DP/Policy Iteration.ipynb

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   "source": [
    "import numpy as np\n",
    "import pprint\n",
    "import sys\n",
    "if \"../\" not in sys.path:\n",
    "  sys.path.append(\"../\") \n",
    "from lib.envs.gridworld import GridworldEnv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "pp = pprint.PrettyPrinter(indent=2)\n",
    "env = GridworldEnv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
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   "source": [
    "# Taken from Policy Evaluation Exercise!\n",
    "\n",
    "def policy_eval(policy, env, discount_factor=1.0, theta=0.00001):\n",
    "    \"\"\"\n",
    "    Evaluate a policy given an environment and a full description of the environment's dynamics.\n",
    "    \n",
    "    Args:\n",
    "        policy: [S, A] shaped matrix representing the policy.\n",
    "        env: OpenAI env. env.P represents the transition probabilities of the environment.\n",
    "            env.P[s][a] is a list of transition tuples (prob, next_state, reward, done).\n",
    "            env.nS is a number of states in the environment. \n",
    "            env.nA is a number of actions in the environment.\n",
    "        theta: We stop evaluation once our value function change is less than theta for all states.\n",
    "        discount_factor: Gamma discount factor.\n",
    "    \n",
    "    Returns:\n",
    "        Vector of length env.nS representing the value function.\n",
    "    \"\"\"\n",
    "    # Start with a random (all 0) value function\n",
    "    V = np.zeros(env.nS)\n",
    "    while True:\n",
    "        delta = 0\n",
    "        # For each state, perform a \"full backup\"\n",
    "        for s in range(env.nS):\n",
    "            v = 0\n",
    "            # Look at the possible next actions\n",
    "            for a, action_prob in enumerate(policy[s]):\n",
    "                # For each action, look at the possible next states...\n",
    "                for  prob, next_state, reward, done in env.P[s][a]:\n",
    "                    # Calculate the expected value\n",
    "                    v += action_prob * prob * (reward + discount_factor * V[next_state])\n",
    "            # How much our value function changed (across any states)\n",
    "            delta = max(delta, np.abs(v - V[s]))\n",
    "            V[s] = v\n",
    "        # Stop evaluating once our value function change is below a threshold\n",
    "        if delta < theta:\n",
    "            break\n",
    "    return np.array(V)"
   ]
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   "source": [
    "def policy_improvement(env, policy_eval_fn=policy_eval, discount_factor=1.0):\n",
    "    \"\"\"\n",
    "    Policy Improvement Algorithm. Iteratively evaluates and improves a policy\n",
    "    until an optimal policy is found.\n",
    "    \n",
    "    Args:\n",
    "        env: The OpenAI envrionment.\n",
    "        policy_eval_fn: Policy Evaluation function that takes 3 arguments:\n",
    "            policy, env, discount_factor.\n",
    "        discount_factor: gamma discount factor.\n",
    "        \n",
    "    Returns:\n",
    "        A tuple (policy, V). \n",
    "        policy is the optimal policy, a matrix of shape [S, A] where each state s\n",
    "        contains a valid probability distribution over actions.\n",
    "        V is the value function for the optimal policy.\n",
    "        \n",
    "    \"\"\"\n",
    "    # Start with a random policy\n",
    "    policy = np.ones([env.nS, env.nA]) / env.nA\n",
    "    \n",
    "    while True:\n",
    "        # Implement this!\n",
    "        break\n",
    "    \n",
    "    return policy, np.zeros(env.nS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy Probability Distribution:\n",
      "[[ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]\n",
      " [ 0.25  0.25  0.25  0.25]]\n",
      "\n",
      "Reshaped Grid Policy (0=up, 1=right, 2=down, 3=left):\n",
      "[[0 0 0 0]\n",
      " [0 0 0 0]\n",
      " [0 0 0 0]\n",
      " [0 0 0 0]]\n",
      "\n",
      "Value Function:\n",
      "[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      "\n",
      "Reshaped Grid Value Function:\n",
      "[[ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "policy, v = policy_improvement(env)\n",
    "print(\"Policy Probability Distribution:\")\n",
    "print(policy)\n",
    "print(\"\")\n",
    "\n",
    "print(\"Reshaped Grid Policy (0=up, 1=right, 2=down, 3=left):\")\n",
    "print(np.reshape(np.argmax(policy, axis=1), env.shape))\n",
    "print(\"\")\n",
    "\n",
    "print(\"Value Function:\")\n",
    "print(v)\n",
    "print(\"\")\n",
    "\n",
    "print(\"Reshaped Grid Value Function:\")\n",
    "print(v.reshape(env.shape))\n",
    "print(\"\")\n",
    "\n"
   ]
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    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 2 decimals\n\n(mismatch 87.5%)\n x: array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n        0.,  0.,  0.])\n y: array([ 0, -1, -2, -3, -1, -2, -3, -2, -2, -3, -2, -1, -3, -2, -1,  0])",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-55581f8eb5c9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Test the value function\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mexpected_v\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0massert_array_almost_equal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpected_v\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/dennybritz/venvs/tf/lib/python3.5/site-packages/numpy/testing/utils.py\u001b[0m in \u001b[0;36massert_array_almost_equal\u001b[0;34m(x, y, decimal, err_msg, verbose)\u001b[0m\n\u001b[1;32m    914\u001b[0m     assert_array_compare(compare, x, y, err_msg=err_msg, verbose=verbose,\n\u001b[1;32m    915\u001b[0m              \u001b[0mheader\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Arrays are not almost equal to %d decimals'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 916\u001b[0;31m              precision=decimal)\n\u001b[0m\u001b[1;32m    917\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    918\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/dennybritz/venvs/tf/lib/python3.5/site-packages/numpy/testing/utils.py\u001b[0m in \u001b[0;36massert_array_compare\u001b[0;34m(comparison, x, y, err_msg, verbose, header, precision)\u001b[0m\n\u001b[1;32m    735\u001b[0m                                 names=('x', 'y'), precision=precision)\n\u001b[1;32m    736\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcond\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 737\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    738\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    739\u001b[0m         \u001b[0;32mimport\u001b[0m \u001b[0mtraceback\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAssertionError\u001b[0m: \nArrays are not almost equal to 2 decimals\n\n(mismatch 87.5%)\n x: array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n        0.,  0.,  0.])\n y: array([ 0, -1, -2, -3, -1, -2, -3, -2, -2, -3, -2, -1, -3, -2, -1,  0])"
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    "# Test the value function\n",
    "expected_v = np.array([ 0, -1, -2, -3, -1, -2, -3, -2, -2, -3, -2, -1, -3, -2, -1,  0])\n",
    "np.testing.assert_array_almost_equal(v, expected_v, decimal=2)"
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