Basic Q-Learning algorithm using Tensorflow

Q-Net Learning Clean.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q-Network Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "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": [
      "INFO:gym.envs.registration:Making new env: FrozenLake-v0\n",
      "[2016-08-25 11:47:05,546] 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": 381,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "tf.reset_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "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": 383,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent of succesful episodes: 0.352%\n"
     ]
    }
   ],
   "source": [
    "init = tf.initialize_all_variables()\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": 384,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11a81e610>]"
      ]
     },
     "execution_count": 384,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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N/LpZyiZyy9RR5v3TxrUIIftC6DYvqi3ngNvSjyq4eieu5IJ+6hZ1CoJTG2liu2JcckF/\n0X+Rzar99R9/z7RPB9PqLtLmoso2+b4ybcz6BBbSj6J9bctRIVfvxJPSuJML+gCA6Vod9Lt29U7o\nujLlQrXt6p1Ft18WV++gr1od9MtoMpFbtI1ZZcomFduWyG3yG7kkctvTjypI5MaVXNBPHYlcFMF2\nxbjkgj6J3MWXbfJ9ZdogkdvuOrsgpXEnF/QBANO1OuiTyC2ORG759pvuE1CHVgd91Celj69t0Jb5\nbEs/qiCRG1eyQT/V++kv6uod7qff7r6VleKYUE2yQb8O3E+/vKb71od5J5EbT0rjJugDQI+0Ouh3\nLZHL/fTD13M/faAZrQ76AIC4kg36TSRyQ+6nX/T9RTV1G4ayn1jadK405pF+m8bVdVy9E1eyQb8O\nJHLLa7pvfZh3ErnxpDRugj4A9AhBHwB6pNVBv2tX74Suq6NcW67eWXT7ZXH1Dvqq1UG/ilS/kTtP\n2xK5bbif/qLKz5LSOeCmkciNK9mgXwcSueU13bc+zDuJ3HhSGjdBHwB6hKAPAD3S6qBPIrd8ORK5\nxdtvuk9AHVod9KsgkRtWjkRu+fKo3yIP1GbhnD4kkcitoum+Nd0+0BSCPhDZrH9sX3c/ulBnkTar\ntl/2n9y3YXvGQtAHgB4JCvpmttHMDpjZrWZ20YT1bzSzG7PHN83s+TE617VELvfTD1/P/fSBZswN\n+mZ2jKTLJZ0rab2kzWZ2+lixn0j6E3d/gaR/kHRl7I6GqhJMQgLwvGBapI1ZZRZ9Vcz4PJVNYle9\ntfIihewLodscSEXIkf4GSQfd/ZC7H5G0U9KmfAF3/667/yp7+V1Jq+N2sxvacD/9rkl1zKmOqwnc\nhiGukKC/WtKdudd3aXZQf6ukr1TpVBWL3jj5JF2ZtsbfM+0PRd1XBtW9U9fZ3qw/xiH9KJv8a1oq\nidw2SGncq2JWZmYvl3S+pLOnldm2bdtjzweDgQaDQcwuAEAC9mSP+EKC/mFJa3Ov12TLljGzMyVt\nl7TR3e+fVlk+6M9DIjds3aRyJHJnI5GLdhtkjyWXRKs55PTOXknrzOxkMztW0nmSduULmNlaSddK\nepO7/zha70ogkVusHIncyc+nlQG6bu6RvrsfNbOtknZr+Edih7vvN7Mtw9W+XdLfSzpe0sfNzCQd\ncfcNi+x4G5HILS7VMac6riaQyI0r6Jy+u18n6bSxZVfknl8g6YK4XSuHRO7sumeVrfOItkuJ3Bjt\nNSHlsdUtpXHzjVwA6BGCPgD0SKuDfteu3gldV0e5tly9s+j2y+LqHfRVq4N+EbOuRilaR9n3twH3\n0y/fVsyrd1I6B9y0NiRyU5JM0G8C99Mvr+m+9WHeSeTGk9K4CfoA0CMEfQDokVYHfRK55cuRyC3e\nftN9AurQ6qBfBIncIRK55dsikdtOJHLjSiboN4FEbnlN960P804iN56Uxk3QB4AeIegDQI+0Ouh3\nLZHL/fTD13M/faAZrQ76RZDIHWpbIrdK3VU1mcgF2iqZoN+E0Nskh9YRO1nU5uRT0/cpJ5Hbnjrb\n2GbKCPoA0CMEfQDoEYI+APRIq4N+lYRiSKIy5OqbSe8t+g+3Zy2fdsVP2W+yFr16p2gidl498+qq\n86qdovsAiVz0QauDfl9VCTKx7+VTVz1tkNJYUkIiNy6CfkEp/2P0OvGP0Rcv5bGhPII+APQIQR8A\neqTVQZ9E7vz6ptVPIpdELjBJq4N+X5HIbUZKY0kJeYS4CPoFkciNg0Tu4qU8NpRH0AeAHiHoA0CP\ntDrody2ROy0pO63MrPf0JZG7yPPoJHKBlVod9FFc2xK5XQqYXeorUBZBv6BZidyQ++mHvGfW8iLa\nkMidN746EoN1J3LbIpVEbsrbqAkEfQDoEYI+APQIQR8AeqTVQb+NV+8U7U+Z98zqc5U6Yrc1rZ6Q\nq3fqULQtrt5BHwQFfTPbaGYHzOxWM7toSpmPmtlBM7vBzM6K202EatvVO12S0lgkErmYbG7QN7Nj\nJF0u6VxJ6yVtNrPTx8q8UtKp7v4cSVskfXIBfcUKe5ruQFLuu29P011IyJ6mO4ApQo70N0g66O6H\n3P2IpJ2SNo2V2STpakly9+9JOs7MTozaU0ywp+kOJIWgH9OepjuAKUKC/mpJd+Ze35Utm1Xm8IQy\nAICGraq7wVe/OrzsI4+Ev+/o0eHP971PuvJK6de/Hr5+29tWtv/gg8Pn73iHdNxxo3W/+c3y+ia1\nefPN0v33L+/fUrlbbhmVO//84c+rrpIOHx4tf/jh5fV+6UujOu6+e/j8s58d9X/JxRev7Msk73//\n8OcVV0g//OH8chdcMPz56KOjdW9/e1hbknTNNcOfr3+9tCrbmx5+eLT+W99aXv7BB4djXerbxz4W\n3lZR118/bOuOO1auu+mm4bp9+0bLDh2aXM+3v12s3aNHpdWrpYMHi70vtkcflU45RfrpT5fv21Uc\n08ClHyecMHp+0knS7beXr+ukk6Rf/jK8/KmnDueviXEvivmc7JWZvUTSNnffmL1+tyR39w/mynxS\n0tfd/TPZ6wOS/tTd7x2rK7FUGQDUw92jpLRDjvT3SlpnZidLulvSeZI2j5XZJelCSZ/J/kg8MB7w\npXidBgCUMzfou/tRM9sqabeGOYAd7r7fzLYMV/t2d/+ymb3KzG6T9JCk8xfbbQBAGXNP7wAA0lFb\neiLkC15YzsxuN7Mbzex6M/t+tuypZrbbzH5kZl81s+Ny5d+TfUFuv5md01zP28HMdpjZvWa2L7es\n8PyZ2QvNbF+2736k7nG0xZT5vNjM7jKzH2SPjbl1zOcUZrbGzP7LzH5oZjeZ2d9kyxe/f7r7wh8a\n/nG5TdLJkh4v6QZJp9fRdpcfkn4i6aljyz4o6V3Z84skfSB7/jxJ12t4yu5Z2Xxb02NoeP7OlnSW\npH1V5k/S9yS9OHv+ZUnnNj22Fs3nxZL+bkLZP2A+Z87lMySdlT1/kqQfSTq9jv2zriP9kC94YSXT\nyk9jmyRdlT2/StJrsud/IWmnu//W3W+XdFDDee8td/+mpPvHFheaPzN7hqQnu/verNzVuff0ypT5\nlIb76bhNYj6ncvd73P2G7PmDkvZLWqMa9s+6gn7IF7ywkkv6mpntNbO3ZstO9OzKKHe/R9LTs+V8\nQS7M0wvO32oN99cl7Lsrbc3uufWvudMRzGcgM3uWhp+gvqviv9+F5zOhrxwk6WXu/kJJr5J0oZn9\nsYZ/CPLIxFfD/FXzcUnPdvezJN0j6UMN96dTzOxJkj4n6W+zI/6F/37XFfQPS1qbe70mW4YZ3P3u\n7OfPJX1ew9M19y7d1yj7aHdfVvywpGfm3s4cT1Z0/pjXGdz9556dTJZ0pUanFJnPOcxslYYB/9/d\n/QvZ4oXvn3UF/ce+4GVmx2r4Ba9dNbXdSWb2u9lRgMzsiZLOkXSThvP2lqzYX0la2ll2STrPzI41\ns1MkrZP0/Vo73U6m5eecC81f9hH7V2a2wcxM0ptz7+mjZfOZBaYlr5V0c/ac+Zzv3yTd4u6X5ZYt\nfv+sMVu9UcMM9UFJ7246e972h6RTNLzK6XoNg/27s+XHS/qPbC53S/q93Hveo2FWf7+kc5oeQ9MP\nSZ+W9DNJ/yfpDg2/NPjUovMn6Q+zbXBQ0mVNj6tl83m1pH3Zvvp5Dc9JM5/z5/Jlko7mfsd/kMXI\nwr/fReeTL2cBQI+QyAWAHiHoA0CPEPQBoEcI+gDQIwR9AOgRgj4A9AhBHwB6hKAPAD3y/87pqc4G\nbAPBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c226450>"
      ]
     },
     "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": 385,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119bd5dd0>]"
      ]
     },
     "execution_count": 385,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hRCsACCHmAeicMg8mJf5O0n+snsuGpzoTyBOb6qAyd0o2YDuBdJRyTYCIfgKg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\nScI0boE9bMHeFoV+1T74IH0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TQRqDqAiBjh2r1qZt21Z35kj/PfKgbhP22af6Oc4fkD+c\nRMeVA1BdJwgzhAoihYDOHvdguUzwDzD8KixbHdj669fOBqTxWZaE/ZYS1eeUv49OZ1t0ddB3v6u2\nhuaKJO+qWZL7TODGG71R+DXXVB1S+bnrrmrnsNFGwPXXq6W71VbRHd3VV9d+D7qcfeghTy8fhtzm\nuP/+1WsXXKBWJtlh7bijt28/OM0eNqz2MI8w8jpoXb7UYY69wjjkEM/WQIU0C6g771y/JqHLXXd5\nJ0ZJHn00eodTI3HzzV5bV6FvX3X1xTXXRB9laZtBg5LdXqTh2mtr33VdnnlGfQ0pN4QQufwBEICo\nYfJkIbzuRoj11hM19wEh5s4V4r33qmHi/rbdthoPEOKaa6qf/dcBIc4/v/aaEEI8+WR4uuef7/1/\n+eX68kX9yfvjxnn/r7zSu3biibVpqPDEE8lxgnnb4Isv6tMDhOjdO33aXbrYLSvDNDJet22vL3Y2\nEyCiI4loKhFNJ6KQQwu9vdt+NtrIW5zbYgvvRDC/a+e11/am1lts4W0XDRrjnH2293+33bwzQOV3\nqeft0cPTbcrZQY8ewJ//7H2WxkP+8w3kFs1f/rJ67aijvPWDHj08dYffSVinTt4s5Te/8dRbvXp5\nIxSZ/4YbemU/7LCqu+BTTwVOOy2sZqLZY49k3+O77eY9m4oqRpWOHesPDzn66HBLXF0uu0zP6R/D\nMPYg4UB5R0RtAEwH0B3AXADvAOgphJjqCyNc5N2sjBw5Ei2qG9iZRLg+7cF1aRcighDCmr2xq5nA\nvgBmCCFmCSFWAHgUwLEJcZgUjBw5Mu8iNBRcn/bguiw2roTAZgA+9n2fU7nGMAzDFIjcdwcxDMMw\n+eFqTWB/AP2FEEdWvl8Fb0X7Zl8YXhBgGIYxwOaagCsh0BbANHgLw58CGA2glxBiivXMGIZhGGOc\nWAwLIVYR0UUAXoSnchrAAoBhGKZ4OJkJMAzDMOUgl4VhFUMyphYi+oiIxhPRWCIaXbm2ARG9SETT\niOgFIurkC9+XiGYQ0RQiSnE8fGNARAOIqJWIJviuadcfEe1JRBMqbfd/s36OohBRn/2IaA4Rjan8\nHem7x/UZARFtTkQjiGgSEb1PRJdUrmfTPm2aH6v8wRM8HwDYCsAaAMYB2CHrcpTtD8BMABsErt0M\n4MrK5z4Abqp83gnAWHjqvi6V+qa8nyHn+jsYwO4AJqSpPwBvA9in8vl5AD/O+9kKVJ/9APw2JOyO\nXJ+xdbkJgN0rn9eBt566Q1btM4+ZABuSmUGon7kdC2Bg5fNAABUHGDgGwKNCiJVCiI8AzIBX702L\nEGIUgEWBy1r1R0SbAFhXCPFOJdxDvjhNRUR9Al47DXIsuD4jEULME0KMq3xeAmAKgM2RUfvMQwiw\nIZkZAsB/iOgdIvpF5drGQohWwGtIADpXrgfr+BNwHYfRWbP+NoPXXiXcduu5iIjGEdH9PvUF16ci\nRNQF3gzrLei/30b1ycZi5eEgIcSeAI4C8Csi6gZPMPjhVf50cP2l4y4A2wghdgcwD8D/5FyeUkFE\n6wB4EsCllRlBJu93HkLgEwBb+r5vXrnGxCCE+LTyfz6AZ+Cpd1qJaGMAqEwFP6sE/wSA7zh3ruMI\ndOuP6zUGIcR8UVFGA7gPVRUk12cCRNQOngB4WAghT7PIpH3mIQTeAbAdEW1FRO0B9AQwJIdylAYi\nWqsySgARrQ3gCADvw6u3MyvBzgAgG88QAD2JqD0RbQ1gO3gGe80OoVZnrVV/lSn5YiLal4gIwOm+\nOM1ITX1WOirJCQAmVj5zfSbzdwCThRC3+65l0z5zWg0/Et4K+AwAV+W9Ol/0PwBbw9tFNRZe539V\n5fqGAIZX6vJFAOv74vSFt2tgCoAj8n6GvP8A/AOeW/NlAGYDOAvABrr1B2Cvym8wA8DteT9Xwerz\nIQATKm31GXg6ba7P5Lo8CMAq3zs+ptJHar/fJvXJxmIMwzBNDC8MMwzDNDEsBBiGYZoYFgIMwzBN\nDAsBhmGYJoaFAMMwTBPDQoBhGKaJYSHAMAzTxLAQYBiGaWL+H4KnWBkpJymUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a1d16d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(jList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}