Q-Network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Reinforcement Learning with Tensorflow: Part 0 - Q-Networks\n",
    "In this iPython notebook we implement a Q-Network algorithm that solves the FrozenLake problem. To learn more, read here: https://medium.com/@awjuliani/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0\n",
    "\n",
    "For more reinforcment learning tutorials, see:\n",
    "https://github.com/awjuliani/DeepRL-Agents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "\n",
    "import gym\n",
    "import numpy as np\n",
    "import random\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2017-03-09 18:45:29,847] Making new env: FrozenLake-v0\n"
     ]
    }
   ],
   "source": [
    "env = gym.make('FrozenLake-v0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Q-Network Approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing the network itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "tf.reset_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#These lines establish the feed-forward part of the network used to choose actions\n",
    "inputs1 = tf.placeholder(shape=[1,16],dtype=tf.float32)\n",
    "W = tf.Variable(tf.random_uniform([16,4],0,0.01))\n",
    "Qout = tf.matmul(inputs1,W)\n",
    "predict = tf.argmax(Qout,1)\n",
    "\n",
    "#Below we obtain the loss by taking the sum of squares difference between the target and prediction Q values.\n",
    "nextQ = tf.placeholder(shape=[1,4],dtype=tf.float32)\n",
    "loss = tf.reduce_sum(tf.square(nextQ - Qout))\n",
    "trainer = tf.train.GradientDescentOptimizer(learning_rate=0.1)\n",
    "updateModel = trainer.minimize(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent of succesful episodes: 0.2685%\n"
     ]
    }
   ],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Set learning parameters\n",
    "y = .99\n",
    "e = 0.1\n",
    "num_episodes = 2000\n",
    "#create lists to contain total rewards and steps per episode\n",
    "jList = []\n",
    "rList = []\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "    for i in range(num_episodes):\n",
    "        #Reset environment and get first new observation\n",
    "        s = env.reset()\n",
    "        rAll = 0\n",
    "        d = False\n",
    "        j = 0\n",
    "        #The Q-Network\n",
    "        while j < 99:\n",
    "            j+=1\n",
    "            #Choose an action by greedily (with e chance of random action) from the Q-network\n",
    "            a,allQ = sess.run([predict,Qout],feed_dict={inputs1:np.identity(16)[s:s+1]})\n",
    "            if np.random.rand(1) < e:\n",
    "                a[0] = env.action_space.sample()\n",
    "            #Get new state and reward from environment\n",
    "            s1,r,d,_ = env.step(a[0])\n",
    "            #Obtain the Q' values by feeding the new state through our network\n",
    "            Q1 = sess.run(Qout,feed_dict={inputs1:np.identity(16)[s1:s1+1]})\n",
    "            #Obtain maxQ' and set our target value for chosen action.\n",
    "            maxQ1 = np.max(Q1)\n",
    "            targetQ = allQ\n",
    "            targetQ[0,a[0]] = r + y*maxQ1\n",
    "            #Train our network using target and predicted Q values\n",
    "            _,W1 = sess.run([updateModel,W],feed_dict={inputs1:np.identity(16)[s:s+1],nextQ:targetQ})\n",
    "            rAll += r\n",
    "            s = s1\n",
    "            if d == True:\n",
    "                #Reduce chance of random action as we train the model.\n",
    "                e = 1./((i/50) + 10)\n",
    "                break\n",
    "        jList.append(j)\n",
    "        rList.append(rAll)\n",
    "print(\"Percent of succesful episodes: \" + str(sum(rList)/num_episodes) + \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some statistics on network performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the network beings to consistly reach the goal around the 750 episode mark."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1211d9e90>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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tE7T7FPAD4FgB66s6+lCLhK9cLpC9DDiYdL89mjbCzJYBvw18o3CliYhIrgrVofo3wH3u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\ncBcRCdD/BzyrMqQv30C5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11de39990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rList)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It also begins to progress through the environment for longer than chance aroudn the 750 mark as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1216d8750>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vw1IMoIfWhUQ0hYhWENGKsrLwbCzAmMNIea0p0E7xa5TUTL+e6GnJ5xftRH1j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\n2cwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1212b9fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(jList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:py2]",
   "language": "python",
   "name": "conda-env-py2-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}