DDDQN-VizDoom.ipynb

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   "cell_type": "raw",
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   "cell_type": "markdown",
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   "source": [
    "# Simple Reinforcement Learning with Tensorflow Part 4: Deep Q-Networks and Beyond\n",
    "\n",
    "In this iPython notebook I implement a Deep Q-Network using both Double DQN and Dueling DQN. The agent learn to kill creature in VizDoom. \n",
    "\n",
    "To learn more, read here: https://medium.com/p/8438a3e2b8df\n",
    "\n",
    "For more reinforcment learning tutorials, see:\n",
    "https://github.com/awjuliani/DeepRL-Agents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "\n",
    "\n",
    "import gym\n",
    "\n",
    "import numpy as np\n",
    "import random\n",
    "import tensorflow as tf\n",
    "import tensorflow.contrib.slim as slim\n",
    "from helper import make_gif\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.misc\n",
    "import os\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the game environment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Feel free to change the Vizdoom map!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[True, False, False], [False, True, False], [False, False, True]]\n"
     ]
    }
   ],
   "source": [
    "from vizdoom import *\n",
    "a_size = 3 # Agent can move Left, Right, or Fire\n",
    "\n",
    "#The Below code is related to setting up the Doom environment\n",
    "game = DoomGame()\n",
    "game.set_doom_scenario_path(\"defend_the_center.wad\")  #This corresponds to the simple task we will pose our agent\n",
    "game.load_config(\"../../scenarios/rocket_basic.cfg\")\n",
    "game.set_doom_map(\"map01\")\n",
    "game.set_screen_resolution(ScreenResolution.RES_160X120)\n",
    "game.set_screen_format(ScreenFormat.GRAY8)\n",
    "game.set_render_hud(False)\n",
    "game.set_render_crosshair(False)\n",
    "game.set_render_weapon(True)\n",
    "game.set_render_decals(False)\n",
    "game.set_render_particles(False)\n",
    "\n",
    "game.add_available_button(Button.TURN_LEFT)\n",
    "game.add_available_button(Button.TURN_RIGHT)\n",
    "game.add_available_button(Button.ATTACK)\n",
    "actions_list = np.identity(a_size,dtype=bool).tolist()\n",
    "print(actions_list)\n",
    "\n",
    "game.add_available_game_variable(GameVariable.AMMO2)\n",
    "game.add_available_game_variable(GameVariable.POSITION_X)\n",
    "game.add_available_game_variable(GameVariable.POSITION_Y)\n",
    "game.set_episode_timeout(300)\n",
    "game.set_episode_start_time(10)\n",
    "game.set_window_visible(False)\n",
    "game.set_sound_enabled(False)\n",
    "#game.set_living_reward(-1)\n",
    "game.set_mode(Mode.PLAYER)\n",
    "game.init()\n",
    "\n",
    "#End Doom set-up\n",
    "\n",
    "env = game\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above is an example of a starting environment in our simple game. The agent controls the blue square, and can move up, down, left, or right. The goal is to move to the green square (for +1 reward) and avoid the red square (for -1 reward). The position of the three blocks is randomized every episode."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing the network itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Qnetwork():\n",
    "    def __init__(self,h_size):\n",
    "        #The network recieves a frame from the game, flattened into an array.\n",
    "        #It then resizes it and processes it through four convolutional layers.\n",
    "        self.scalarInput =  tf.placeholder(shape=[None,7056],dtype=tf.float32)\n",
    "        self.imageIn = tf.reshape(self.scalarInput,shape=[-1,84,84,1])\n",
    "        self.conv1 = slim.conv2d( \\\n",
    "            inputs=self.imageIn,num_outputs=32,kernel_size=[8,8],stride=[4,4],padding='VALID', biases_initializer=None)\n",
    "        self.conv2 = slim.conv2d( \\\n",
    "            inputs=self.conv1,num_outputs=64,kernel_size=[4,4],stride=[2,2],padding='VALID', biases_initializer=None)\n",
    "        self.conv3 = slim.conv2d( \\\n",
    "            inputs=self.conv2,num_outputs=64,kernel_size=[3,3],stride=[1,1],padding='VALID', biases_initializer=None)\n",
    "        self.conv4 = slim.conv2d( \\\n",
    "            inputs=self.conv3,num_outputs=h_size,kernel_size=[7,7],stride=[1,1],padding='VALID', biases_initializer=None)\n",
    "        \n",
    "        #We take the output from the final convolutional layer and split it into separate advantage and value streams.\n",
    "        self.streamAC,self.streamVC = tf.split(self.conv4,2,3)\n",
    "        self.streamA = slim.flatten(self.streamAC)\n",
    "        self.streamV = slim.flatten(self.streamVC)\n",
    "        xavier_init = tf.contrib.layers.xavier_initializer()\n",
    "        self.AW = tf.Variable(xavier_init([h_size//2,a_size]))\n",
    "        self.VW = tf.Variable(xavier_init([h_size//2,1]))\n",
    "        self.Advantage = tf.matmul(self.streamA,self.AW)\n",
    "        self.Value = tf.matmul(self.streamV,self.VW)\n",
    "        \n",
    "        #Then combine them together to get our final Q-values.\n",
    "        self.Qout = self.Value + tf.subtract(self.Advantage,tf.reduce_mean(self.Advantage,axis=1,keep_dims=True))\n",
    "        self.predict = tf.argmax(self.Qout,1)\n",
    "        \n",
    "        #Below we obtain the loss by taking the sum of squares difference between the target and prediction Q values.\n",
    "        self.targetQ = tf.placeholder(shape=[None],dtype=tf.float32)\n",
    "        self.actions = tf.placeholder(shape=[None],dtype=tf.int32)\n",
    "        self.actions_onehot = tf.one_hot(self.actions,a_size,dtype=tf.float32)\n",
    "        \n",
    "        self.Q = tf.reduce_sum(tf.multiply(self.Qout, self.actions_onehot), axis=1)\n",
    "        \n",
    "        self.td_error = tf.square(self.targetQ - self.Q)\n",
    "        self.loss = tf.reduce_mean(self.td_error)\n",
    "        self.trainer = tf.train.AdamOptimizer(learning_rate=0.0001)\n",
    "        self.updateModel = self.trainer.minimize(self.loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experience Replay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This class allows us to store experies and sample then randomly to train the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class experience_buffer():\n",
    "    def __init__(self, buffer_size = 50000):\n",
    "        self.buffer = []\n",
    "        self.buffer_size = buffer_size\n",
    "    \n",
    "    def add(self,experience):\n",
    "        if len(self.buffer) + len(experience) >= self.buffer_size:\n",
    "            self.buffer[0:(len(experience)+len(self.buffer))-self.buffer_size] = []\n",
    "        self.buffer.extend(experience)\n",
    "            \n",
    "    def sample(self,size):\n",
    "        return np.reshape(np.array(random.sample(self.buffer,size)),[size,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a simple function to resize our game frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def processState(states):\n",
    "    return np.reshape(states,[21168])\n",
    "\n",
    "# Processes Doom screen image to produce cropped and resized image. \n",
    "def process_frame(frame):\n",
    "    s = frame[10:-10,30:-30]\n",
    "    s = scipy.misc.imresize(s,[84,84])\n",
    "    s = np.reshape(s,[np.prod(s.shape)]) / 255.0\n",
    "    return s\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These functions allow us to update the parameters of our target network with those of the primary network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def updateTargetGraph(tfVars,tau):\n",
    "    #tfVars are all the trainable values of the computation graph, e.i. all the weights of the networks (main and target)\n",
    "    #tau is the the ratio to which we update the Target network with respect to the Main network\n",
    "    total_vars = len(tfVars)\n",
    "    op_holder = []\n",
    "    #Here we need to understand the structure of the tfVars array.\n",
    "    #The first half entries are the trainable values of the Main Network\n",
    "    #The last half entries are the trainable values of the Main Network\n",
    "    for idx,var in enumerate(tfVars[0:total_vars//2]):\n",
    "        #New_targetNet_values = tau * New_MainNet_values + (1 - tau) * Old_MainNet_values\n",
    "        op_holder.append(tfVars[idx+total_vars//2].assign((var.value()*tau) + ((1-tau)*tfVars[idx+total_vars//2].value())))\n",
    "    return op_holder\n",
    "\n",
    "#This function just runs the session to compute the above expression\n",
    "def updateTarget(op_holder,sess):\n",
    "    for op in op_holder:\n",
    "        sess.run(op)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting all the training parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 32 #How many experiences to use for each training step.\n",
    "update_freq = 4 #How often to perform a training step.\n",
    "y = .99 #Discount factor on the target Q-values\n",
    "startE = 1 #Starting chance of random action\n",
    "endE = 0.1 #Final chance of random action\n",
    "annealing_steps = 10000. #How many steps of training to reduce startE to endE.\n",
    "num_episodes = 10000 #How many episodes of game environment to train network with.\n",
    "pre_train_steps = 10000 #How many steps of random actions before training begins.\n",
    "max_epLength = 300 #The max allowed length of our episode.\n",
    "load_model = False #Whether to load a saved model.\n",
    "path = \"./dqn\" #The path to save our model to.\n",
    "h_size = 512 #The size of the final convolutional layer before splitting it into Advantage and Value streams.\n",
    "tau = 0.001 #Rate to update target network toward primary network\n",
    "saveframes = True\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": true
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      "Saved Model\n"
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      "Percent of succesful episodes: 65.931%\n"
     ]
    }
   ],
   "source": [
    "\n",
    "if saveframes == True:\n",
    "    if not os.path.exists('./DDDQN_VizDoom_frames'):\n",
    "        os.makedirs('./DDDQN_VizDoom_frames')\n",
    "        \n",
    "tf.reset_default_graph()\n",
    "mainQN = Qnetwork(h_size)\n",
    "targetQN = Qnetwork(h_size)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "#trainable variables of the Main Network and the Target Network\n",
    "trainables = tf.trainable_variables()\n",
    "\n",
    "targetOps = updateTargetGraph(trainables,tau)\n",
    "\n",
    "myBuffer = experience_buffer()\n",
    "\n",
    "#Set the rate of random action decrease. \n",
    "e = startE\n",
    "stepDrop = (startE - endE)/annealing_steps\n",
    "\n",
    "#create lists to contain total rewards and steps per episodes\n",
    "jList = []\n",
    "rList = []\n",
    "total_steps = 0\n",
    "\n",
    "\n",
    "#Make a path for our model to be saved in.\n",
    "if not os.path.exists(path):\n",
    "    os.makedirs(path)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "    if load_model == True:\n",
    "        print('Loading Model...')\n",
    "        ckpt = tf.train.get_checkpoint_state(path)\n",
    "        saver.restore(sess,ckpt.model_checkpoint_path)\n",
    "    for i in range(num_episodes):\n",
    "        #GAther episode frames to create gifs eventuly\n",
    "        episode_frames = []\n",
    "        episodeBuffer = experience_buffer()\n",
    "        #Reset environment and get first new observation\n",
    "        env.new_episode()\n",
    "        s = env.get_state().screen_buffer\n",
    "        s = process_frame(s)\n",
    "        d = False\n",
    "        rAll = 0\n",
    "        j = 0\n",
    "        #The Q-Network\n",
    "        while j < max_epLength: #If the agent takes longer than 200 moves to reach either of the blocks, end the trial.\n",
    "            j+=1\n",
    "            #Choose an action by greedily (with e chance of random action) from the Q-network\n",
    "            if np.random.rand(1) < e or total_steps < pre_train_steps:\n",
    "                a = np.random.randint(0,a_size)\n",
    "            else:\n",
    "                a = sess.run(mainQN.predict,feed_dict={mainQN.scalarInput:[s]})[0] #Feed through main network to predict action\n",
    "            \n",
    "            r = env.make_action(actions_list[a])\n",
    "            d = env.is_episode_finished()\n",
    "            if d == False:\n",
    "                s1 = env.get_state().screen_buffer\n",
    "            else:\n",
    "                break\n",
    "            episode_frames.append(s1)\n",
    "            s1 = process_frame(s1)\n",
    "            total_steps += 1\n",
    "            episodeBuffer.add(np.reshape(np.array([s,a,r,s1,d]),[1,5])) #Save the experience to our episode buffer.\n",
    "            \n",
    "            if total_steps > pre_train_steps:\n",
    "                if e > endE:\n",
    "                    e -= stepDrop #epsilon annealing\n",
    "                \n",
    "                if total_steps % (update_freq) == 0:\n",
    "                    #Get a random batch of experiences from the episode buffer\n",
    "                    trainBatch = myBuffer.sample(batch_size)\n",
    "                    \n",
    "                    #Below we perform the Double-DQN update to the target Q-values\n",
    "                    \n",
    "                    #First we calculate the best actions for state s1 in each experience of the batch using our Main Network\n",
    "                    A = sess.run(mainQN.predict,feed_dict={mainQN.scalarInput:np.vstack(trainBatch[:,3])})\n",
    "                    \n",
    "                    #Then we calculate the Qvalues for every selected experiences in the batch using our Target Network.\n",
    "                    #So Q2 is a 2D-array containing a vector of Q-values for each randomly selected experiences in the batch\n",
    "                    Q2 = sess.run(targetQN.Qout,feed_dict={targetQN.scalarInput:np.vstack(trainBatch[:,3])})\n",
    "                    \n",
    "                    #the end multiplier goes to zero if the experience is an \"end of game\", so the target Q-value = the reward\n",
    "                    end_multiplier = -(trainBatch[:,4] - 1) \n",
    "                    \n",
    "                    #doubleQs are the Q-values estimated from Q2 at state s1 given action A = argmax(Q1(s1,:)). \n",
    "                    #So doubleQ is a vector containing the estimated Q-values for the best action possible \n",
    "                    #for each randomly selected experience in the batch.\n",
    "                    doubleQ = Q2[range(batch_size),A]\n",
    "                    \n",
    "                    # Target-Q = r + gamma*(doubleQ) for non \"end-of-game\" experiences. Otherwise Target-Q = Reward\n",
    "                    targetQ = trainBatch[:,2] + (y*doubleQ * end_multiplier)\n",
    "                    \n",
    "                    #Update the Main network with our target Q-values.\n",
    "                    _ = sess.run(mainQN.updateModel, \\\n",
    "                                   #loss function to optimize                    \n",
    "                        feed_dict={mainQN.scalarInput:np.vstack(trainBatch[:,0]),mainQN.targetQ:targetQ, mainQN.actions:trainBatch[:,1]})\n",
    "                    \n",
    "                    #Update the Target network toward the main network but slowly (with a tau rate)\n",
    "                    updateTarget(targetOps,sess)\n",
    "                    \n",
    "            rAll += r\n",
    "            s = s1\n",
    "\n",
    "        \n",
    "        myBuffer.add(episodeBuffer.buffer)\n",
    "        jList.append(j)\n",
    "        rList.append(rAll)\n",
    "        #Periodically save the model. \n",
    "        if i % 500 == 0:\n",
    "            saver.save(sess,path+'/model-'+str(i)+'.ckpt')\n",
    "            print(\"Saved Model\")\n",
    "            time_per_step = 0.05\n",
    "            gif_cnt_down = 10\n",
    "            \n",
    "        if saveframes == True and 0 < gif_cnt_down < 11:\n",
    "            images = np.array(episode_frames)\n",
    "            make_gif(images,'./DDDQN_VizDoom_frames/image'+str(i)+'.gif', \n",
    "                     duration=len(images)*time_per_step,true_image=True,salience=False)\n",
    "            gif_cnt_down -= 1\n",
    "            \n",
    "        if len(rList) % 10 == 0:\n",
    "            print(total_steps,np.mean(rList[-10:]), e)\n",
    "    saver.save(sess,path+'/model-'+str(i)+'.ckpt')\n",
    "print(\"Percent of succesful episodes: \" + str(sum(rList)/num_episodes) + \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking network learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean reward over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x188c06aa630>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hv8A596hzrsA5V5CVldVNxez9mlv8fOXpVdz/1mYu/+0/OOf+d/njP7Yf8jVriqpJSojj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\nLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1886900c5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rMat = np.resize(np.array(rList),[len(rList)//100,100])\n",
    "rMean = np.average(rMat,1)\n",
    "plt.plot(rMean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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