PolicyGradient/CliffWalk Actor Critic Solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import itertools\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import sys\n",
    "import tensorflow as tf\n",
    "import collections\n",
    "\n",
    "if \"../\" not in sys.path:\n",
    "  sys.path.append(\"../\") \n",
    "from lib.envs.cliff_walking import CliffWalkingEnv\n",
    "from lib import plotting\n",
    "\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "env = CliffWalkingEnv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class PolicyEstimator():\n",
    "    \"\"\"\n",
    "    Policy Function approximator. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, learning_rate=0.01, scope=\"policy_estimator\"):\n",
    "        with tf.variable_scope(scope):\n",
    "            self.state = tf.placeholder(tf.int32, [], \"state\")\n",
    "            self.action = tf.placeholder(dtype=tf.int32, name=\"action\")\n",
    "            self.target = tf.placeholder(dtype=tf.float32, name=\"target\")\n",
    "\n",
    "            # This is just table lookup estimator\n",
    "            state_one_hot = tf.one_hot(self.state, int(env.observation_space.n))\n",
    "            self.output_layer = tf.contrib.layers.fully_connected(\n",
    "                inputs=tf.expand_dims(state_one_hot, 0),\n",
    "                num_outputs=env.action_space.n,\n",
    "                activation_fn=None,\n",
    "                weights_initializer=tf.zeros_initializer)\n",
    "\n",
    "            self.action_probs = tf.squeeze(tf.nn.softmax(self.output_layer))\n",
    "            self.picked_action_prob = tf.gather(self.action_probs, self.action)\n",
    "\n",
    "            # Loss and train op\n",
    "            self.loss = -tf.log(self.picked_action_prob) * self.target\n",
    "\n",
    "            self.optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)\n",
    "            self.train_op = self.optimizer.minimize(\n",
    "                self.loss, global_step=tf.contrib.framework.get_global_step())\n",
    "    \n",
    "    def predict(self, state, sess=None):\n",
    "        sess = sess or tf.get_default_session()\n",
    "        return sess.run(self.action_probs, { self.state: state })\n",
    "\n",
    "    def update(self, state, target, action, sess=None):\n",
    "        sess = sess or tf.get_default_session()\n",
    "        feed_dict = { self.state: state, self.target: target, self.action: action  }\n",
    "        _, loss = sess.run([self.train_op, self.loss], feed_dict)\n",
    "        return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ValueEstimator():\n",
    "    \"\"\"\n",
    "    Value Function approximator. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, learning_rate=0.1, scope=\"value_estimator\"):\n",
    "        with tf.variable_scope(scope):\n",
    "            self.state = tf.placeholder(tf.int32, [], \"state\")\n",
    "            self.target = tf.placeholder(dtype=tf.float32, name=\"target\")\n",
    "\n",
    "            # This is just table lookup estimator\n",
    "            state_one_hot = tf.one_hot(self.state, int(env.observation_space.n))\n",
    "            self.output_layer = tf.contrib.layers.fully_connected(\n",
    "                inputs=tf.expand_dims(state_one_hot, 0),\n",
    "                num_outputs=1,\n",
    "                activation_fn=None,\n",
    "                weights_initializer=tf.zeros_initializer)\n",
    "\n",
    "            self.value_estimate = tf.squeeze(self.output_layer)\n",
    "            self.loss = tf.squared_difference(self.value_estimate, self.target)\n",
    "\n",
    "            self.optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)\n",
    "            self.train_op = self.optimizer.minimize(\n",
    "                self.loss, global_step=tf.contrib.framework.get_global_step())        \n",
    "    \n",
    "    def predict(self, state, sess=None):\n",
    "        sess = sess or tf.get_default_session()\n",
    "        return sess.run(self.value_estimate, { self.state: state })\n",
    "\n",
    "    def update(self, state, target, sess=None):\n",
    "        sess = sess or tf.get_default_session()\n",
    "        feed_dict = { self.state: state, self.target: target }\n",
    "        _, loss = sess.run([self.train_op, self.loss], feed_dict)\n",
    "        return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def actor_critic(env, estimator_policy, estimator_value, num_episodes, discount_factor=1.0):\n",
    "    \"\"\"\n",
    "    Actor Critic Algorithm. Optimizes the policy \n",
    "    function approximator using policy gradient.\n",
    "    \n",
    "    Args:\n",
    "        env: OpenAI environment.\n",
    "        estimator_policy: Policy Function to be optimized \n",
    "        estimator_value: Value function approximator, used as a baseline\n",
    "        num_episodes: Number of episodes to run for\n",
    "        discount_factor: Time-discount factor\n",
    "    \n",
    "    Returns:\n",
    "        An EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.\n",
    "    \"\"\"\n",
    "\n",
    "    # Keeps track of useful statistics\n",
    "    stats = plotting.EpisodeStats(\n",
    "        episode_lengths=np.zeros(num_episodes),\n",
    "        episode_rewards=np.zeros(num_episodes))    \n",
    "    \n",
    "    Transition = collections.namedtuple(\"Transition\", [\"state\", \"action\", \"reward\", \"next_state\", \"done\"])\n",
    "    \n",
    "    for i_episode in range(num_episodes):\n",
    "        # Reset the environment and pick the fisrst action\n",
    "        state = env.reset()\n",
    "        \n",
    "        episode = []\n",
    "        \n",
    "        # One step in the environment\n",
    "        for t in itertools.count():\n",
    "            \n",
    "            # Take a step\n",
    "            action_probs = estimator_policy.predict(state)\n",
    "            action = np.random.choice(np.arange(len(action_probs)), p=action_probs)\n",
    "            next_state, reward, done, _ = env.step(action)\n",
    "            \n",
    "            # Keep track of the transition\n",
    "            episode.append(Transition(\n",
    "              state=state, action=action, reward=reward, next_state=next_state, done=done))\n",
    "            \n",
    "            # Update statistics\n",
    "            stats.episode_rewards[i_episode] += reward\n",
    "            stats.episode_lengths[i_episode] = t\n",
    "            \n",
    "            # Calculate TD Target\n",
    "            value_next = estimator_value.predict(next_state)\n",
    "            td_target = reward + discount_factor * value_next\n",
    "            td_error = td_target - estimator_value.predict(state)\n",
    "            \n",
    "            # Update the value estimator\n",
    "            estimator_value.update(state, td_target)\n",
    "            \n",
    "            # Update the policy estimator\n",
    "            # using the td error as our advantage estimate\n",
    "            estimator_policy.update(state, td_error, action)\n",
    "            \n",
    "            # Print out which step we're on, useful for debugging.\n",
    "            print(\"\\rStep {} @ Episode {}/{} ({})\".format(\n",
    "                    t, i_episode + 1, num_episodes, stats.episode_rewards[i_episode - 1]), end=\"\")\n",
    "\n",
    "            if done:\n",
    "                break\n",
    "                \n",
    "            state = next_state\n",
    "    \n",
    "    return stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 12 @ Episode 300/300 (-13.0)"
     ]
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "global_step = tf.Variable(0, name=\"global_step\", trainable=False)\n",
    "policy_estimator = PolicyEstimator()\n",
    "value_estimator = ValueEstimator()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.initialize_all_variables())\n",
    "    # Note, due to randomness in the policy the number of episodes you need to learn a good\n",
    "    # policy may vary. ~300 seemed to work well for me.\n",
    "    stats = actor_critic(env, policy_estimator, value_estimator, 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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BPQXZ2dnNHqMXtiBvwoQJTJgwAfBv1fPOO+9w++23U1RUREpKCsYYPvnkE7p06QL4F/Bc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\nhBBCeCBJ8oQQQgghPND/A9ecK9SQ5fZsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119472a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JyVi/fj0mTZoEAPKaacUnaSQmJho0gRat0s4YY4wxVh2sW7dO/j00NNRg3Upj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\n8r0Oiz23282BAwdatV18fMstt/glEGPMJW179+5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zc4mNjb3SX0OuQO/evX3KeXNsLGfB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11945add8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6GuBnACJb610JOSCrt+Tt27cPr7/+Opo3b46wsDDs3LkTCxcuxIsvvog2bdpc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119dff278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x119472a58>,\n",
       " <matplotlib.figure.Figure at 0x11945add8>,\n",
       " <matplotlib.figure.Figure at 0x119dff278>)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotting.plot_episode_stats(stats, smoothing_window=10)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}