Cart-Pole_RBF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inspired by https://github.com/dennybritz/reinforcement-learning\n",
    "import gym\n",
    "import os\n",
    "import sys\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from gym import wrappers\n",
    "from datetime import datetime\n",
    "from sklearn.pipeline import FeatureUnion\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.kernel_approximation import RBFSampler\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_running_avg(totalrewards):\n",
    "    N = len(totalrewards)\n",
    "    running_avg = np.empty(N)\n",
    "    for t in range(N):\n",
    "        running_avg[t] = totalrewards[max(0, t-100):(t+1)].mean()\n",
    "    plt.plot(running_avg)\n",
    "    plt.title(\"Running Average\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SGDRegressor:\n",
    "    def __init__(self, D):\n",
    "        self.w = np.random.randn(D) / np.sqrt(D)\n",
    "        self.lr = 0.1\n",
    "    def partial_fit(self, X, Y):\n",
    "        self.w += self.lr*(Y - X.dot(self.w)).dot(X)\n",
    "\n",
    "    def predict(self, X):\n",
    "        return X.dot(self.w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class FeatureTransformer:\n",
    "    def __init__(self, env):\n",
    "        # observation_examples = np.array([env.observation_space.sample() for x in range(10000)])\n",
    "        # NOTE!! state samples are poor, b/c you get velocities --> infinity\n",
    "        observation_examples = np.random.random((20000, 4))*2 - 1\n",
    "        scaler = StandardScaler()\n",
    "        scaler.fit(observation_examples)\n",
    "\n",
    "        # Used to converte a state to a featurizes represenation.\n",
    "        # We use RBF kernels with different variances to cover different parts of the space\n",
    "        featurizer = FeatureUnion([\n",
    "                (\"rbf1\", RBFSampler(gamma=0.05, n_components=1000)),\n",
    "                (\"rbf2\", RBFSampler(gamma=1.0, n_components=1000)),\n",
    "                (\"rbf3\", RBFSampler(gamma=0.5, n_components=1000)),\n",
    "                (\"rbf4\", RBFSampler(gamma=0.1, n_components=1000))\n",
    "                ])\n",
    "        feature_examples = featurizer.fit_transform(scaler.transform(observation_examples))\n",
    "\n",
    "        self.dimensions = feature_examples.shape[1]\n",
    "        self.scaler = scaler\n",
    "        self.featurizer = featurizer\n",
    "\n",
    "    def transform(self, observations):\n",
    "        scaled = self.scaler.transform(observations)\n",
    "        return self.featurizer.transform(scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Holds one SGDRegressor for each action\n",
    "class Model:\n",
    "    def __init__(self, env, feature_transformer):\n",
    "        self.env = env\n",
    "        self.models = []\n",
    "        self.feature_transformer = feature_transformer\n",
    "        for i in range(env.action_space.n):\n",
    "            model = SGDRegressor(feature_transformer.dimensions)\n",
    "            self.models.append(model)\n",
    "\n",
    "    def predict(self, s):\n",
    "        X = self.feature_transformer.transform(np.atleast_2d(s))\n",
    "        result = np.stack([m.predict(X) for m in self.models]).T\n",
    "        return result\n",
    "    \n",
    "    def update(self, s, a, G):\n",
    "        X = self.feature_transformer.transform(np.atleast_2d(s))\n",
    "        self.models[a].partial_fit(X, [G])\n",
    "\n",
    "    def sample_action(self, s, eps):\n",
    "        if np.random.random() < eps:\n",
    "              return self.env.action_space.sample()\n",
    "        else:\n",
    "              return np.argmax(self.predict(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_one(env, model, eps, gamma):\n",
    "    observation = env.reset()\n",
    "    done = False\n",
    "    totalreward = 0\n",
    "    iters = 0\n",
    "    while not done and iters < 2000:\n",
    "        # if we reach 2000, just quit, don't want this going forever\n",
    "        # the 200 limit seems a bit early\n",
    "        action = model.sample_action(observation, eps)\n",
    "        prev_observation = observation\n",
    "        observation, reward, done, info = env.step(action)\n",
    "\n",
    "        if done:\n",
    "            reward = -200\n",
    "\n",
    "    # update the model\n",
    "        next = model.predict(observation)\n",
    "        # print(next.shape)\n",
    "        assert(next.shape == (1, env.action_space.n))\n",
    "        G = reward + gamma*np.max(next)\n",
    "        model.update(prev_observation, action, G)\n",
    "\n",
    "        if reward == 1: # if we changed the reward to -200\n",
    "            totalreward += reward\n",
    "        iters += 1\n",
    "\n",
    "    return totalreward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def main():\n",
    "    env = gym.make('CartPole-v0')\n",
    "    ft = FeatureTransformer(env)\n",
    "    model = Model(env, ft)\n",
    "    gamma = 0.99\n",
    "\n",
    "    if 'monitor' in sys.argv:\n",
    "        filename = os.path.basename(__file__).split('.')[0]\n",
    "        monitor_dir = './' + filename + '_' + str(datetime.now())\n",
    "        env = wrappers.Monitor(env, monitor_dir)\n",
    "\n",
    "\n",
    "    N = 700\n",
    "    totalrewards = np.empty(N)\n",
    "    costs = np.empty(N)\n",
    "    for n in range(N):\n",
    "        eps = 1.0/np.sqrt(n+1)\n",
    "        totalreward = play_one(env, model, eps, gamma)\n",
    "        totalrewards[n] = totalreward\n",
    "        if n % 100 == 0:\n",
    "            print(\"episode:\", n, \"total reward:\", totalreward, \"eps:\", eps, \"avg reward (last 100):\", totalrewards[max(0, n-100):(n+1)].mean())\n",
    "\n",
    "    print(\"avg reward for last 100 episodes:\", totalrewards[-100:].mean())\n",
    "    print(\"total steps:\", totalrewards.sum())\n",
    "\n",
    "    plt.plot(totalrewards)\n",
    "    plt.title(\"Rewards\")\n",
    "    plt.show()\n",
    "\n",
    "    plot_running_avg(totalrewards)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARN: gym.spaces.Box autodetected dtype as <class 'numpy.float32'>. Please provide explicit dtype.\u001b[0m\n",
      "episode: 0 total reward: 11.0 eps: 1.0 avg reward (last 100): 11.0\n",
      "episode: 100 total reward: 199.0 eps: 0.099503719021 avg reward (last 100): 99.5148514851\n",
      "episode: 200 total reward: 147.0 eps: 0.0705345615859 avg reward (last 100): 142.069306931\n",
      "episode: 300 total reward: 93.0 eps: 0.0576390417704 avg reward (last 100): 179.910891089\n",
      "episode: 400 total reward: 146.0 eps: 0.0499376169439 avg reward (last 100): 156.95049505\n",
      "episode: 500 total reward: 155.0 eps: 0.0446767051609 avg reward (last 100): 164.138613861\n",
      "episode: 600 total reward: 193.0 eps: 0.0407908508224 avg reward (last 100): 186.128712871\n",
      "avg reward for last 100 episodes: 184.32\n",
      "total steps: 111299.0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEICAYAAABRSj9aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nt1gsljbHKnqLxWJpc/4/G4mh54KJuXgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116bc2860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEICAYAAABRSj9aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTJj7/8oNEGN46lF/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104025cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach :\n",
    "  The previous implementations of KBRL are unable to converge thus we now move to a different choice of kernel and method of implementation. We decide to use the Radial Basis Function (RBF) kernel.\n",
    "  \n",
    "  The RBF kernel model can be thought of as a linear  model with feature extraction where the feature extractor is a RBF kernel.\n",
    "  \n",
    "  Mathematically the RBF kernel can be expressed as:\n",
    "  $$\\phi (x)=exp(-\\frac{||x-c||^{2}}{\\sigma^{2}})$$\n",
    "  \n",
    "  where:\n",
    "         $x$= input vector\n",
    "         $c$ = center or exemplar vector\n",
    "         $\\sigma$ = scale parameter.\n",
    "         \n",
    "  Note that $c$ is a hyper-parameter and needs to be found by experimentation.\n",
    "  \n",
    "  We use the RBF-sampler from scikit-learn and sample from the state space to train a linear regresor to learns its feature.\n",
    "  \n",
    "  Since we are not sure which scale parameter $\\sigma$ is good we use multiple RBF kernels with different scale parameters. We also use one step of a gradient descent to integrate it with the Q learning mechanism.\n",
    "  \n",
    "Another implementation detail worth noting is that we only extract the features from the state $s$ and learn a different linear-model for each action which will give us the Q value for a different action.\n",
    "\n",
    "We use the partial_fit function from scikit learn library which implements one step gradient descent. Note that one complication in this implenetation is that since we are using Q-Learning we need to predict  $\\underset{a}{max}\\> Q(s,a)$ hence, we need to make a prediction before using the fit funtion. Thus one workaround for this issue is calling the partial fit funtion on dummy values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:py3k]",
   "language": "python",
   "name": "conda-env-py3k-py"
  },
  "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
}