zlL3/hueee45prrqmy\nf9KkSXz00UdMmzaNdevWVTv/oYce4ty5c9x333288MIL3HLLLXaNySgvL+fdd9/l7rvv5t577yUv\nL4/bb7+9NukLYTfpOiuEEKJGcmchhBCiRlIshBBC1EiKhRBCiBpJsRBCCFEjKRZCCCFqJMVCCCFE\njaRYCCGEqJEUCyGEEDWSYiGEEKJG/x/tbw2fo1NQ3gAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1107ba828>"
+       "<matplotlib.figure.Figure at 0x7f06d456c940>"
       ]
      },
      "metadata": {},
@@ -428,6 +399,123 @@
     "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. "
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 1: Average Return = 18.26\n",
+      "Iteration 2: Average Return = 17.99\n",
+      "Iteration 3: Average Return = 22.59\n",
+      "Iteration 4: Average Return = 23.06\n",
+      "Iteration 5: Average Return = 22.91\n",
+      "Iteration 6: Average Return = 24.21\n",
+      "Iteration 7: Average Return = 25.64\n",
+      "Iteration 8: Average Return = 29.37\n",
+      "Iteration 9: Average Return = 32.05\n",
+      "Iteration 10: Average Return = 32.12\n",
+      "Iteration 11: Average Return = 36.49\n",
+      "Iteration 12: Average Return = 38.94\n",
+      "Iteration 13: Average Return = 36.69\n",
+      "Iteration 14: Average Return = 37.84\n",
+      "Iteration 15: Average Return = 37.39\n",
+      "Iteration 16: Average Return = 38.23\n",
+      "Iteration 17: Average Return = 42.77\n",
+      "Iteration 18: Average Return = 45.92\n",
+      "Iteration 19: Average Return = 42.51\n",
+      "Iteration 20: Average Return = 47.85\n",
+      "Iteration 21: Average Return = 49.33\n",
+      "Iteration 22: Average Return = 46.89\n",
+      "Iteration 23: Average Return = 54.39\n",
+      "Iteration 24: Average Return = 53.58\n",
+      "Iteration 25: Average Return = 51.39\n",
+      "Iteration 26: Average Return = 53.61\n",
+      "Iteration 27: Average Return = 50.12\n",
+      "Iteration 28: Average Return = 53.24\n",
+      "Iteration 29: Average Return = 54.07\n",
+      "Iteration 30: Average Return = 54.88\n",
+      "Iteration 31: Average Return = 59.19\n",
+      "Iteration 32: Average Return = 58.64\n",
+      "Iteration 33: Average Return = 58.3\n",
+      "Iteration 34: Average Return = 56.11\n",
+      "Iteration 35: Average Return = 59.79\n",
+      "Iteration 36: Average Return = 64.27\n",
+      "Iteration 37: Average Return = 61.94\n",
+      "Iteration 38: Average Return = 62.97\n",
+      "Iteration 39: Average Return = 61.88\n",
+      "Iteration 40: Average Return = 65.74\n",
+      "Iteration 41: Average Return = 66.39\n",
+      "Iteration 42: Average Return = 71.52\n",
+      "Iteration 43: Average Return = 68.88\n",
+      "Iteration 44: Average Return = 70.66\n",
+      "Iteration 45: Average Return = 67.98\n",
+      "Iteration 46: Average Return = 72.06\n",
+      "Iteration 47: Average Return = 63.96\n",
+      "Iteration 48: Average Return = 68.72\n",
+      "Iteration 49: Average Return = 78.58\n",
+      "Iteration 50: Average Return = 77.61\n",
+      "Iteration 51: Average Return = 77.39\n",
+      "Iteration 52: Average Return = 77.69\n",
+      "Iteration 53: Average Return = 80.74\n",
+      "Iteration 54: Average Return = 78.22\n",
+      "Iteration 55: Average Return = 81.51\n",
+      "Iteration 56: Average Return = 88.52\n",
+      "Iteration 57: Average Return = 84.35\n",
+      "Iteration 58: Average Return = 92.7\n",
+      "Iteration 59: Average Return = 99.19\n",
+      "Iteration 60: Average Return = 101.56\n",
+      "Iteration 61: Average Return = 124.86\n",
+      "Iteration 62: Average Return = 122.72\n",
+      "Iteration 63: Average Return = 130.9\n",
+      "Iteration 64: Average Return = 143.11\n",
+      "Iteration 65: Average Return = 148.85\n",
+      "Iteration 66: Average Return = 160.9\n",
+      "Iteration 67: Average Return = 158.84\n",
+      "Iteration 68: Average Return = 164.05\n",
+      "Iteration 69: Average Return = 166.94\n",
+      "Iteration 70: Average Return = 162.39\n",
+      "Iteration 71: Average Return = 165.6\n",
+      "Iteration 72: Average Return = 167.21\n",
+      "Iteration 73: Average Return = 170.23\n",
+      "Iteration 74: Average Return = 168.84\n",
+      "Iteration 75: Average Return = 168.77\n",
+      "Iteration 76: Average Return = 172.72\n",
+      "Iteration 77: Average Return = 170.56\n",
+      "Iteration 78: Average Return = 181.94\n",
+      "Iteration 79: Average Return = 179.89\n",
+      "Iteration 80: Average Return = 183.08\n",
+      "Iteration 81: Average Return = 185.56\n",
+      "Iteration 82: Average Return = 185.34\n",
+      "Iteration 83: Average Return = 184.34\n",
+      "Iteration 84: Average Return = 191.06\n",
+      "Iteration 85: Average Return = 189.96\n",
+      "Iteration 86: Average Return = 190.95\n",
+      "Iteration 87: Average Return = 187.77\n",
+      "Iteration 88: Average Return = 196.36\n",
+      "Solve at 88 iterations, which equals 8800 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, avg_return_list = po.train()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -453,6 +541,61 @@
     "If you answer is right, your will solve CartPole with roughly ~ 80 iterations."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "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",
+    "            #without  generalized advantage estimation\n",
+    "            # YOUR CODE HERE >>>>>>>>\n",
+    "            #a = util.discount(a, self.discount_rate * LAMBDA) \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": "markdown",
    "metadata": {},
@@ -523,6 +666,7 @@
     "            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, LAMBDA * self.discount_rate)\n",
     "            # <<<<<<<\n",
     "            p[\"returns\"] = target_v\n",
     "            p[\"baselines\"] = b\n",
@@ -543,7 +687,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {
     "scrolled": true
    },
@@ -552,90 +696,80 @@
      "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 = 22.45\n",
+      "Iteration 2: Average Return = 22.66\n",
+      "Iteration 3: Average Return = 23.18\n",
+      "Iteration 4: Average Return = 26.35\n",
+      "Iteration 5: Average Return = 30.45\n",
+      "Iteration 6: Average Return = 31.85\n",
+      "Iteration 7: Average Return = 31.36\n",
+      "Iteration 8: Average Return = 33.17\n",
+      "Iteration 9: Average Return = 36.0\n",
+      "Iteration 10: Average Return = 39.98\n",
+      "Iteration 11: Average Return = 39.3\n",
+      "Iteration 12: Average Return = 41.77\n",
+      "Iteration 13: Average Return = 44.65\n",
+      "Iteration 14: Average Return = 45.37\n",
+      "Iteration 15: Average Return = 46.24\n",
+      "Iteration 16: Average Return = 48.56\n",
+      "Iteration 17: Average Return = 50.33\n",
+      "Iteration 18: Average Return = 51.93\n",
+      "Iteration 19: Average Return = 50.4\n",
+      "Iteration 20: Average Return = 49.76\n",
+      "Iteration 21: Average Return = 50.6\n",
+      "Iteration 22: Average Return = 56.73\n",
+      "Iteration 23: Average Return = 56.08\n",
+      "Iteration 24: Average Return = 57.1\n",
+      "Iteration 25: Average Return = 57.95\n",
+      "Iteration 26: Average Return = 59.08\n",
+      "Iteration 27: Average Return = 60.34\n",
+      "Iteration 28: Average Return = 60.77\n",
+      "Iteration 29: Average Return = 60.34\n",
+      "Iteration 30: Average Return = 62.95\n",
+      "Iteration 31: Average Return = 65.9\n",
+      "Iteration 32: Average Return = 69.17\n",
+      "Iteration 33: Average Return = 65.59\n",
+      "Iteration 34: Average Return = 64.4\n",
+      "Iteration 35: Average Return = 73.22\n",
+      "Iteration 36: Average Return = 72.33\n",
+      "Iteration 37: Average Return = 72.85\n",
+      "Iteration 38: Average Return = 75.06\n",
+      "Iteration 39: Average Return = 78.24\n",
+      "Iteration 40: Average Return = 82.66\n",
+      "Iteration 41: Average Return = 89.02\n",
+      "Iteration 42: Average Return = 92.59\n",
+      "Iteration 43: Average Return = 92.62\n",
+      "Iteration 44: Average Return = 99.64\n",
+      "Iteration 45: Average Return = 104.78\n",
+      "Iteration 46: Average Return = 104.25\n",
+      "Iteration 47: Average Return = 123.27\n",
+      "Iteration 48: Average Return = 143.53\n",
+      "Iteration 49: Average Return = 148.6\n",
+      "Iteration 50: Average Return = 165.49\n",
+      "Iteration 51: Average Return = 171.91\n",
+      "Iteration 52: Average Return = 175.98\n",
+      "Iteration 53: Average Return = 177.66\n",
+      "Iteration 54: Average Return = 176.62\n",
+      "Iteration 55: Average Return = 177.87\n",
+      "Iteration 56: Average Return = 182.12\n",
+      "Iteration 57: Average Return = 171.36\n",
+      "Iteration 58: Average Return = 170.21\n",
+      "Iteration 59: Average Return = 171.64\n",
+      "Iteration 60: Average Return = 179.67\n",
+      "Iteration 61: Average Return = 176.21\n",
+      "Iteration 62: Average Return = 182.38\n",
+      "Iteration 63: Average Return = 187.55\n",
+      "Iteration 64: Average Return = 184.0\n",
+      "Iteration 65: Average Return = 191.32\n",
+      "Iteration 66: Average Return = 192.08\n",
+      "Iteration 67: Average Return = 192.25\n",
+      "Iteration 68: Average Return = 194.47\n",
+      "Iteration 69: Average Return = 194.28\n",
+      "Iteration 70: Average Return = 193.1\n",
+      "Iteration 71: Average Return = 194.04\n",
+      "Iteration 72: Average Return = 194.81\n",
+      "Iteration 73: Average Return = 196.2\n",
+      "Solve at 73 iterations, which equals 7300 episodes.\n"
      ]
     }
    ],
@@ -658,14 +792,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 11,
    "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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075u2+sv/jvr0X8IlHzFhsGD8rXBi6L/WO8yeDvj3O2IJr4GvSPTk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\nRwghhMdI0RFCCOEx/wESM6tyyrVcFwAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1278b4d30>"
+       "<matplotlib.figure.Figure at 0x7f06d4447c88>"
       ]
      },
      "metadata": {},
@@ -673,9 +807,9 @@
     },
     {
      "data": {
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DUS1DoFsfq0sWos7USVgsWrSI/fv3k5eXx8yZM5k0aRIjRoy4oAsKYP/+/axZswY3Nzds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\nyo892QAAAABJRU5ErkJggg==\n",
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DxSIsLIyDBw/W25aVlUV4eLhTQgnRlunqKvTfV0FUd9SouEafL4QrONRn8Zvf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\njZJiIYQQolH/H9zJFPYWwfuXAAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x127a02390>"
+       "<matplotlib.figure.Figure at 0x7f06d4447e80>"
       ]
      },
      "metadata": {},
@@ -713,7 +847,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.3"
+   "version": "3.6.2"
   }
  },
  "nbformat": 4,
diff --git a/imgs/tanh.png b/imgs/tanh.png
new file mode 100644
index 0000000..649af8b
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diff --git a/imgs/wrong-award.png b/imgs/wrong-award.png
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diff --git a/imgs/wrong-loss.png b/imgs/wrong-loss.png
new file mode 100644
index 0000000..afd22b3
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diff --git a/policy_gradient/__pycache__/__init__.cpython-36.pyc b/policy_gradient/__pycache__/__init__.cpython-36.pyc
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index 0000000..fc8c8dc
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diff --git a/policy_gradient/__pycache__/policy.cpython-36.pyc b/policy_gradient/__pycache__/policy.cpython-36.pyc
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diff --git a/policy_gradient/__pycache__/util.cpython-36.pyc b/policy_gradient/__pycache__/util.cpython-36.pyc
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diff --git a/policy_gradient/baselines/__pycache__/__init__.cpython-36.pyc b/policy_gradient/baselines/__pycache__/__init__.cpython-36.pyc
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diff --git a/policy_gradient/baselines/__pycache__/base.cpython-36.pyc b/policy_gradient/baselines/__pycache__/base.cpython-36.pyc
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diff --git a/policy_gradient/baselines/__pycache__/linear_feature_baseline.cpython-36.pyc b/policy_gradient/baselines/__pycache__/linear_feature_baseline.cpython-36.pyc
new file mode 100644
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diff --git a/policy_gradient/policy.py b/policy_gradient/policy.py
index 99fecf3..bf26f32 100644
--- a/policy_gradient/policy.py
+++ b/policy_gradient/policy.py
@@ -31,6 +31,11 @@ def __init__(self, in_dim, out_dim, hidden_dim, optimizer, session):
         """
         # YOUR CODE HERE >>>>>>
         # <<<<<<<<
+        hidden1 = tf.layers.dense(inputs=self._observations, units=hidden_dim, activation=tf.nn.tanh, name='hidden1')
+        #hidden2 = tf.layers.dense(inputs=hidden1, units=out_dim, activation=tf.nn.tanh, name='hidden2')
+        #mistake tf.nn.tanh as the activation function for the second layer
+        hidden2 = tf.layers.dense(inputs=hidden1, units=out_dim, activation=None, name='hidden2')
+        probs = tf.nn.softmax(hidden2)
 
         # --------------------------------------------------
         # This operation (variable) is used when choosing action during data sampling phase
@@ -72,6 +77,7 @@ 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..184a93d 100644
--- a/policy_gradient/util.py
+++ b/policy_gradient/util.py
@@ -32,6 +32,9 @@ def discount_bootstrap(x, discount_rate, b):
     Sample code should be about 3 lines
     """
     # YOUR CODE >>>>>>>>>>>>>>>>>>>
+    b[0] = 0    
+    return x + discount_rate * np.roll(b, -1)
+    
     # <<<<<<<<<<<<<<<<<<<<<<<<<<<<
  
 def plot_curve(data, key, filename=None):
diff --git a/report.md b/report.md
index 1e5017e..a38b09f 100644
--- a/report.md
+++ b/report.md
@@ -1,3 +1,21 @@
-# Homework3-Policy-Gradient report
+# Homework2 report
+In this lab, I complete the some parts of different kinds of policy gradient. Following problems I met is what I think worth mentioned.
 
-TA: try to elaborate the algorithms that you implemented and any details worth mentioned.
+1. For Problem 1, I didn't notice the activation function tanh is only for the 1st layer. I set the activation of the 2rd layer as tanh, too. Although the network could still converge, it took much longer time to solve the CartPole problem. I tried several times and the shortest one is solving the problem in 120 iterations. Generally, it takes about 160 iterations to solve the problem, which is 2~3 times slower compared to 60 iterations in the correct implementation. The loss curve and average return during my first slower implementation is shown below.
+![alt text](imgs/wrong-loss.png)
+![alt text](imgs/wrong-award.png)
+![alt text](imgs/tanh.png)
+
+This makes sense because tanh function maps the output of the second layer into (0,1), and the softmax function maps the output to (0,1) again. The relatively numerical value makes the gradient relatively smaller and thux, it takes longer time to solve the given problem.
+
+
+2. Following table shows experiment results I got at last.
+
+| Problem Num   | Algorithm           | Num of Iterations to solve the problem  |
+| ---------- |:-------------:| -----:|
+| 1,2,3    | with baseline in gradient estimate | 70 |
+| 4	   | without baseline      |   80 |
+| 5 | Actor-Critic algorithm (with bootstrapping)      |    200 |
+| 6 | Generalized Advantage Estimation      |   76 |
+
+3. Actually I found the number of iterations needed to solve the problem is unstable. Take problem 6 for example, number varies from 70 to 100 iterations. This might also depend on concrete algorithm.