FA/Q-Learning with Value Function Approximation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import itertools\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import sys\n",
    "import sklearn.pipeline\n",
    "import sklearn.preprocessing\n",
    "\n",
    "if \"../\" not in sys.path:\n",
    "  sys.path.append(\"../\") \n",
    "\n",
    "from lib import plotting\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn.kernel_approximation import RBFSampler\n",
    "\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2016-09-14 09:57:25,042] Making new env: MountainCar-v0\n"
     ]
    }
   ],
   "source": [
    "env = gym.envs.make(\"MountainCar-v0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FeatureUnion(n_jobs=1,\n",
       "       transformer_list=[('rbf1', RBFSampler(gamma=5.0, n_components=100, random_state=None)), ('rbf2', RBFSampler(gamma=2.0, n_components=100, random_state=None)), ('rbf3', RBFSampler(gamma=1.0, n_components=100, random_state=None)), ('rbf4', RBFSampler(gamma=0.5, n_components=100, random_state=None))],\n",
       "       transformer_weights=None)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Feature Preprocessing: Normalize to zero mean and unit variance\n",
    "# We use a few samples from the observation space to do this\n",
    "observation_examples = np.array([env.observation_space.sample() for x in range(10000)])\n",
    "scaler = sklearn.preprocessing.StandardScaler()\n",
    "scaler.fit(observation_examples)\n",
    "\n",
    "# Used to convert a state to a featurized representation.\n",
    "# We use RBF kernels with different variances to cover different parts of the space\n",
    "featurizer = sklearn.pipeline.FeatureUnion([\n",
    "        (\"rbf1\", RBFSampler(gamma=5.0, n_components=100)),\n",
    "        (\"rbf2\", RBFSampler(gamma=2.0, n_components=100)),\n",
    "        (\"rbf3\", RBFSampler(gamma=1.0, n_components=100)),\n",
    "        (\"rbf4\", RBFSampler(gamma=0.5, n_components=100))\n",
    "        ])\n",
    "featurizer.fit(scaler.transform(observation_examples))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Estimator():\n",
    "    \"\"\"\n",
    "    Value Function approximator. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        # We create a separate model for each action in the environment's\n",
    "        # action space. Alternatively we could somehow encode the action\n",
    "        # into the features, but this way it's easier to code up.\n",
    "        self.models = []\n",
    "        for _ in range(env.action_space.n):\n",
    "            model = SGDRegressor(learning_rate=\"constant\")\n",
    "            # We need to call partial_fit once to initialize the model\n",
    "            # or we get a NotFittedError when trying to make a prediction\n",
    "            # This is quite hacky.\n",
    "            model.partial_fit([self.featurize_state(env.reset())], [0])\n",
    "            self.models.append(model)\n",
    "    \n",
    "    def featurize_state(self, state):\n",
    "        \"\"\"\n",
    "        Returns the featurized representation for a state.\n",
    "        \"\"\"\n",
    "        scaled = scaler.transform([state])\n",
    "        featurized = featurizer.transform(scaled)\n",
    "        return featurized[0]\n",
    "    \n",
    "    def predict(self, s, a=None):\n",
    "        \"\"\"\n",
    "        Makes value function predictions.\n",
    "        \n",
    "        Args:\n",
    "            s: state to make a prediction for\n",
    "            a: (Optional) action to make a prediction for\n",
    "            \n",
    "        Returns\n",
    "            If an action a is given this returns a single number as the prediction.\n",
    "            If no action is given this returns a vector or predictions for all actions\n",
    "            in the environment where pred[i] is the prediction for action i.\n",
    "            \n",
    "        \"\"\"\n",
    "        # TODO: Implement this!\n",
    "        return 0 if a else np.zeros(env.action_space.n)\n",
    "    \n",
    "    def update(self, s, a, y):\n",
    "        \"\"\"\n",
    "        Updates the estimator parameters for a given state and action towards\n",
    "        the target y.\n",
    "        \"\"\"\n",
    "        # TODO: Implement this!\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_epsilon_greedy_policy(estimator, epsilon, nA):\n",
    "    \"\"\"\n",
    "    Creates an epsilon-greedy policy based on a given Q-function approximator and epsilon.\n",
    "    \n",
    "    Args:\n",
    "        estimator: An estimator that returns q values for a given state\n",
    "        epsilon: The probability to select a random action . float between 0 and 1.\n",
    "        nA: Number of actions in the environment.\n",
    "    \n",
    "    Returns:\n",
    "        A function that takes the observation as an argument and returns\n",
    "        the probabilities for each action in the form of a numpy array of length nA.\n",
    "    \n",
    "    \"\"\"\n",
    "    def policy_fn(observation):\n",
    "        A = np.ones(nA, dtype=float) * epsilon / nA\n",
    "        q_values = estimator.predict(observation)\n",
    "        best_action = np.argmax(q_values)\n",
    "        A[best_action] += (1.0 - epsilon)\n",
    "        return A\n",
    "    return policy_fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def q_learning(env, estimator, num_episodes, discount_factor=1.0, epsilon=0.1, epsilon_decay=1.0):\n",
    "    \"\"\"\n",
    "    Q-Learning algorithm for off-policy TD control using Function Approximation.\n",
    "    Finds the optimal greedy policy while following an epsilon-greedy policy.\n",
    "    \n",
    "    Args:\n",
    "        env: OpenAI environment.\n",
    "        estimator: Action-Value function estimator\n",
    "        num_episodes: Number of episodes to run for.\n",
    "        discount_factor: Gamma discount factor.\n",
    "        epsilon: Chance the sample a random action. Float betwen 0 and 1.\n",
    "        epsilon_decay: Each episode, epsilon is decayed by this 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",
    "    for i_episode in range(num_episodes):\n",
    "        \n",
    "        # The policy we're following\n",
    "        policy = make_epsilon_greedy_policy(\n",
    "            estimator, epsilon * epsilon_decay**i_episode, env.action_space.n)\n",
    "        \n",
    "        # Print out which episode we're on, useful for debugging.\n",
    "        # Also print reward for last episode\n",
    "        last_reward = stats.episode_rewards[i_episode - 1]\n",
    "        print(\"\\rEpisode {}/{} ({})\".format(i_episode + 1, num_episodes, last_reward), end=\"\")\n",
    "        sys.stdout.flush()\n",
    "        \n",
    "        # TODO: Implement this!\n",
    "    \n",
    "    return stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "estimator = Estimator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 100/100 (0.0)"
     ]
    }
   ],
   "source": [
    "# Note: For the Mountain Car we don't actually need an epsilon > 0.0\n",
    "# because our initial estimate for all states is too \"optimistic\" which leads\n",
    "# to the exploration of all states.\n",
    "stats = q_learning(env, estimator, 100, epsilon=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
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SUvr8kSNHcMcdd2D27NmYPn16Rq6Hkzq9zrCwW2RTbfedLxUd1tyAXGlQZOK9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\n8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Mc//oHz58/jn//8p2h6pKfxVgXNixcvoqqqCsuXL4fRaERLSwvWrl2LP/zhDzbHEx0d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\nzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11047e0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xQ5LUtWtXXX311crKylJgYKAmT57s9WFiAAAAs/Aq+JWXl2vAgAGeCwYGqqGh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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109b7860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bb7+Nr7/+GoMHDzb7zt7mns9jS9gT09gX0x61vrRs2RKDBw/G0aNH7+txHrW+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\nhBBCCCF04l9jFdkPt0mbZAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ef2c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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g+7U9e/YoPz9fHTt21P79+xUdHS3pSOj75ZdfglwdAABAw9RgAt2hQ4f05JNP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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110aa9d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotting.plot_cost_to_go_mountain_car(env, estimator)\n",
    "plotting.plot_episode_stats(stats, smoothing_window=25)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}