Chapter 2.ipynb

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   "source": [
    "# Multi-armedBandits - Chapter 2"
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    "## A k-armed Bandit Problem\n",
    "Bandit problem is a simplified setting for reinforcement learning in which you are faced repeatedly with a choice among k different options (actions).After each choice you receive a numerical reward chosen from a stationary probability distribution that depends on the action you selected. Your objective is to maximize the expected total\n",
    "reward over some time period, for example, over 1000 action selections, or time steps.\n"
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    "In our k-armed bandit problem, each of the k actions has an expected or mean reward given that\n",
    "that action is selected; let us call this the value of that action. We denote the action selected on time\n",
    "step t as At , and the corresponding reward as Rt . The value then of an arbitrary **action a**, denoted\n",
    "q∗ (a), is the **expected reward** given that a is selected:\n",
    "$$q_{*}(a) = E \\{ \\ R_t \\ | \\ A_t=a \\} $$"
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    "If you knew the value of each action, then it would be trivial to solve the k-armed bandit problem: you\n",
    "would always select the action with highest value. We assume that you do not know the action values\n",
    "with certainty, although you may have estimates. We denote the **estimated value** of action a at time\n",
    "step t as ** $Q_t(a)$ **. We would like $Q_t(a)$ to be close to $q_∗$(a).\n",
    "\n",
    "If you maintain estimates of the action values, then at any time step there is at least one action whose\n",
    "estimated value is greatest. We call these the **greedy actions**. When you select one of these actions,\n",
    "we say that you are **exploiting** your current knowledge of the values of the actions. If instead you\n",
    "select one of the nongreedy actions, then we say you are **exploring**, because this enables you to improve\n",
    "your estimate of the nongreedy action’s value. \n",
    "\n",
    "**Exploitation** $\\to$ Maximize the expected reward on the **one step**.\n",
    "\n",
    "**Exploration** $\\to$ Produce the greater total reward in the **long run**.\n",
    "\n",
    "Whether it is better to explore or exploit depends in a complex way on the precise values of the estimates, uncertainties, and the number of remaining steps."
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    "import numpy as np\n",
    "np.warnings.filterwarnings('ignore')\n",
    "from enum import Enum\n",
    "\n",
    "\n",
    "class EstimationMethod(Enum):\n",
    "    \"\"\"This is an enum for representing different methods of estimating the value of each action\"\"\"\n",
    "    SAMPLE_AVERAGE_INCREMENTAL = 1\n",
    "    CONSTANT_STEP_SIZE = 2\n",
    "    GRADIENT_BANDIT = 3\n",
    "\n",
    "\n",
    "class ActionSelectionMethod(Enum):\n",
    "    \"\"\"This is an enum representing different methods of selecting the action\"\"\"\n",
    "    EPSILON_GREEDY = 1\n",
    "    UPPER_CONFIDENCE_BOUND = 2\n",
    "    GRADIENT_BANDIT = 3\n",
    "\n",
    "\n",
    "class Bandit:\n",
    "    \"\"\"This class represents a Bandit problem\n",
    "\n",
    "    k-armed bandit problem is a problem in reinforcement learning with simplified setting. You are\n",
    "    faced repeatedly with a choice among k different options, or actions. After each choice you\n",
    "    receive a numerical reward chosen from a stationary probability distribution that depends\n",
    "    on the action you selected.\n",
    "\n",
    "    Attributes:\n",
    "        arms (int) : number of arms of the problem (k)\n",
    "        estimation_method (EstimationMethod) : the method of estimating the action value\n",
    "        action_selection_method (ActionSelectionMethod) : the method of selecting next action\n",
    "        c (float) : it is the coefficient of UCB (c > 0)\n",
    "        epsilon (float) : it is the probability of acting randomly in epsilon-greedy algorithm\n",
    "        alpha (float) : is the step size in gradient abd constant step size algorithm\n",
    "        random_walk (float) : is the standard derivation of normal distribution for adding to Q*\n",
    "        start_equal (bool) : a boolean representing whether all q* start in equal values (Q*(a)=0)\n",
    "        initial_value_estimation (float) : initial value for actions estimation value\n",
    "        q_star_mean (float) : normal distribution with given mean for Q*(a)\n",
    "        gradient_baseline (bool) : whether the gradient has baseline or not\n",
    "        time (int) : time step which we are in\n",
    "        action_probability (np,array) : the probability of choosing each action (gradient algorithm)\n",
    "        average_reward (float) : average reward until the current time\n",
    "        q_estimations (np.array) : estimation of values for each action\n",
    "        action_counts (np.array) : number of times which each action have been chosen\n",
    "        q_true_values (np.array) : the true value of each action (Q*(a))\n",
    "    \"\"\"\n",
    "    def __init__(self, arms=10, estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                 epsilon=0.1,gradient_baseline=False,alpha=0.1, start_equal=False, random_walk=0,\n",
    "                 action_selection_method=ActionSelectionMethod.EPSILON_GREEDY, c=2,\n",
    "                 initial_value_estimation=0.0, start_time=0,q_star_mean=0):\n",
    "\n",
    "        # parameters\n",
    "        self.arms = arms\n",
    "        self.estimation_method = estimation_method\n",
    "        self.action_selection_method = action_selection_method\n",
    "        self.c = c\n",
    "        self.epsilon = epsilon\n",
    "        self.alpha = alpha\n",
    "        self.random_walk = random_walk\n",
    "        self.start_equal = start_equal\n",
    "        self.initial_value_estimation = initial_value_estimation\n",
    "        self.start_time = start_time\n",
    "        self.q_star_mean = q_star_mean\n",
    "        self.gradient_baseline = gradient_baseline\n",
    "\n",
    "        # environment\n",
    "        self.time = self.start_time\n",
    "        self.action_probability = np.zeros(self.arms)\n",
    "        self.action_probability.fill(1)\n",
    "        self.average_reward = 0\n",
    "        self.q_estimations = np.zeros(self.arms)\n",
    "        self.q_estimations.fill(self.initial_value_estimation)\n",
    "        self.action_counts = np.zeros(self.arms)\n",
    "        self.q_true_values = np.zeros(self.arms)\n",
    "        if not self.start_equal:\n",
    "            self.q_true_values = np.random.normal(self.q_star_mean, 1, self.arms)\n",
    "\n",
    "    def start_new_environment(self):\n",
    "        \"\"\"reset all the environment parameters\"\"\"\n",
    "        self.time = self.start_time\n",
    "        self.action_probability = np.zeros(self.arms)\n",
    "        self.action_probability.fill(1)\n",
    "        self.average_reward = 0\n",
    "        self.q_estimations = np.zeros(self.arms)\n",
    "        self.q_estimations.fill(self.initial_value_estimation)\n",
    "        self.action_counts = np.zeros(self.arms)\n",
    "        self.q_true_values = np.zeros(self.arms)\n",
    "        if not self.start_equal:\n",
    "            self.q_true_values = np.random.normal(self.q_star_mean, 1, self.arms)\n",
    "\n",
    "    def select_action(self):\n",
    "        \"\"\"select one of the action according to action selection method\"\"\"\n",
    "        if self.action_selection_method == ActionSelectionMethod.EPSILON_GREEDY:\n",
    "\n",
    "            if np.random.random_sample() < self.epsilon:\n",
    "                # select one of the actions randomly\n",
    "                return np.random.choice(np.arange(self.arms))\n",
    "            else:\n",
    "                # argmax by break tie randomly\n",
    "                return np.random.choice(np.flatnonzero(self.q_estimations==self.q_estimations.max()))\n",
    "\n",
    "        elif self.action_selection_method == ActionSelectionMethod.UPPER_CONFIDENCE_BOUND:\n",
    "            ucb_value = self.q_estimations + \\\n",
    "                        self.c * np.sqrt(np.log(self.time) / self.action_counts)\n",
    "            return np.argmax(ucb_value)\n",
    "\n",
    "        elif self.action_selection_method == ActionSelectionMethod.GRADIENT_BANDIT:\n",
    "            exp_h = np.exp(self.q_estimations)\n",
    "            self.action_probability = exp_h / exp_h.sum()\n",
    "            return np.random.choice(np.arange(self.arms), p=self.action_probability)\n",
    "\n",
    "    def step(self, action):\n",
    "        \"\"\"simulate one step and return the reward\"\"\"\n",
    "        reward = np.random.normal(self.q_true_values[action], scale=1.0)\n",
    "\n",
    "        self.time += 1\n",
    "\n",
    "        self.average_reward = (self.average_reward * (self.time - 1) + reward) / self.time\n",
    "\n",
    "        self.action_counts[action] += 1\n",
    "\n",
    "        if self.random_walk != 0:\n",
    "            mu, sigma = 0, self.random_walk # mean and standard deviation\n",
    "            self.q_true_values += np.random.normal(mu, sigma, self.arms)\n",
    "\n",
    "        if self.estimation_method == EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL:\n",
    "            self.q_estimations[action]+=(reward-self.q_estimations[action])/self.action_counts[action]\n",
    "        elif self.estimation_method == EstimationMethod.CONSTANT_STEP_SIZE:\n",
    "            self.q_estimations[action] += self.alpha * (reward - self.q_estimations[action])\n",
    "        elif self.estimation_method == EstimationMethod.GRADIENT_BANDIT:\n",
    "            if self.gradient_baseline:\n",
    "                baseline = self.average_reward\n",
    "            else:\n",
    "                baseline = 0\n",
    "            one = np.zeros(self.arms)\n",
    "            one[action] = 1\n",
    "            self.q_estimations -= self.alpha*(reward-baseline)*(self.action_probability-one)\n",
    "        return reward\n",
    "\n",
    "    def simulate(self, runs=2000, time_steps=1000):\n",
    "        \"\"\"simulate for given number of runs with the given number of time steps\"\"\"\n",
    "        best_action_counts = np.zeros((runs, time_steps))\n",
    "        rewards = np.zeros((runs, time_steps))\n",
    "\n",
    "        for r in range(runs):\n",
    "            self.start_new_environment()\n",
    "            for t in range(time_steps):\n",
    "                action = self.select_action()\n",
    "                reward = self.step(action)\n",
    "                rewards[r, t] = reward\n",
    "                if action == np.argmax(self.q_true_values):\n",
    "                    # it was the best action\n",
    "                    best_action_counts[r, t] = 1\n",
    "\n",
    "        # mean of all rewards and best action of all runs count in a particular time step\n",
    "        return best_action_counts.mean(axis=0), rewards.mean(axis=0)\n"
   ]
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    "## Action-value Methods\n",
    "We begin by looking more closely at some simple methods for estimating the values of actions and for using the estimates to make action selection decisions. Recall that the true value of an action is the mean reward when that action is selected. One natural way to estimate this is by **averaging the rewards** actually received:\n",
    "\n",
    "$$ Q_t(a) = \\frac{sum \\ of \\ rewards\\ when \\ a \\ taken \\ prior \\ to \\ t}{number \\ of \\ times \\ a \\ taken \\ prior \\ to \\ t} = \\frac{\\sum_{i=1}^{t-1}R_i \\ . \\ 1_{A_i=a}}{\\sum_{i=1}^{t-1} 1_{A_i=a}}$$\n",
    "\n",
    "*$1_{predicate}$ denotes the random variable that is 1 if predicate is true and 0 if it is not.*\n",
    "\n",
    "We call this the **sample-average** method for **estimating action values**. Of course this is just one way to estimate action values, and not necessarily the best one.\n",
    "\n",
    "The simplest action selection rule is to select **one of the actions** with the **highest estimated value**,\n",
    "that is, one of the greedy actions as defined in the previous section. If there is **more than one greedy\n",
    "action**, then a selection is made among them in some arbitrary way, perhaps **randomly**. We write this\n",
    "greedy action selection method as:\n",
    "\n",
    "$$A_t = argmax \\ Q_t(a)$$\n",
    "\n",
    "A simple alternative is to behave **greedily most of the time**, but every once in a while, say with small\n",
    "**probability ε**, instead **select randomly from among all the actions** with equal probability, independently\n",
    "of the action-value estimates. We call methods using this near-greedy action selection rule **ε-greedy**\n",
    "methods.\n",
    "\n",
    "**Exercise 2.1 In $\\epsilon$-greedy action selection, for the case of two actions and $\\epsilon$ = 0.5, what is\n",
    "the probability that the greedy action is selected?**\n",
    "\n",
    "0.5 (there is a $\\epsilon$ probablity of choosing greedy) + 0.5 (there is a 1-$\\epsilon$ probability of choosing randomly ) * 0.5 (choosing one of the action is 1/2) = 0.75\n",
    "\n"
   ]
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   "source": [
    "## The 10-armed Testbed\n"
   ]
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       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\" width=\"638.888905813665\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Reward distribution')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "#Figure 2.1\n",
    "%matplotlib notebook\n",
    "\n",
    "#a sample from normal distribution with mean zero and unit variance for each action\n",
    "q_star_value = np.random.randn(10) \n",
    "# a mean q_star_value, unit variance normal distribution\n",
    "rewards = np.random.randn(500,10) + q_star_value \n",
    "plt.violinplot(dataset=rewards , showmeans=True)\n",
    "plt.xlabel(\"Action\")\n",
    "plt.ylabel(\"Reward distribution\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707ece75c0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Figure 2.2\n",
    "epsilons = [0, 0.1, 0.01]\n",
    "epsilon_greedy_bandits = [Bandit(arms=10,\n",
    "                                 estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                                 action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                                 epsilon=eps)\n",
    "                          for eps in epsilons]\n",
    "\n",
    "epsilon_greedy_best_action, epsilon_greedy_rewards = [], []\n",
    "for bandit in epsilon_greedy_bandits:\n",
    "    result = bandit.simulate(2000, 1000)\n",
    "    epsilon_greedy_best_action.append(result[0])\n",
    "    epsilon_greedy_rewards.append(result[1])\n",
    "    \n",
    "%matplotlib inline\n",
    "plt.figure()\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "for eps, rewards in zip(epsilons, epsilon_greedy_rewards):\n",
    "    plt.plot(rewards, label='epsilon = {}'.format(eps))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('average reward')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "for eps, counts in zip(epsilons, epsilon_greedy_best_action):\n",
    "    plt.plot(counts * 100, label='epsilon = {}'.format(eps))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('% optimal action')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2.2: Bandit example Consider a k-armed bandit problem with k = 4 actions,\n",
    "denoted 1, 2, 3, and 4. Consider applying to this problem a bandit algorithm using\n",
    "$\\epsilon$-greedy action selection, sample-average action-value estimates, and initial estimates\n",
    "of Q1 (a) = 0, for all a. Suppose the initial sequence of actions and rewards is A1 = 1,\n",
    "R1 = 1, A2 = 2, R2 = 1, A3 = 2, R3 = 2, A4 = 2, R4 = 2, A5 = 3, R5 = 0. On some\n",
    "of these time steps the \" case may have occurred, causing an action to be selected at\n",
    "random. On which time steps did this definitely occur? On which time steps could this\n",
    "possibly have occurred?** \n",
    "\n",
    "after one time step : $A_1 = 1 , R_1 = -1 \\to Q_2(1) = \\frac{-1}{1} = -1 , Q_2(2) = 0 , Q_2(3) = 0 , Q_2(4) = 0$ (this choice of action could be both random and greedy)\n",
    "\n",
    "after two time step : $A_2 = 2 , R_2 = 1 \\to Q_3(1) = -1 , Q_3(2) = \\frac{1}{1} = 1 , Q_3(3) = 0, Q_3(4)=0$ (this choice of action could be both random and greedy)\n",
    "\n",
    "after three time step : $A_3 = 2 , R_3 = 2 \\to Q_4(1) = -1 , Q_4(2) = \\frac{1+2}{1+1} = 1.5 , Q_4(3) = 0 , Q_4(4) = 0$(this choice of action could be both random and greedy) \n",
    "\n",
    "after four time step : $A_4 = 2 , R_4 = 2 \\to Q_5(1) = -1 , Q_5(2) = \\frac{1+2+2}{1+1+1} = \\frac{5}{3} , Q_5(3) = 0, Q_5(4) = 0$(this choice of action could be both random and greedy)\n",
    "\n",
    "after five time step : $A_5 = 3 , R_5 = 0 \\to Q_6(1) = -1 , Q_6(2) = \\frac{5}{3} , Q_6(3)=0,Q_6(4)=0$ (this one definitely was chosen randomly)\n",
    "\n",
    "**Exercise 2.3 In the comparison shown in Figure 2.2, which method will perform best in\n",
    "the long run in terms of cumulative reward and probability of selecting the best action?\n",
    "How much better will it be? Express your answer quantitatively.**\n",
    "\n",
    "plotting both the cumlative average reward and the probility of slecting the best action we see that in both case strategiy with exploration will do better however smaller epsilon like 0.01 will improve slowly but eventually would perform better than epsilon=0.1. For 1000 steps the epsilon=0.1 startegy obtain  a cumulative total reward of about 1300 while the greedy strategy obtains a total reward of about 1000 or an improvement of 30%.\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incremental Implementation\n",
    "The action-value methods we have discussed so far all estimate action values as sample\n",
    "averages of observed rewards. We now turn to the question of how these averages can be\n",
    "computed in a computationally **efficient** manner, in particular, with **constant memory**\n",
    "and constant per-time-step computation.\n",
    "\n",
    "$Q_n \\ = \\ \\frac{R_1 \\ + R_2 \\ + \\ ... \\ + \\ R_{n-1}}{n-1}$\n",
    "\n",
    "\n",
    "$Q_{n+1} \\ = \\ \\frac{1}{n} \\ \\sum_{i=1}^{n} \\ R_i$\n",
    "\n",
    "\n",
    "$ = \\ \\frac{1}{n} \\ (R_n \\ + \\ \\sum_{i=1}^{n-1} \\ R_i )$\n",
    "\n",
    "\n",
    "$ = \\ \\frac{1}{n} \\ ( \\ R_n \\ + \\ (n-1) \\ \\frac{1}{n-1} \\ \\sum_{i=1}^{n-1} \\ R_i \\ )$\n",
    "\n",
    "\n",
    "$ = \\ \\frac{1}{n} \\ ( \\ R_n \\ + \\ (n-1) \\ Q_n \\ )$\n",
    "\n",
    "\n",
    "$ = \\ \\frac{1}{n} \\ ( \\ R_n \\ + \\ n Q_n \\ - \\ Q_n \\ )$\n",
    "\n",
    "\n",
    "$ = \\ Q_n \\ + \\ \\frac{1}{n} \\ [ \\ R_n \\ - \\ Q_n \\ ]$\n",
    "\n",
    "**NewEstimate <- OldEstimate + StepSize \\[ Target - OldEstimatei \\]**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tracking a Nonstationary Problem\n",
    "We someties face problems which are not stationary (which means **rewards probability change** over time) so it is a good idea to give **more weight** to **recent rewards** than the past rewards. One of ways to do so is by using a **constant step-size** parameter.\n",
    "\n",
    "\n",
    "$ Q_{n+1} \\ = \\ Q_n \\ + \\ \\alpha \\ [ \\ R_n \\ - \\ Q_n \\ ]$\n",
    "\n",
    "$ = \\ \\alpha \\ R_n \\ + \\ (1-\\alpha) \\ Q_n$\n",
    "\n",
    "$ = \\ \\alpha \\ R_n \\ + \\ (1-\\alpha) \\ [ \\ \\alpha \\ R_{n-1} \\ + \\ (1-\\alpha) \\ Q_{n-1} \\ ]$\n",
    "\n",
    "$ = \\alpha \\ R_n \\ + \\ (1-\\alpha) \\ \\alpha \\ R_{n-1} \\ + \\ (1-\\alpha)^{2} \\ Q_{n-1}$\n",
    "\n",
    "$ = \\alpha \\ R_n \\ + \\ (1-\\alpha) \\ \\alpha \\ R_{n-1} \\ + \\ (1-\\alpha)^2 \\ \\alpha \\ R_{n-2} \\ + \\ ... \\ + \\ (1-\\alpha)^{n-1} \\ \\alpha \\ R_1 \\ + (1-\\alpha)^n \\ Q_1$\n",
    "\n",
    "$ = \\ (1-\\alpha)^n \\ Q_1 \\ + \\sum_{i=1}^{n} \\ \\alpha \\ (1-\\alpha)^{n-i} \\ R_i$\n",
    "\n",
    "**exponential recency-weighted average** $\\to$ *weight decays exponentially according to the exponent on* $1-\\alpha$\n",
    "\n",
    "\n",
    "**for ensuring convergence wih probability 1 : **\n",
    "\n",
    "$$ \\sum_{n=1}^{\\infty} \\ \\alpha_{n}(a) \\ = \\ \\infty \\ \\ and \\ \\ \\sum_{n=1}^{\\infty} \\ \\alpha_{n}^{2}(a) \\ < \\ \\infty$$\n",
    "\n",
    "**first conditon** $\\to$ *steps are large enough to eventually overcome any initial conditions*\n",
    "\n",
    "**second conditon** $\\to$ *eventually the steps become small enough to assure convergence.*\n",
    "\n",
    "$\\alpha_n(a) \\ = \\ \\frac{1}{n}$ (sample average) $\\to$ converges\n",
    "\n",
    "$\\alpha_n(a) \\ = \\ \\alpha$ (constan step-size) $\\to$ never completely converge but continue to vary in response to the most recently received rewards and this is a good thing for nonstationary problems\n",
    "\n",
    "**Exercise 2.4 If the step-size parameters, $\\alpha_n$ , are not constant, then the estimate $Q_n$ is\n",
    "a weighted average of previously received rewards with a weighting different from that\n",
    "given by (2.6). What is the weighting on each prior reward for the general case, analogous\n",
    "to (2.6), in terms of the sequence of step-size parameters?**\n",
    "\n",
    "$Q_{n+1} \\ = \\ Q_n \\ + \\ \\alpha_n \\ [ \\ R_n \\ - \\ Q_n \\ ]$\n",
    "\n",
    "$ = \\ \\alpha_n \\ R_n \\ + \\ (1-\\alpha_n) \\ Q_n$\n",
    "\n",
    "$ = \\ \\alpha_n \\ R_n \\ + \\ (1-\\alpha_n) \\ [ \\ \\alpha_{n-1} \\ R_{n-1} \\ + \\ (1-\\alpha_{n-1}) \\ Q_{n-1} \\ ]$\n",
    "\n",
    "$ = \\ \\alpha_n \\ R_n \\ + \\ (1-\\alpha_n) \\ \\alpha_{n-1} \\ R_{n-1} \\ + \\ (1-\\alpha_n) \\ (1-\\alpha_{n-1}) \\ Q_{n-1}$\n",
    "\n",
    "$ = \\ \\alpha_n \\ R_n \\ + \\ (1-\\alpha_n) \\ \\alpha_{n-1} \\ R_{n-1} \\ + \\ (1-\\alpha_n) \\ (1-\\alpha_{n-1}) \\ \\alpha_{n-2} \\ R_{n-2} \\ + \\ ... \\ + \\ (1-\\alpha_n) \\ (1-\\alpha_{n-1}) \\ ... \\ (1-\\alpha_1) \\ Q_1$ \n",
    "\n",
    "$ = \\ \\prod_{i=1}^{n} \\ (1-\\alpha_i) \\ Q_1 + \\ \\sum_{i=1}^{n} \\ \\alpha_i \\ \\prod_{j=i+1}^{n} \\ (1-\\alpha_j) \\ R_i$\n",
    " \n",
    "**Exercise 2.5 (programming) Design and conduct an experiment to demonstrate the\n",
    "difficulties that sample-average methods have for nonstationary problems. Use a modified\n",
    "version of the 10-armed testbed in which all the $q_*$(a) start out equal and then take\n",
    "independent random walks (say by adding a normally distributed increment with mean\n",
    "zero and standard deviation 0.01 to all the $q_*$(a) on each step). Prepare plots like\n",
    "Figure 2.2 for an action-value method using sample averages, incrementally computed,\n",
    "and another action-value method using a constant step-size parameter, $\\alpha$ = 0.1. Use $\\epsilon$ = 0.1 and longer runs, say of 10,000 steps.**\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707ebd40b8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Exercise 2.5 \n",
    "sample_average_bandit = Bandit(arms=10,\n",
    "                               estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                               action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                               epsilon=0.1,start_equal=True, random_walk=0.01)\n",
    "\n",
    "constant_step_size_bandit = Bandit(arms=10, estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                                   alpha=0.1,random_walk=0.01,epsilon=0.1, start_equal=True,\n",
    "                                   action_selection_method=ActionSelectionMethod.EPSILON_GREEDY)\n",
    "\n",
    "epsilon_greedy_best_action, epsilon_greedy_rewards = [], []\n",
    "\n",
    "sample_average_result = sample_average_bandit.simulate(2000, 10000)\n",
    "sample_average_best_action = sample_average_result[0]\n",
    "sample_average_rewards = sample_average_result[1]\n",
    "\n",
    "constant_step_size_result = constant_step_size_bandit.simulate(2000, 10000)\n",
    "constant_step_size_best_action = constant_step_size_result[0]\n",
    "constant_step_size_rewards = constant_step_size_result[1]\n",
    "\n",
    "%matplotlib inline\n",
    "plt.figure()\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(sample_average_rewards, label='epsilon = {}'.format(0.1))\n",
    "plt.plot(constant_step_size_rewards, label='epsilon = {}, alpha = {}'.format(0.1, 0.1))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('average reward')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(sample_average_best_action * 100, label='epsilon = {}'.format(0.1))\n",
    "plt.plot(constant_step_size_best_action * 100, label='epsilon = {}, alpha = {}'.format(0.1, 0.1))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('% optimal action')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimistic Initial Values\n",
    "Initial action values can be used as a simple way to encourage **exploration**. Suppose that instead of setting the initial values to zero, we set them all to 5 then because it is really **optimistic** ($q_*(a)$ is a normal distribution with mean 0 and variance 1) then the reward will be leass than the starting estimates so the agent will switch to other actions and will explore more actions, but it is **not well suited** to **nonstationary** problems because its drive for exploration is inherently temporary. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707eb5a748>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Figure 2.3\n",
    "optimistic_initial_value_bandit =Bandit(arms=10,\n",
    "                                        estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                                        alpha=0.1,\n",
    "                                        action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                                        epsilon=0,initial_value_estimation=5.0)\n",
    "\n",
    "realistic_initial_value_bandit =Bandit(arms=10,\n",
    "                                       estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                                       alpha=0.1,\n",
    "                                       action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                                       epsilon=0.1,initial_value_estimation=0)\n",
    "\n",
    "optimistic_result = optimistic_initial_value_bandit.simulate(2000, 1000)\n",
    "optimistic_best_action = optimistic_result[0]\n",
    "\n",
    "realistic_result = realistic_initial_value_bandit.simulate(2000, 1000)\n",
    "realistic_best_action = realistic_result[0]\n",
    "\n",
    "%matplotlib inline\n",
    "plt.plot(optimistic_best_action * 100, label='Q1 = {} , epsilon = {}'.format(5, 0))\n",
    "plt.plot(realistic_best_action * 100, label='Q1 = {} , epsilon = {}'.format(0, 0.1))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('% optimal action')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2.6: Mysterious Spikes The results shown in Figure 2.3 should be quite reliable\n",
    "because they are averages over 2000 individual, randomly chosen 10-armed bandit tasks.\n",
    "Why, then, are there oscillations and spikes in the early part of the curve for the optimistic\n",
    "method? In other words, what might make this method perform particularly better or\n",
    "worse, on average, on particular early steps?**\n",
    "\n",
    "If the initial action selected when using the optimistic method are by chance ones of the better\n",
    "choices then the action value estimates Q(a) for these plays will be magnified resulting in an\n",
    "emphasis to continue playing this action. This results in large actions values being received\n",
    "on the initial draws and consequently very good initial play. In the same way, if the algorithm\n",
    "initially selects poor plays then initially the algorithm will perform poorly resulting in very\n",
    "poor initial play.\n",
    "\n",
    "**Exercise 2.7: Unbiased Constant-Step-Size Trick In most of this chapter we have used\n",
    "sample averages to estimate action values because sample averages do not produce the\n",
    "initial bias that constant step sizes do (see the analysis leading to (2.6)). However, sample\n",
    "averages are not a completely satisfactory solution because they may perform poorly\n",
    "on nonstationary problems. Is it possible to avoid the bias of constant step sizes while\n",
    "retaining their advantages on nonstationary problems? One way is to use a step size of**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Upper-Confidence-Bound Action Selection\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707ea56400>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Figure 2.4\n",
    "ucb_bandit = Bandit(arms=10, estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                    action_selection_method=ActionSelectionMethod.UPPER_CONFIDENCE_BOUND,\n",
    "                    c=2, start_time=1)\n",
    "\n",
    "epsilon_greedy_bandit = Bandit(arms=10, \n",
    "                               estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                               action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                               epsilon=0.1,\n",
    "                               start_time=1)\n",
    "\n",
    "ucb_result = ucb_bandit.simulate(2000, 1000)\n",
    "ucb_rewards = ucb_result[1]\n",
    "\n",
    "epsilon_greedy_result = epsilon_greedy_bandit.simulate(2000, 1000)\n",
    "epsilon_greedy_rewards = epsilon_greedy_result[1]\n",
    "\n",
    "%matplotlib inline\n",
    "plt.plot(ucb_rewards, label='c = {}'.format(2))\n",
    "plt.plot(epsilon_greedy_rewards, label='epsilon = {}'.format(0.1))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('average reward')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Bandit Algorithms\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707ea04a20>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Figure 2.5\n",
    "gradient_small_alpha_base_bandit=Bandit(arms=10,\n",
    "                                        estimation_method=EstimationMethod.GRADIENT_BANDIT,\n",
    "                                        alpha=0.1,gradient_baseline=True, q_star_mean=4,\n",
    "                                        action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT)\n",
    "gradient_small_alpha_base_best_action=gradient_small_alpha_base_bandit.simulate(2000, 1000)[0]\n",
    "\n",
    "gradient_big_alpha_base_bandit=Bandit(arms=10,\n",
    "                                      estimation_method=EstimationMethod.GRADIENT_BANDIT,\n",
    "                                      alpha=0.4,gradient_baseline=True, q_star_mean=4,\n",
    "                                      action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT)\n",
    "gradient_big_alpha_base_best_action=gradient_big_alpha_base_bandit.simulate(2000, 1000)[0]\n",
    "\n",
    "gradient_small_alpha_bandit=Bandit(arms=10, estimation_method=EstimationMethod.GRADIENT_BANDIT,\n",
    "                                   alpha=0.1, gradient_baseline=False, q_star_mean=4,\n",
    "                                   action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT)\n",
    "gradient_small_alpha_best_action=gradient_small_alpha_bandit.simulate(2000,1000)[0]\n",
    "\n",
    "gradient_big_alpha_bandit = Bandit(arms=10, estimation_method=EstimationMethod.GRADIENT_BANDIT,\n",
    "                                   alpha=0.4, gradient_baseline=False, q_star_mean=4,\n",
    "                                   action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT)\n",
    "gradient_big_alpha_best_action = gradient_big_alpha_bandit.simulate(2000, 1000)[0]\n",
    "\n",
    "%matplotlib inline\n",
    "plt.plot(gradient_small_alpha_base_best_action * 100,label='with baseline , alpha = {}'.format(0.1))\n",
    "plt.plot(gradient_big_alpha_base_best_action * 100,label='with baseline , alpha = {}'.format(0.4))\n",
    "plt.plot(gradient_small_alpha_best_action * 100, label='without baseline , alpha = {}'.format(0.1))\n",
    "plt.plot(gradient_big_alpha_best_action * 100, label='without baseline , alpha = {}'.format(0.4))\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('% optimal action')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Associative Search (Contextual Bandits)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f707e985be0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Figure 2.6\n",
    "epsilon_greedy_bandits = [Bandit(action_selection_method=ActionSelectionMethod.EPSILON_GREEDY, \n",
    "                                 epsilon=2**power,\n",
    "                                 estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL)\n",
    "                          for power in range(-7, -1)]\n",
    "\n",
    "average_rewards_epsilon_greedy = []\n",
    "for bandit in epsilon_greedy_bandits:\n",
    "    reward = bandit.simulate(2000,1000)[1].mean()\n",
    "    average_rewards_epsilon_greedy.append(reward)\n",
    "gradient_bandit_bandits = [Bandit(action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT,\n",
    "                                  alpha=2**power,\n",
    "                                  estimation_method=EstimationMethod.GRADIENT_BANDIT,\n",
    "                                  gradient_baseline=True) for power in range(-5, 3)]\n",
    "average_rewards_gradient = []\n",
    "for bandit in gradient_bandit_bandits:\n",
    "    reward = bandit.simulate(2000, 1000)[1].mean()\n",
    "    average_rewards_gradient.append(reward)\n",
    "\n",
    "ucb_bandits = [Bandit(estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                      action_selection_method=ActionSelectionMethod.UPPER_CONFIDENCE_BOUND,\n",
    "                      c=2**power,start_time=1) for power in range(-4, 3)]\n",
    "average_rewards_ucb = []\n",
    "for bandit in ucb_bandits:\n",
    "    reward = bandit.simulate(2000, 1000)[1].mean()\n",
    "    average_rewards_ucb.append(reward)\n",
    "\n",
    "optimistic_bandits = [Bandit(arms=10, estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                             alpha=0.1,\n",
    "                             action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                             epsilon=0,\n",
    "                             initial_value_estimation=2**power) for power in range(-2, 3)]\n",
    "\n",
    "average_rewards_optimistic = []\n",
    "for bandit in optimistic_bandits:\n",
    "    reward = bandit.simulate(2000, 1000)[1].mean()\n",
    "    average_rewards_optimistic.append(reward)\n",
    "\n",
    "%matplotlib inline   \n",
    "plt.xticks(range(-7, 3), ('1/128', '1/64', '1/32', '1/16', '1/8', '1/4', '1/2', '1', '2', '4'))\n",
    "\n",
    "plt.plot(range(-7, -1), average_rewards_epsilon_greedy, label='epsilon-greedy parameter:epsilon')\n",
    "plt.plot(range(-5, 3), average_rewards_gradient, label='gradient bandit parameter:alpha')\n",
    "plt.plot(range(-4, 3), average_rewards_ucb, label='UCB parameter:c')\n",
    "plt.plot(range(-2, 3), average_rewards_optimistic,\n",
    "         label='greedy with optimistic initialization α = 0.1parameter:Q1')\n",
    "\n",
    "plt.xlabel('Parameter')\n",
    "plt.ylabel('Average reward')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2.11 (programming) Make a figure analogous to Figure 2.6 for the nonstationary\n",
    "case outlined in Exercise 2.5. Include the constant-step-size $\\epsilon$-greedy algorithm with\n",
    "$\\alpha$ = 0.1. Use runs of 200,000 steps and, as a performance measure for each algorithm and\n",
    "parameter setting, use the average reward over the last 100,000 steps.**\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7b673c8198>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#excercise 2.11\n",
    "runs=500\n",
    "times=20000\n",
    "epsilon_greedy_bandits = [\n",
    "    Bandit(action_selection_method=ActionSelectionMethod.EPSILON_GREEDY, epsilon=2 ** power,\n",
    "           estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "           start_equal=True, random_walk=0.01)\n",
    "    for power in range(-7, -1)]\n",
    "average_rewards_epsilon_greedy = []\n",
    "for bandit in epsilon_greedy_bandits:\n",
    "    reward = bandit.simulate(runs, times)[1][int(times / 2):].mean()\n",
    "    average_rewards_epsilon_greedy.append(reward)\n",
    "\n",
    "gradient_bandit_bandits = [\n",
    "    Bandit(action_selection_method=ActionSelectionMethod.GRADIENT_BANDIT, alpha=2 ** power,\n",
    "           estimation_method=EstimationMethod.GRADIENT_BANDIT, gradient_baseline=True,\n",
    "           start_equal=True,random_walk=0.01) for power in range(-5, 3)]\n",
    "average_rewards_gradient = []\n",
    "for bandit in gradient_bandit_bandits:\n",
    "    reward = bandit.simulate(runs, times)[1][int(times / 2):].mean()\n",
    "    average_rewards_gradient.append(reward)\n",
    "\n",
    "ucb_bandits = [Bandit(estimation_method=EstimationMethod.SAMPLE_AVERAGE_INCREMENTAL,\n",
    "                      action_selection_method=ActionSelectionMethod.UPPER_CONFIDENCE_BOUND,\n",
    "                      c=2 ** power,\n",
    "                      start_equal=True, random_walk=0.01, start_time=1) for power in range(-4, 3)]\n",
    "average_rewards_ucb = []\n",
    "for bandit in ucb_bandits:\n",
    "    reward = bandit.simulate(runs, times)[1][int(times / 2):].mean()\n",
    "    average_rewards_ucb.append(reward)\n",
    "\n",
    "optimistic_bandits = [Bandit(arms=10, estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                             alpha=0.1,\n",
    "                             action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                             epsilon=0,\n",
    "                             start_equal=True, random_walk=0.01,\n",
    "                             initial_value_estimation=2 ** power) for power in range(-2, 3)]\n",
    "average_rewards_optimistic = []\n",
    "for bandit in optimistic_bandits:\n",
    "    reward = bandit.simulate(runs, times)[1][int(times / 2):].mean()\n",
    "    average_rewards_optimistic.append(reward)\n",
    "\n",
    "constant_step_size_bandits = [Bandit(arms=10,\n",
    "                                     estimation_method=EstimationMethod.CONSTANT_STEP_SIZE,\n",
    "                                     alpha=0.1,\n",
    "                                     random_walk=0.01,\n",
    "                                     action_selection_method=ActionSelectionMethod.EPSILON_GREEDY,\n",
    "                                     epsilon=2**power, start_equal=True) for power in range(-7, -1)]\n",
    "average_rewards_step_size = []\n",
    "for bandit in constant_step_size_bandits:\n",
    "    reward = bandit.simulate(runs, times)[1][int(times / 2):].mean()\n",
    "    average_rewards_step_size.append(reward)\n",
    "\n",
    "%matplotlib inline \n",
    "plt.xticks(range(-7, 3), ('1/128', '1/64', '1/32', '1/16', '1/8', '1/4', '1/2', '1', '2', '4'))\n",
    "\n",
    "plt.plot(range(-7, -1), average_rewards_epsilon_greedy, label='epsilon-greedy parameter:epsilon')\n",
    "plt.plot(range(-7, -1), average_rewards_step_size, label='constant alpha=0.1 parameter:epsilon')\n",
    "plt.plot(range(-5, 3), average_rewards_gradient, label='gradient bandit parameter:alpha')\n",
    "plt.plot(range(-4, 3), average_rewards_ucb, label='UCB parameter:c')\n",
    "plt.plot(range(-2, 3), average_rewards_optimistic,\n",
    "         label='greedy with optimistic initialization α = 0.1 parameter:Q1')\n",
    "\n",
    "plt.xlabel('Parameter')\n",
    "plt.ylabel('Average reward over 10000 time step')\n",
    "plt.legend()\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
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   "file_extension": ".py",
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