obedience.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Should Robots Be Obedient?\n",
    "\n",
    "This is the accompanying Jupyter notebook for the paper  \n",
    "*\"Should Robots Be Obedient?\"* Smitha Milli, Dylan Hadfield-Menell, Anca Dragan, and Stuart Russell. IJCAI 2017. [arxiv](https://arxiv.org/abs/1705.09990)\n",
    "\n",
    "Every experiment in the paper can be replicated by running this notebook. In addition, it should be easy to play around and explore your own ideas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math, csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
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       "<matplotlib.figure.Figure at 0x115ee8f60>"
      ]
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     "metadata": {},
     "output_type": "display_data"
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   "source": [
    "default_palette = sns.cubehelix_palette(5, start=2.6, rot=0, dark=0.1, light=.8)\n",
    "sns.set_style('white')\n",
    "sns.set_context('paper', font_scale=1.4)\n",
    "sns.set_style({\n",
    "    'axes.linewidth' : 0.5, \n",
    "    'axes.edgecolor': '#cccccc',\n",
    "    'lines.markersize': 3,\n",
    "    'axes.spines.top': False,\n",
    "    'axes.spines.right': False,\n",
    "    'lines.marker': 'o',\n",
    "    'markers.fillstyle': 'full',\n",
    "    'errorbar.capsize': 2\n",
    "})\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Game:\n",
    "    \n",
    "    def __init__(self, num_actions, horizon,\n",
    "                 reward_mean_prior, reward_cov_prior,\n",
    "                 feat_mean_prior, feat_cov_prior):\n",
    "        \"\"\"\n",
    "        Params:\n",
    "            reward_mean_prior [np.ndarray]: E[theta]\n",
    "            reward_cov_prior [np.ndarray]: Cov[theta]\n",
    "            feat_mean_prior [np.ndarray]: E[phi]\n",
    "            feat_cov_prior [np.ndarray]: Cov[phi]\n",
    "            num_actions [int]: number of actions at each step\n",
    "            horizon [int]: horizon of game\n",
    "        \"\"\"\n",
    "        self.reward_mean_prior = reward_mean_prior\n",
    "        self.reward_cov_prior = reward_cov_prior\n",
    "        self.feat_mean_prior = feat_mean_prior\n",
    "        self.feat_cov_prior = feat_cov_prior\n",
    "        self.num_true_feats = len(self.feat_mean_prior)\n",
    "        self.num_extra_feats = len(feat_mean_prior) - len(reward_mean_prior)\n",
    "        self.feat_weights = np.random.multivariate_normal(\n",
    "            self.reward_mean_prior, self.reward_cov_prior)\n",
    "        self.feat_weights = np.hstack(\n",
    "            [self.feat_weights, np.zeros(self.num_extra_feats)])\n",
    "        self.num_actions = num_actions\n",
    "        self.horizon = horizon\n",
    "        self.action_matrix = np.random.multivariate_normal(\n",
    "            self.feat_mean_prior, self.feat_cov_prior, \n",
    "            size=(self.horizon, self.num_actions))\n",
    "        self.action_vals = np.dot(self.action_matrix, self.feat_weights.T)\n",
    "        \n",
    "    def get_reward(self, action, time):\n",
    "        reward = self.action_vals[time][action]\n",
    "        return reward\n",
    "    \n",
    "    def get_max_reward(self, time):\n",
    "        return np.max(self.action_vals[time])\n",
    "    \n",
    "    def get_action_matrix_at_steps(self, steps):\n",
    "        return self.action_matrix[steps]\n",
    "    \n",
    "    def get_action_matrix(self, max_step=None):\n",
    "        if max_step:\n",
    "            return self.action_matrix[:max_step]\n",
    "        return self.action_matrix\n",
    "        \n",
    "class Human:\n",
    "    \n",
    "    def __init__(self, rationality):\n",
    "        self.rationality = rationality\n",
    "        \n",
    "    def get_orders(self, game):\n",
    "        probs = self.get_prob_orders(game.action_vals)\n",
    "        inds = np.arange(game.num_actions)\n",
    "        orders = np.array(\n",
    "            [np.random.choice(inds, p=probs[i]) for i in range(len(probs))])\n",
    "        return orders\n",
    "    \n",
    "    def get_prob_orders(self, action_vals):\n",
    "        human_vals = action_vals/self.rationality\n",
    "        max_vals = np.array(np.max(human_vals, axis=1))[:,np.newaxis]\n",
    "        human_vals = human_vals - max_vals\n",
    "        unnormalized_probs = np.exp(human_vals)\n",
    "        normalizations = np.sum(unnormalized_probs, axis=1)\n",
    "        probs = unnormalized_probs/normalizations[:,np.newaxis]\n",
    "        return probs\n",
    "        \n",
    "class Robot:\n",
    "    \n",
    "    def __init__(self, num_feats):\n",
    "        \"\"\"\n",
    "        Params:\n",
    "            num_feats [int]: the number of feats the robot thinks theta has\n",
    "        \"\"\"\n",
    "        self.num_feats = num_feats\n",
    "        \n",
    "    def choose_action(self, game, time, theta_est):\n",
    "        action_matrix = game.action_matrix[time,:,:self.num_feats]\n",
    "        robot_action = np.argmax(np.matmul(action_matrix, theta_est))\n",
    "        return robot_action\n",
    "    \n",
    "    def get_robot_action_matrix(self, action_matrix):\n",
    "        \"\"\"\n",
    "        Truncates action matrix to features that robot thinks are important.\n",
    "        \"\"\"\n",
    "        return action_matrix[:,:,:self.num_feats]\n",
    "\n",
    "    def calc_mle_theta(self, orders, action_matrix, human, max_iter=500):\n",
    "        \"\"\"\n",
    "        Params:\n",
    "            orders [list(int)]: the action ids the human chooses at diff rounds\n",
    "            action_matrix [np.array((num_steps, num_actions, num_feats))]: \n",
    "                the feature vectors for the rounds corresponding to orders\n",
    "            human [Human]\n",
    "        \"\"\"\n",
    "        theta = np.zeros(self.num_feats)\n",
    "        action_matrix = self.get_robot_action_matrix(action_matrix)\n",
    "        empirical_feats = action_matrix[[i for i in range(len(orders))], orders]\n",
    "        empirical_feats = np.sum(empirical_feats, axis=0)\n",
    "        expected_feats = np.zeros(len(empirical_feats))\n",
    "        diff = empirical_feats - expected_feats\n",
    "        i = 0\n",
    "        while np.linalg.norm(diff) > 0.1 and i < max_iter:\n",
    "            action_vals = np.matmul(action_matrix, theta)\n",
    "            prob_orders = human.get_prob_orders(action_vals)\n",
    "            expected_feats = action_matrix * prob_orders[:,:,np.newaxis]\n",
    "            expected_feats = np.sum(expected_feats, axis=(0, 1))\n",
    "            diff = empirical_feats - expected_feats # gradient\n",
    "            theta += 1/(i+1) * diff\n",
    "            if any(np.isnan(diff)):\n",
    "                print(expected_feats)\n",
    "            i += 1\n",
    "        return theta\n",
    "    \n",
    "def get_obedience(robot_action, order):\n",
    "    return 1 if robot_action == order else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autonomy Advantage vs Obedience\n",
    "\n",
    "Autonomy advantage and obedience come at a tradeoff. Following code reproduces exps shown in Figure 1a and 1b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_data_at_time(game, robot, human, orders, time):\n",
    "    \"\"\"\n",
    "    Returns [obedience, is opt order, adv, max adv]\n",
    "    \"\"\"\n",
    "    prev_orders = orders[:time+1]\n",
    "    curr_order = prev_orders[-1]\n",
    "    theta_est = robot.calc_mle_theta(\n",
    "        prev_orders, game.get_action_matrix(len(prev_orders)), human)\n",
    "    robot_action = robot.choose_action(game, time, theta_est)\n",
    "    obd = get_obedience(robot_action, curr_order)\n",
    "    human_reward = game.get_reward(curr_order, time)\n",
    "    max_reward = game.get_max_reward(time)\n",
    "    is_order_opt = 1 if human_reward == max_reward else 0\n",
    "    adv = game.get_reward(robot_action, time) - human_reward\n",
    "    max_adv = max_reward - human_reward\n",
    "    return np.array([obd, is_order_opt, adv, max_adv])\n",
    "\n",
    "def get_mean_stderr(data):\n",
    "    mean = np.average(data, axis=0)\n",
    "    std_error = np.sqrt(np.sum(np.square(data - mean), axis=0))/len(data)\n",
    "    return mean, std_error\n",
    "\n",
    "def sim_adv_obd_by_time(\n",
    "    rationality=2, num_feats=10, num_actions=10, horizon=50, time_step=5, num_sims=100):\n",
    "    times = range(0, horizon+1, time_step)\n",
    "    # last index is [obedience, is order opt, adv, max adv]\n",
    "    data = np.zeros((num_sims, len(times), 4))\n",
    "    human = Human(rationality)\n",
    "    robot = Robot(num_feats)\n",
    "    for sim_num in range(num_sims):\n",
    "        game = Game(num_actions, horizon+1, \n",
    "            np.zeros(num_feats), np.identity(num_feats), \n",
    "            np.zeros(num_feats), np.identity(num_feats))\n",
    "        orders = human.get_orders(game)\n",
    "        for time_ind, time in enumerate(times):\n",
    "            data[sim_num][time_ind] = get_data_at_time(game, robot, human, orders, time)\n",
    "    return data, times\n",
    "    \n",
    "def plot_sim_by_time(exps, times, ylabel, data_labels, linestyles):\n",
    "    plt.figure()\n",
    "    for exp_ind, data_label, linestyle in zip(\n",
    "        range(exps.shape[-1]), data_labels, linestyles):\n",
    "        mean, stderr = get_mean_stderr(exps[:,:,exp_ind])\n",
    "        (_, caps, _) = plt.errorbar(\n",
    "            times, mean, yerr=stderr, marker='o', \n",
    "            label=data_label, capsize=2, linestyle=linestyle)\n",
    "        for cap in caps:\n",
    "            cap.set_markeredgewidth(1)\n",
    "        plt.xlabel('Time')\n",
    "    plt.legend()\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.locator_params(axis='y', nbins=3)\n",
    "    sns.despine()\n",
    "    \n",
    "def save_adv_obd_data(filename, data, times):\n",
    "    \"\"\"\n",
    "    Saves the adv and obed by time data in a csv file.\n",
    "    \"\"\"\n",
    "    csv_data = np.zeros((data.shape[1], 1 + 2*data.shape[2]))\n",
    "    csv_data[:, 0] = times\n",
    "    for exp_ind in range(data.shape[-1]):\n",
    "        mean, std = get_mean_stderr(data[:,:,exp_ind])\n",
    "        csv_data[:,1+2*exp_ind] = mean\n",
    "        csv_data[:, 2+2*exp_ind] = std\n",
    "    with open(filename, 'w', newline='') as csvfile:\n",
    "        writer = csv.writer(csvfile)\n",
    "        writer.writerow(['Time', 'Obedience', 'Obedience Error', 'Opt Order', 'Opt Order Error', \n",
    "                         'Advantage', 'Advantage Error', 'Maximum Advantage', 'Maximum Advantage Error'])\n",
    "        writer.writerows(csv_data)\n",
    "        \n",
    "def fig_1ab(num_sims=100, save_file=None):\n",
    "    data, times = sim_adv_obd_by_time(num_sims=num_sims, time_step=10, horizon=100)\n",
    "    if save_file:\n",
    "        save_adv_obd_data(save_file, data, times)\n",
    "    plot_sim_by_time(data[:,:,:2], times, 'Obedience ($\\mathcal{O}$)', \n",
    "        ['Robot obedience', 'Prob opt order'], ['-', '--'])\n",
    "    plot_sim_by_time(data[:,:,2:4], times, 'Autonomy Advantage ($\\Delta$)', \n",
    "        ['Advantage', 'Max advantage'], ['-', '--'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
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nyg1otNiCXQ4REXVDXof8Cy+8gJ9++gkbNmyA3W7HJ598guXLl/uztl4vOzkc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\neQgA8N2pn5BfWwCZWIqDVUc81vjhoY/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dOHCAcDhMOp3G5/MRDodxOp0Wphw/qqqqCIVC\nTJo0iWAwqA5zcOzYMWKxGIZhUFdXx9y5c9VhjlKpFPv376enp4d0Ok11dTWLFi1Sj8PU1dXF7t27\naW9v582bN4P21t7ezuXLlzEMg+3bt1NRUTGqGTTkRUREbEqH60VERGxKQ15ERMSmNORFRERsSkNe\nRETEpjTkRUREbEqf7iIig2psbOTx48ek02nevXtnXkK6ceNGHA4HmzdvtjihiPyOLqETkX/U1dVF\ndXU1t2/ftjqKiORIe/IikpMfN92oqalh5cqVrFmzhkePHjFz5kwqKyvNu74dPXqUsrIy3r59SygU\n4tOnT+Tn5xMMBikpKbH4txCZGHROXkRGrLe3l/Lycm7evAn8eYvmaDRKTU0N58+fB6ChoYH6+nqu\nXbtGU1MTdXV1VkYWmVC0Jy8i/4rf7wdgzpw5lJaWAjB79mw+f/5MKpUiHo+zb98+8/lfvnyhr6+P\n6dOnW5JXZCLRkBeRf8Xlcplf//oZ5tlsFpfLxfXr183HEokEXq/3f8snMpHpcL2I/Gc8Hg/z5s0z\nh/z9+/fZsmWLxalEJg7tyYvIf6qlpYVQKERrayuTJ0/mxIkTOBwOq2OJTAi6hE5ERMSmdLheRETE\npjTkRUREbEpDXkRExKY05EVERGxKQ15ERMSmNORFRERsSkNeRETEpjTkRUREbOoP9rJeRHVhdhAA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fe14630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ec7LjAWhyODlUWOO5Bn6owE5BWT0fbS3o8DWaHC6+dk4qU8emMDix4w8TEfEt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eaf3470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_1ab(num_sims=5000, save_file='fig1ab.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Effect of Rationality on Autonomy Advantage\n",
    "\n",
    "Eventually, the robot can gain a higher autonomy advantage for more irrational humans. But, with a more rational human it takes longer for the robot to converge to the maximum advantage because the evidence the robot gets about the reward is noisier. Following code reproduces experiment shown from Figure 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sim_adv_by_rat(rationalities, times, num_feats=10, num_actions=10, num_sims=100):\n",
    "    horizon = max(times)\n",
    "    robot = Robot(num_feats)\n",
    "    humans = [Human(rationality) for rationality in rationalities]\n",
    "    data = np.zeros((len(times), num_sims, len(rationalities)))\n",
    "    max_advs = np.zeros((num_sims*len(times), len(rationalities)))\n",
    "    for sim_num in range(num_sims):\n",
    "        game = Game(num_actions, horizon+1, \n",
    "            np.zeros(num_feats), np.identity(num_feats), \n",
    "            np.zeros(num_feats), np.identity(num_feats))\n",
    "        for human_ind, human in enumerate(humans):\n",
    "            orders = human.get_orders(game)\n",
    "            for time_ind, time in enumerate(times):\n",
    "                curr_data = get_data_at_time(game, robot, human, orders, time)\n",
    "                data[time_ind][sim_num][human_ind] = curr_data[2]\n",
    "                max_advs[sim_num*len(times)+time_ind][human_ind] = curr_data[3]\n",
    "    return data, max_advs\n",
    "\n",
    "def plot_adv_by_rat(data, rationalities, max_advs, times):\n",
    "    palette = sns.cubehelix_palette(5, start=2.6, rot=0, dark=0.1, light=.8)\n",
    "    for time, exp_at_time in zip(times, data):\n",
    "        mean, stderrs = get_mean_stderr(exp_at_time)\n",
    "        with palette:\n",
    "            (_, caps, _) = plt.errorbar(x=rationalities, y=mean, yerr=stderrs, \n",
    "                label='{0}'.format(time), marker='o', markersize=4)\n",
    "            for cap in caps:\n",
    "                cap.set_markeredgewidth(1)\n",
    "    mean, stderrs = get_mean_stderr(max_advs)\n",
    "    (_, caps, _) = plt.errorbar(x=rationalities, y=mean, yerr=stderrs,\n",
    "                 label='$\\infty$', linestyle='--', color=palette[-1], marker='o', markersize=4)\n",
    "    for cap in caps:\n",
    "        cap.set_markeredgewidth(1)\n",
    "    plt.xticks(np.arange(0, max(rationalities)+1, 1.0))\n",
    "    #plt.locator_params(axis='y', nticks=3)\n",
    "    #plt.locator_params(axis='x', nticks=3)\n",
    "    plt.xlim(min(rationalities))\n",
    "    plt.legend(loc='upper left', title= 'Time:')\n",
    "    \n",
    "def save_adv_by_rat_data(filename, data, rationalities, max_advs, times):\n",
    "    # copy and pasted from above csv\n",
    "    csv_data = []\n",
    "    for time, exp_at_time in zip(times, data):\n",
    "        mean, stderrs = get_mean_stderr(exp_at_time)\n",
    "        csv_data.append([time] + mean.tolist() + stderrs.tolist())\n",
    "    max_adv_mean, max_adv_err = get_mean_stderr(max_advs)\n",
    "    csv_data.append(['Max'] + max_adv_mean.tolist() + max_adv_err.tolist())\n",
    "    with open(filename, 'w', newline='') as csvfile:\n",
    "        writer = csv.writer(csvfile)\n",
    "        writer.writerow(['Time'] + ['Rationality: {0}'.format(rat) for rat in rationalities]\n",
    "                        + ['Stderr Rationality: {0}'.format(rat) for rat in rationalities])\n",
    "        writer.writerows(csv_data)\n",
    "\n",
    "def fig2(num_sims, save_file=None):\n",
    "    rationalities = [1, 2, 5, 10]\n",
    "    times = [0, 10, 100, 500]\n",
    "    data, max_advs = sim_adv_by_rat(rationalities, times, num_sims=num_sims, num_actions=10)\n",
    "    if save_file is not None:\n",
    "        save_adv_by_rat_data(save_file, data, rationalities, max_advs, times)\n",
    "    plot_adv_by_rat(data, rationalities, max_advs, times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bo+HLbb/w9Y5faFS7Jkv+MxrnymIbW0EoVlIxe/Tokd6vefnWXcmr53Dp8q27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\nL7FZcmZFAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10befa4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2(num_sims=1000, save_file='fig2.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Misspecification of Features\n",
    "\n",
    "If the robot has the wrong model of the space of reward parameters, the autonomy advantage can easily turn into the rebellion regret. Figure 3 shows how autonomy advantage changes as a function of the number of features the robot has.\n",
    "\n",
    "If the human is rational enough, MLE-R should almost always obey on the first order. Thus, one way R can detect a misspecified $\\Theta$ is to estimate its obedience to H's first order. If R's obedience is too low, R probably has the wrong model. Figure 4 shows the improvement in performance with a robot that tries detecting misspecification.\n",
    "\n",
    "Following code reproduces experiments from Figure 3 and 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sim_wrong_feats(\n",
    "    time_step, pos_num_feats, true_num_feats,\n",
    "    rationality=2, num_actions=10, num_sims=1000,\n",
    "    cutoff=0.8, calc_sample_obed=False):\n",
    "    \"\"\"\n",
    "    Params:\n",
    "        -time_step [int]: the step of game to calculate adv/obedience for\n",
    "        -pos_num_feats [list(int)]: all possible num of features that robot could believe reward has\n",
    "        -true_num_feats [int]: the true number of features the reward has\n",
    "        -cutoff [float]: if sample obedience is less than this cutoff, act obediently\n",
    "        -rationality [float]: rationality of human\n",
    "        -num_actions [int]\n",
    "        -num_sims [int]\n",
    "    \n",
    "    Returns:\n",
    "        adv_exp, obd_exp, detect_adv_exp, detect_obd_exp\n",
    "    \"\"\"\n",
    "    robots = [Robot(num_feats) for num_feats in pos_num_feats]\n",
    "    human = Human(rationality)\n",
    "    pos_num_feats = sorted(pos_num_feats)\n",
    "    max_num_feats = pos_num_feats[-1]\n",
    "    adv_exp, obd_exp, detect_adv_exp, detect_obd_exp = [\n",
    "        np.zeros((num_sims, max_num_feats)) for _ in range(4)]\n",
    "    if not calc_sample_obed:\n",
    "        detect_adv_exp, detect_obd_exp = None, None\n",
    "    for sim in range(num_sims):\n",
    "        game = Game(num_actions, time_step + 1, \n",
    "            np.zeros(true_num_feats), np.identity(true_num_feats), \n",
    "            np.zeros(max_num_feats), np.identity(max_num_feats))\n",
    "        orders = human.get_orders(game)\n",
    "        curr_order = orders[-1]\n",
    "        human_reward = game.get_reward(curr_order, time_step)\n",
    "        for num_feats, robot in zip(pos_num_feats, robots):\n",
    "            theta_est = robot.calc_mle_theta(orders, game.get_action_matrix(len(orders)), human)\n",
    "            robot_action = robot.choose_action(game, time_step, theta_est)\n",
    "            obd = get_obedience(robot_action, curr_order)\n",
    "            adv = game.get_reward(robot_action, time_step) - human_reward\n",
    "            adv_exp[sim][num_feats-1] = adv\n",
    "            obd_exp[sim][num_feats-1] = obd\n",
    "            if calc_sample_obed:\n",
    "                sample_obedience = calc_sample_obedience(robot, orders[:-1], game, human)\n",
    "                if sample_obedience < cutoff:\n",
    "                    detect_adv_exp[sim][num_feats-1] = 0\n",
    "                    detect_obd_exp[sim][num_feats-1] = 1\n",
    "                else:\n",
    "                    detect_adv_exp[sim][num_feats-1] = adv\n",
    "                    detect_obd_exp[sim][num_feats-1] = obd\n",
    "    return adv_exp, obd_exp, detect_adv_exp, detect_obd_exp\n",
    "\n",
    "def plot_wrong_feats(exp, pos_num_feats, true_num_feats, ylabel='', title=''):\n",
    "    plt.figure()\n",
    "    red = sns.color_palette('muted')[2]\n",
    "    green = sns.color_palette('muted')[1]\n",
    "    means, stderrs = get_mean_stderr(exp)\n",
    "    (_, caps, _) = plt.errorbar(x=pos_num_feats, y=means, yerr=stderrs, \n",
    "        marker='o', markersize=4)\n",
    "    for cap in caps:\n",
    "        cap.set_markeredgewidth(1)\n",
    "    #plt.locator_params(axis='x', nticks=2)\n",
    "    plt.xlim(min(pos_num_feats))\n",
    "    plt.xticks([\n",
    "        min(pos_num_feats), true_num_feats, max(pos_num_feats)])\n",
    "    ymin, ymax = plt.gca().get_ylim()\n",
    "    plt.yticks([ymin, 0, ymax])\n",
    "    plt.xlabel('Number Features')\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.title(title)\n",
    "    #plt.legend(loc='upper left', title= 'Time:')\n",
    "    \n",
    "def plot_mult_exps(exps, steps, true_num_feats, yticks=None, ylabel=''):\n",
    "    red = sns.color_palette('muted')[2]\n",
    "    green = sns.color_palette('muted')[1]\n",
    "    f, axes = plt.subplots(1, len(exps), sharey=True, figsize=(10, 3))\n",
    "    for i, (ax, step, exp) in enumerate(zip(axes, steps, exps)):\n",
    "        ttl = ax.set_title('Step {0}'.format(step))\n",
    "        ttl.set_position([.5, 1.05])\n",
    "        if i == 0:\n",
    "            ax.set_ylabel(ylabel)\n",
    "        max_feats = exp.shape[1]\n",
    "        mean, stderr = get_mean_stderr(exp)\n",
    "        ax.errorbar(range(1, true_num_feats + 1), mean[:true_num_feats], \n",
    "                    yerr=stderr[:true_num_feats], color=red)\n",
    "        ax.errorbar(range(true_num_feats, max_feats + 1), mean[true_num_feats-1:], \n",
    "                    yerr=stderr[true_num_feats-1:], color=green)\n",
    "        ax.axvline(x=true_num_feats, color=default_palette[-1], linestyle='--', \n",
    "                   linewidth=0.25, marker=None)\n",
    "        if yticks is None:\n",
    "            start, end = ax.get_ylim()\n",
    "            ax.set_yticks([int(min(start, mean.min())), 0, int(max(mean.max(), end))])\n",
    "        else:\n",
    "            ax.set_yticks(yticks)\n",
    "        ax.set_xlim(xmin=1)\n",
    "        ax.set_xticks([1, true_num_feats, len(mean)])\n",
    "    \n",
    "def calc_sample_obedience(robot, orders, game, human):\n",
    "    \"\"\"\n",
    "    Calculates sample obedience to first order.\n",
    "    \"\"\"\n",
    "    sample_obed = 0\n",
    "    for step, order in enumerate(orders):\n",
    "        theta_est = robot.calc_mle_theta(\n",
    "            [order], game.get_action_matrix_at_steps(np.array([step])), human)\n",
    "        robot_action = robot.choose_action(game, step, theta_est)\n",
    "        curr_obed = 1 if robot_action == order else 0\n",
    "        sample_obed += curr_obed\n",
    "    sample_obed /= len(orders)\n",
    "    return sample_obed\n",
    "        \n",
    "def plot_detect_adv(adv_exp, detect_adv_exp, true_num_feats, title='', xlabel='', ylabel=''):\n",
    "    red = sns.color_palette('muted')[2]\n",
    "    green = sns.color_palette('muted')[1]\n",
    "    tint_factor = 0.9\n",
    "    muted_red = red + (0.4,)\n",
    "    muted_green = green + (0.4,)\n",
    "    f, ax = plt.subplots()\n",
    "    ttl = ax.set_title(title)\n",
    "    ttl.set_position([.5, 1.05])\n",
    "    ax.set_ylabel(ylabel)\n",
    "    ax.set_xlabel(xlabel)\n",
    "    for i, exp in enumerate([detect_adv_exp, adv_exp]):\n",
    "        max_feats = exp.shape[1]\n",
    "        mean, stderr = get_mean_stderr(exp)\n",
    "        if i == 0:\n",
    "            red_color = red\n",
    "            green_color = green\n",
    "        else:\n",
    "            red_color = muted_red\n",
    "            green_color = muted_green\n",
    "        ax.errorbar(range(1, true_num_feats + 1), mean[:true_num_feats], \n",
    "                    yerr=stderr[:true_num_feats], color=red_color)\n",
    "        ax.errorbar(range(true_num_feats, max_feats + 1), mean[true_num_feats-1:], \n",
    "                    yerr=stderr[true_num_feats-1:], color=green_color)\n",
    "        ax.axvline(x=true_num_feats, color=default_palette[-1], linestyle='--', \n",
    "                   linewidth=0.25, marker=None)\n",
    "        ax.locator_params(axis='y', nbins=3)\n",
    "        start, end = ax.get_ylim()\n",
    "        ax.set_yticks([int(min(start, mean.min())), 0, int(max(mean.max(), end))])\n",
    "    ax.set_xlim(xmin=1)\n",
    "    ax.set_xticks([1, true_num_feats, len(mean)])\n",
    "    \n",
    "def write_exp(save_file, pos_num_feats, exps):\n",
    "    with open(save_file, 'w', newline='') as csvfile:\n",
    "        writer = csv.writer(csvfile)\n",
    "        header = ['Features', 'Adv', 'Adv Err', 'Obd', 'Obd Err', 'Detect Adv', 'Detect Adv Err']\n",
    "        writer.writerow(header)\n",
    "        rows = np.zeros((len(pos_num_feats), len(header)))\n",
    "        rows[:,0] = pos_num_feats\n",
    "        for i, exp in enumerate(exps):\n",
    "            mean, stderr = get_mean_stderr(exp)\n",
    "            rows[:,2*i+1] = mean\n",
    "            rows[:,2*i+2] = stderr\n",
    "        writer.writerows(rows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sim_fig34(num_sims=100, save_file_prefix=''):\n",
    "    \"\"\"\n",
    "    Simulates Figure 3 and 4.\n",
    "    \"\"\"\n",
    "    steps = [0, 10, 100]\n",
    "    pos_num_feats = range(1, 21)\n",
    "    detect_at = 10\n",
    "    true_num_feats = 10\n",
    "    adv_exps, obd_exps = [], []\n",
    "    for step in steps:\n",
    "        if detect_at == step:\n",
    "            calc_sample_obed=True\n",
    "        else:\n",
    "            calc_sample_obed=False\n",
    "        adv_exp, obd_exp, detect_adv_exp, detect_obd_exp = sim_wrong_feats(\n",
    "            time_step=step, pos_num_feats=pos_num_feats, \n",
    "            true_num_feats=true_num_feats, \n",
    "            rationality=2, num_sims=num_sims, calc_sample_obed=calc_sample_obed)\n",
    "        if detect_at == step:\n",
    "            # Figure 4\n",
    "            plot_detect_adv(adv_exp, detect_adv_exp, true_num_feats, \n",
    "                title='Step 10', xlabel='Number Features', ylabel='Autonomy Advantage ($\\Delta$)')\n",
    "            write_exp('{0}_step_{1}.csv'.format(save_file_prefix, step), pos_num_feats, [adv_exp, obd_exp, detect_adv_exp])\n",
    "        else:\n",
    "            write_exp('{0}_step_{1}.csv'.format(save_file_prefix, step), pos_num_feats, [adv_exp, obd_exp])\n",
    "        adv_exps.append(adv_exp)\n",
    "        obd_exps.append(obd_exp)\n",
    "        \n",
    "    # Figure 3\n",
    "    plot_mult_exps(adv_exps, steps, true_num_feats, ylabel='Autonomy Advantage ($\\Delta$)')\n",
    "    plot_mult_exps(obd_exps, steps, true_num_feats, ylabel='Obedience ($\\mathcal{O}$)', yticks=[0, 0.5, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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DD6JNmzbYtWsX5HI5Xn31VfTo0QMnT57E+PHjhcooOolcjqCUFOR/+ikseXlQ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\nSBAsGCIiEgQLhoiIBPH/OJNdsS03D3EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1203943c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1httUKhWSk5OxYsUKAMDOnTudm4waJLZVS86AIboOa4KakpIjRwAAmsGD0ewOr1jDmhCv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\nyZIlyM/Ph1arxbZ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ttzB16lS33hNmOHUKABDYq5fgJETux3D2LCrOnkX0rFlcBSOvVHb8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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1203946d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EMgKRykgAMnxduhW9Int7N5BNnz4dEyZMQHV1NaZNm4b9+/djwYIFHr1gW3Ja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\nZP8PAUDbII5JMH8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fdf54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_fig34(num_sims=1000, save_file_prefix='fig34')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questions, comments, changes?\n",
    "\n",
    "Send me an email (smilli @ berkeley.edu) or submit an issue / pull request."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}