Exp8.ipynb

{
 "metadata": {
  "name": "Exp8"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Mountain Car\n",
      "from stuff import *\n",
      "from pylab import *\n",
      "from random import *\n",
      "import numpy\n",
      "from rl import *\n",
      "\n",
      "ACTION_SPACE=[-1,0,1] #Departing from the convention A = [0..card(A)] may be a bad idea. FIXME change this when I get around to it.\n",
      "\n",
      "def mountain_car_next_state(state,action):\n",
      "    position,speed=state\n",
      "    next_speed = squeeze(speed+action*0.001+cos(3*position)*(-0.0025))\n",
      "    next_position = squeeze(position+next_speed)\n",
      "    if not -0.07 <= next_speed <= 0.07:\n",
      "        next_speed = sign(next_speed)*0.07\n",
      "    if not -1.2 <= next_position <= 0.6:\n",
      "        next_speed=0.\n",
      "        next_position = -1.2 if next_position < -1.2 else 0.6\n",
      "    return array([next_position,next_speed])\n",
      "\n",
      "def mountain_car_uniform_state():\n",
      "    return array([numpy.random.uniform(low=-1.2,high=0.6),numpy.random.uniform(low=-0.07,high=0.07)])\n",
      "mountain_car_mu_position, mountain_car_mu_speed = meshgrid(linspace(-1.2,0.6,7),linspace(-0.07,0.07,7))\n",
      "\n",
      "mountain_car_sigma_position = 2*pow((0.6+1.2)/10.,2)\n",
      "mountain_car_sigma_speed = 2*pow((0.07+0.07)/10.,2)\n",
      "\n",
      "def mountain_car_single_psi(state):\n",
      "    position,speed=state\n",
      "    psi=[]\n",
      "    for mu in zip_stack(mountain_car_mu_position, mountain_car_mu_speed).reshape(7*7,2):\n",
      "        psi.append(exp( -pow(position-mu[0],2)/mountain_car_sigma_position \n",
      "                        -pow(speed-mu[1],2)/mountain_car_sigma_speed))\n",
      "    psi.append(1.)\n",
      "    return array(psi).reshape((7*7+1,1))\n",
      "\n",
      "mountain_car_psi= non_scalar_vectorize(mountain_car_single_psi,(2,),(50,1))\n",
      "\n",
      "def mountain_car_single_phi(sa):\n",
      "    state=sa[:2]\n",
      "    index_action = int(sa[-1])+1\n",
      "    answer=zeros(((7*7+1)*3,1))\n",
      "    answer[index_action*(7*7+1):index_action*(7*7+1)+7*7+1] = mountain_car_single_psi(state)\n",
      "    return answer\n",
      "\n",
      "mountain_car_phi= non_scalar_vectorize(mountain_car_single_phi,(3,),(150,1))\n",
      "\n",
      "def mountain_car_reward(sas):\n",
      "    position=sas[0]\n",
      "    return 1 if position > 0.5 else 0\n",
      "\n",
      "def mountain_car_episode_length(initial_position,initial_speed,policy):\n",
      "    answer = 0\n",
      "    reward = 0.\n",
      "    state = array([initial_position,initial_speed])\n",
      "    while answer < 300 and reward == 0. :\n",
      "        action = policy(state)\n",
      "        next_state = mountain_car_next_state(state,action)\n",
      "        reward = mountain_car_reward(hstack([state, action, next_state]))\n",
      "        state=next_state\n",
      "        answer+=1\n",
      "    return answer\n",
      "\n",
      "def mountain_car_episode_vlength(policy):\n",
      "    return vectorize(lambda p,s:mountain_car_episode_length(p,s,policy))\n",
      "\n",
      "\n",
      "def mountain_car_training_data(freward=mountain_car_reward,traj_length=5,nb_traj=1000):\n",
      "    traj = []\n",
      "    random_policy = lambda s:choice(ACTION_SPACE)\n",
      "    for i in range(0,nb_traj):\n",
      "        state = mountain_car_uniform_state()\n",
      "        reward=0\n",
      "        t=0\n",
      "        while t < traj_length and reward == 0:\n",
      "            t+=1\n",
      "            action = random_policy(state)\n",
      "            next_state = mountain_car_next_state(state, action)\n",
      "            reward = freward(hstack([state, action, next_state]))\n",
      "            traj.append(hstack([state, action, next_state, reward]))\n",
      "            state=next_state\n",
      "    return array(traj)\n",
      "def mountain_car_plot( f, draw_contour=True, contour_levels=50, draw_surface=False ):\n",
      "    '''Display a surface plot of function f over the state space'''\n",
      "    pos = linspace(-1.2,0.6,30)\n",
      "    speed = linspace(-0.07,0.07,30)\n",
      "    pos,speed = meshgrid(pos,speed)\n",
      "    Z = f(pos,speed)\n",
      "    #fig = figure()\n",
      "    if draw_surface:\n",
      "        ax=Axes3D(fig)\n",
      "        ax.plot_surface(pos,speed,Z)\n",
      "    if draw_contour:\n",
      "        contourf(pos,speed,Z,levels=linspace(min(Z.reshape(-1)),max(Z.reshape(-1)),contour_levels+1))\n",
      "        colorbar()\n",
      "def mountain_car_plot_policy( policy ):\n",
      "    two_args_pol = lambda p,s:squeeze(policy(zip_stack(p,s)))\n",
      "    mountain_car_plot(two_args_pol,contour_levels=3)\n",
      "\n",
      "def mountain_car_V(omega):\n",
      "    policy = greedy_policy( omega, mountain_car_phi, ACTION_SPACE )\n",
      "    def V(pos,speed):\n",
      "        actions = policy(zip_stack(pos,speed))\n",
      "        Phi=mountain_car_phi(zip_stack(pos,speed,actions))\n",
      "        return squeeze(dot(omega.transpose(),Phi))\n",
      "    return V\n",
      "\n",
      "def mountain_car_interesting_state():\n",
      "    position = numpy.random.uniform(low=-1.2,high=-0.9)\n",
      "    speed = numpy.random.uniform(low=-0.07,high=0)\n",
      "    return array([position,speed])\n",
      "\n",
      "def mountain_car_IRL_traj():\n",
      "    traj = []\n",
      "    state = mountain_car_interesting_state()\n",
      "    reward = 0\n",
      "    while reward == 0:\n",
      "        action = mountain_car_manual_policy(state)\n",
      "        next_state = mountain_car_next_state(state, action)\n",
      "        next_action = mountain_car_manual_policy(next_state)\n",
      "        reward = mountain_car_reward(hstack([state, action, next_state]))\n",
      "        traj.append(hstack([state, action, next_state, next_action, reward]))\n",
      "        state=next_state\n",
      "    return array(traj)\n",
      "\n",
      "def mountain_car_IRL_data(nbsamples):\n",
      "    data = mountain_car_IRL_traj()\n",
      "    while len(data) < nbsamples:\n",
      "        data = vstack([data,mountain_car_IRL_traj()])\n",
      "    return data[:nbsamples]\n",
      "\n",
      "def mountain_car_manual_policy(state):\n",
      "    position,speed = state\n",
      "    return -1. if speed <=0 else 1.\n",
      "\n",
      "TRAJS = mountain_car_IRL_data(1000)\n",
      "scatter(TRAJS[:,0],TRAJS[:,1],c=TRAJS[:,2])\n",
      "axis([-1.2,0.6,-0.07,0.07])\n",
      "phi=mountain_car_phi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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xqNW+YkuU8Gnn+PHjMnTQIOnYurW8/fbbf5vL7bZt2+S5IUNk7AsvyOHDh/32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\nZpLlcjFo8GAmTJzIpUuX+Pzzzzlz+jT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OHz5MmzZt7lg/OzsbrdlcZJ8TkJSYSEZGBrVq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\nyks0jiH24R4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mountain_car_RE_traj():\n",
      "    traj = []\n",
      "    state = mountain_car_interesting_state()\n",
      "    reward = 0\n",
      "    t=0\n",
      "    while reward == 0 and t<60:\n",
      "        t+=1\n",
      "        action = choice(ACTION_SPACE)\n",
      "        next_state = mountain_car_next_state(state, action)\n",
      "        reward = mountain_car_reward(hstack([state, action, next_state]))\n",
      "        traj.append(hstack([state, action, next_state, reward]))\n",
      "        state=next_state\n",
      "    return array(traj)\n",
      "\n",
      "data_r = vstack([mountain_car_RE_traj() for i in range(0,400)])\n",
      "savetxt(\"mountain_car_RE_trajs.mat\",data_r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sqrt(-log2(1-0.0001)/(2*70))*(pow(0.99,(70+1))-1)/(0.99-1)#Epsilon\n",
      "sqrt(-log2(1-0.1)/(2*300))*(pow(0.9,(300+1))-1)/(0.9-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "0.15916610476953783"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "GAMMA = 0.9\n",
      "\n",
      "def end_of_episode(data,i):\n",
      "    try:\n",
      "        if all(data[i,3:5] == data[i+1,:2]):\n",
      "            return False\n",
      "        else:\n",
      "            return True\n",
      "    except:\n",
      "        return True\n",
      "\n",
      "#Relative Entropy\n",
      "class GradientDescent(object):\n",
      "   def alpha( self, t ):\n",
      "      raise NotImplementedError, \"Cannot call abstract method\"\n",
      "\n",
      "   theta_0=None\n",
      "   Threshold=None\n",
      "   T = -1\n",
      "   sign = None\n",
      "        \n",
      "   def run( self, f_grad, f_proj=None, b_norm=False, b_best=True ): #grad is a function of theta\n",
      "      theta = self.theta_0.copy()\n",
      "      best_theta = theta.copy()\n",
      "      best_norm = float(\"inf\")\n",
      "      best_iter = 0\n",
      "      t=0\n",
      "      while True:#Do...while loop\n",
      "         t+=1\n",
      "         DeltaTheta = f_grad( theta )\n",
      "         current_norm = norm( DeltaTheta )\n",
      "         if b_norm and  current_norm > 0.:\n",
      "             DeltaTheta /= norm( DeltaTheta )\n",
      "         theta = theta + self.sign * self.alpha( t )*DeltaTheta\n",
      "         if f_proj:\n",
      "             theta = f_proj( theta )\n",
      "         print \"Norme du gradient : \"+str(current_norm)+\", pas : \"+str(self.alpha(t))+\", iteration : \"+str(t)\n",
      "\n",
      "         if current_norm < best_norm or not b_best:\n",
      "             best_norm = current_norm\n",
      "             best_theta = theta.copy()\n",
      "             best_iter = t\n",
      "         if current_norm < self.Threshold or (self.T != -1 and t >= self.T):\n",
      "             break\n",
      "\n",
      "      print \"Gradient de norme : \"+str(best_norm)+\", a l'iteration : \"+str(best_iter)\n",
      "      return best_theta\n",
      "                            \n",
      "class RelativeEntropy(GradientDescent):\n",
      "    sign=+1.\n",
      "    Threshold=0.01 #Sensible default\n",
      "    T=30 #Sensible default\n",
      "    Epsilon = 0.15 #RelEnt parameter, sensible default\n",
      "\n",
      "    def alpha(self, t):\n",
      "        return 1./(t+1)#Sensible default\n",
      "    \n",
      "    def __init__(self, mu_E, mus):\n",
      "        self.theta_0 = zeros(mu_E.shape)\n",
      "        self.Mu_E = mu_E\n",
      "        self.Mus = mus\n",
      "    \n",
      "    def gradient(self, theta):\n",
      "        numerator = 0\n",
      "        denominator = 0\n",
      "        for mu in self.Mus:\n",
      "            c = exp(dot(theta.transpose(),mu))\n",
      "            numerator += c*mu\n",
      "            denominator += c\n",
      "        assert denominator != 0,\"A sum of exp(...) is null, some black magic happened here.\"\n",
      "        return self.Mu_E - numerator/denominator - sign(theta)*self.Epsilon\n",
      "    \n",
      "    def run(self):\n",
      "        f_grad = lambda theta: self.gradient(theta)\n",
      "        theta = super(RelativeEntropy,self).run( f_grad, b_norm=True, b_best=False)\n",
      "        return theta\n",
      "\n",
      "    \n",
      "data_r_LSPI = genfromtxt(\"mountain_car_batch_data.mat\") #See Exp4 : rho uniform, M=1000, L=5\n",
      "data_r_RE = genfromtxt(\"mountain_car_RE_trajs.mat\") #rho  interesting, M=400, L<=60\n",
      "data_r_Other = mountain_car_training_data( nb_traj=50, traj_length=100) #rho uniform, M=50,L=100\n",
      "\n",
      "#Computing the feature expectations\n",
      "t=0.\n",
      "Mu_E = zeros(((7*7+1)*3,1))\n",
      "for i in range(0,len(TRAJS)):\n",
      "    Mu_E += pow(GAMMA,t)*mountain_car_phi(TRAJS[i,:3])\n",
      "    if end_of_episode(TRAJS,i):\n",
      "        t=0.\n",
      "    else:\n",
      "        t+=1.\n",
      "Mu_E /= float(len(TRAJS))\n",
      "\n",
      "Mus_LSPI=[]\n",
      "mu = zeros(((7*7+1)*3,1))\n",
      "t=0.\n",
      "for i in range(0,len(data_r_LSPI)):\n",
      "    mu += pow(GAMMA,t)*mountain_car_phi(data_r_LSPI[i,:3])\n",
      "    if end_of_episode(data_r_LSPI,i):\n",
      "        mu /= t+1.\n",
      "        Mus_LSPI.append(mu)\n",
      "        t=0.\n",
      "        mu = zeros(((7*7+1)*3,1))\n",
      "    else:\n",
      "        t += 1. \n",
      "#Mus_LSPI.append(Mu_E)\n",
      "\n",
      "#Mus_RE=[]\n",
      "#mu = zeros(((7*7+1)*3,1))\n",
      "#t=0.\n",
      "#for i in range(0,len(data_r_RE)):\n",
      "#    mu += pow(GAMMA,t)*mountain_car_phi(data_r_RE[i,:3])\n",
      "#    if end_of_episode(data_r_RE,i):\n",
      "#        mu /= t+1.\n",
      "#        Mus_RE.append(mu)\n",
      "#        t=0.\n",
      "#        mu = zeros(((7*7+1)*3,1))\n",
      "#    else:\n",
      "#        t += 1. \n",
      "#Mus_RE.append(Mu_E)\n",
      "\n",
      "#Mus_Other=[]\n",
      "#mu = zeros(((7*7+1)*3,1))\n",
      "#t=0.\n",
      "#for i in range(0,len(data_r_Other)):\n",
      "#    mu += pow(GAMMA,t)*mountain_car_phi(data_r_Other[i,:3])\n",
      "#   if end_of_episode(data_r_Other,i):\n",
      "#        mu /= t+1.\n",
      "#        Mus_Other.append(mu)\n",
      "#        t=0.\n",
      "#        mu = zeros(((7*7+1)*3,1))\n",
      "#    else:\n",
      "#        t += 1. \n",
      "#Mus_Other.append(Mu_E)\n",
      "\n",
      "RE_LSPI = RelativeEntropy(Mu_E, Mus_LSPI)\n",
      "theta_RE_LSPI = RE_LSPI.run()\n",
      "     \n",
      "#RE_RE = RelativeEntropy(Mu_E, Mus_RE)\n",
      "#theta_RE_RE = RE_RE.run()\n",
      "\n",
      "#RE_Other = RelativeEntropy(Mu_E, Mus_Other)\n",
      "#theta_RE_Other = RE_Other.run()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Norme du gradient : 0.403574892564, pas : 0.5, iteration : 1\n",
        "Norme du gradient : 1.67951530913, pas : 0.333333333333, iteration : 2\n",
        "Norme du gradient : 1.95114768823, pas : 0.25, iteration : 3\n",
        "Norme du gradient : 1.70436125785, pas : 0.2, iteration : 4\n",
        "Norme du gradient : 1.87219548185, pas : 0.166666666667, iteration : 5\n",
        "Norme du gradient : 1.8001662733, pas : 0.142857142857, iteration : 6"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Norme du gradient : 1.77274207301, pas : 0.125, iteration : 7\n",
        "Norme du gradient : 1.86016926467, pas : 0.111111111111, iteration : 8\n",
        "Norme du gradient : 1.77255412388, pas : 0.1, iteration : 9\n",
        "Norme du gradient : 1.86608461208, pas : 0.0909090909091, iteration : 10\n",
        "Norme du gradient : 1.77936044244, pas : 0.0833333333333, iteration : 11"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Norme du gradient : 1.85611324944, pas : 0.0769230769231, iteration : 12\n",
        "Norme du gradient : 1.79171426553, pas : 0.0714285714286, iteration : 13\n",
        "Norme du gradient : 1.83354296372, pas : 0.0666666666667, iteration : 14\n",
        "Norme du gradient : 1.81994085508, pas : 0.0625, iteration : 15\n",
        "Norme du gradient : 1.77151774373, pas : 0.0588235294118, iteration : 16"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Norme du gradient : 1.86707580598, pas : 0.0555555555556, iteration : 17\n",
        "Norme du gradient : 1.76104649579, pas : 0.0526315789474, iteration : 18\n",
        "Norme du gradient : 1.87440758713, pas : 0.05, iteration : 19\n",
        "Norme du gradient : 1.74790982069, pas : 0.047619047619, iteration : 20\n",
        "Norme du gradient : 1.8922684394, pas : 0.0454545454545, iteration : 21"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Norme du gradient : 1.74472574844, pas : 0.0434782608696, iteration : 22\n",
        "Norme du gradient : 1.90075033167, pas : 0.0416666666667, iteration : 23\n",
        "Norme du gradient : 1.7378467692, pas : 0.04, iteration : 24\n",
        "Norme du gradient : 1.90897213524, pas : 0.0384615384615, iteration : 25\n",
        "Norme du gradient : 1.72844560883, pas : 0.037037037037, iteration : 26"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Norme du gradient : 1.87875335112, pas : 0.0357142857143, iteration : 27\n",
        "Norme du gradient : 1.76844913919, pas : 0.0344827586207, iteration : 28\n",
        "Norme du gradient : 1.8414352556, pas : 0.0333333333333, iteration : 29\n",
        "Norme du gradient : 1.79628586254, pas : 0.0322580645161, iteration : 30\n",
        "Gradient de norme : 1.79628586254, a l'iteration : 30\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def RE_reward_LSPI(sas):\n",
      "    sa = sas[:3]\n",
      "    return squeeze(dot(theta_RE_LSPI.transpose(),mountain_car_phi(sa)))\n",
      "vRE_reward = non_scalar_vectorize( RE_reward_LSPI, (5,),(1,1) )\n",
      "data = genfromtxt(\"mountain_car_batch_data.mat\")\n",
      "data[:,5] = squeeze(vRE_reward(data[:,:5]))\n",
      "policy_RE_LSPI,omega_RE = lspi( data, s_dim=2,a_dim=1, A=ACTION_SPACE, phi=mountain_car_phi, phi_dim=150, iterations_max=20 )\n",
      "\n",
      "#def RE_reward_RE(sas):\n",
      "#    sa = sas[:3]\n",
      "#    return squeeze(dot(theta_RE_RE.transpose(),mountain_car_phi(sa)))\n",
      "#vRE_reward = non_scalar_vectorize( RE_reward_RE, (5,),(1,1) )\n",
      "#data = genfromtxt(\"mountain_car_batch_data.mat\")\n",
      "#data[:,5] = squeeze(vRE_reward(data[:,:5]))\n",
      "#policy_RE_RE,omega_RE = lspi( data, s_dim=2,a_dim=1, A=ACTION_SPACE, phi=mountain_car_phi, phi_dim=150, iterations_max=20 )\n",
      "\n",
      "#def RE_reward_Other(sas):\n",
      "#    sa = sas[:3]\n",
      "#    return squeeze(dot(theta_RE_Other.transpose(),mountain_car_phi(sa)))\n",
      "#vRE_reward = non_scalar_vectorize( RE_reward_Other, (5,),(1,1) )\n",
      "#data = genfromtxt(\"mountain_car_batch_data.mat\")\n",
      "#data[:,5] = squeeze(vRE_reward(data[:,:5]))\n",
      "#policy_RE_Other,omega_RE = lspi( data, s_dim=2,a_dim=1, A=ACTION_SPACE, phi=mountain_car_phi, phi_dim=150, iterations_max=20 )\n",
      "\n",
      "mountain_car_plot_policy(policy_RE_LSPI)\n",
      "#figure()\n",
      "#mountain_car_plot_policy(policy_RE_RE)\n",
      "#figure()\n",
      "#mountain_car_plot_policy(policy_RE_Other)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "LSPI, iter :1, diff : 4.81465117235\n",
        "LSPI, iter :2, diff : 1.18750132058"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "LSPI, iter :3, diff : 0.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plottable_episode_length = mountain_car_episode_vlength(policy_RE)\n",
      "X = linspace(-1.2,0.6,20)\n",
      "Y = linspace(-0.07,0.07,20)\n",
      "X,Y = meshgrid(X,Y)\n",
      "Z2 = plottable_episode_length(X,Y)\n",
      "figure()\n",
      "mountain_car_plot_policy(policy_RE)\n",
      "figure()\n",
      "contourf(X,Y,Z2,50)\n",
      "colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x3ff3758>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RCA52I0tubDYb7747tO6v7uhRI01NW98QQaMRKC3VUF+/89WQlZWRVFXd2vH7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\nQqGIEpTCVigUiihBKWyFQqGIEv4PCchrhYuFViQAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mountain_car_testing_state():\n",
      "    position = numpy.random.uniform(low=-1.2,high=0.5)\n",
      "    speed = numpy.random.uniform(low=-0.07,high=0.07)\n",
      "    return array([position,speed])\n",
      "\n",
      "def mountain_car_mean_performance(policy):\n",
      "    return mean([mountain_car_episode_length(state[0],state[1],policy) for state in [mountain_car_testing_state() for i in range(0,100)]])\n",
      "\n",
      "mountain_car_plot_policy(policy_RE)\n",
      "print mountain_car_mean_performance(policy_RE)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "125.25\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}