Nonstationary_bandits_exercise_2.5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examine sample-average methods for nonstationary problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reproduction of Sutton-Barto 2018 p.27-33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from tqdm import tqdm_notebook\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Env:\n",
    "    def __init__(self, arms):\n",
    "        self.means = np.random.normal(size=arms)\n",
    "        \n",
    "    def __call__(self, action):\n",
    "        reward = np.random.normal(loc=self.means[action])\n",
    "        self.drift()\n",
    "        return reward\n",
    "        \n",
    "    def drift(self):\n",
    "        for i in range(len(self.means)):\n",
    "            self.means[i] += np.random.normal(loc=0, scale=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_average(timesteps, alpha=None, eps=None):\n",
    "    env = Env(arms=k)\n",
    "    estimates = np.zeros(shape=k)\n",
    "    mean_rewards = []\n",
    "    mean_is_optimals = []\n",
    "    for i in range(timesteps):\n",
    "        if eps is None or np.random.binomial(n=1, p=1-eps):\n",
    "            action = np.argmax(estimates)\n",
    "        else:\n",
    "            action = np.random.randint(estimates.shape[0])\n",
    "        reward = env(action)\n",
    "        step_size = 1/(i+1) if alpha is None else alpha\n",
    "        estimates[action] += step_size * (reward - estimates[action])\n",
    "        is_optimal = int(action == np.argmax(env.means))\n",
    "        if len(mean_rewards) > 1:\n",
    "            mean_reward = mean_rewards[-1] + 1/(i+1) * (reward - mean_rewards[-1])\n",
    "            mean_is_optimal = mean_is_optimals[-1] + 1/(i+1) * (is_optimal - mean_is_optimals[-1])\n",
    "        else:\n",
    "            mean_reward = reward\n",
    "            mean_is_optimal = is_optimal\n",
    "        mean_rewards.append(mean_reward)\n",
    "        mean_is_optimals.append(mean_is_optimal)\n",
    "    return mean_rewards, mean_is_optimals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_results(method):\n",
    "    mean_rewards, mean_is_optimals = method(timesteps)    \n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.plot(mean_rewards)\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.ylim(0, 1)\n",
    "    plt.plot(mean_is_optimals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def test_method(method):\n",
    "    final_rewards = []\n",
    "    final_is_optimals = []\n",
    "    for i in range(repeats):\n",
    "        mean_rewards, mean_is_optimals = method(timesteps)\n",
    "        final_reward, final_is_optimal = mean_rewards[-1], mean_is_optimals[-1]\n",
    "        final_rewards.append(final_reward)\n",
    "        final_is_optimals.append(final_is_optimal)\n",
    "    print(np.array(final_rewards).mean())\n",
    "    print(np.array(final_is_optimals).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "k = 10  # number of arms\n",
    "timesteps = 10000\n",
    "repeats = 25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Usual sample-average method with drift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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ltdlktdpktdtktVplsVqVGh5WLp3J9yeX/1zGyGuL1Sqn11MYnUqnUkoPJ2V3OuTyemWx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\nSdrx0p+UiERUfVq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MGTP0+uuva9u2bXrrrbf09NNP67nnniu+5wAAAAAASUWO2G3YsEEb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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HKGyAhZTk5mnntz9q57c/2pcFdw9T9zMG1Be5MwZozDWX61y3ayVJZQWFsiXt\n0v6kXdqftFu2pF3Ky9wvwzDlb40AAJiG0oZ2xdnVVdP+NFe2xF3asOozs+MAaEJuhk25GTZt+nSd\nJMnJ2Vkhkb3U/YyBCuvfV6ED+uqcWdfI2cVFklRZWqb9ybsbytxu7U/apUPp+zi0EgDQrlHa0K6M\nnXmVArt11ft/e4y/xgNtUG1NTUMZ221f5uTsrJA+vRTav6/CBvRVaL8onXnFJXL1cJckVVdWKWt3\nqvYn7bKXuey0dNVUcbETAED7QGlDu+EV4K8Jt96gnd/+qNRfNpodB0Azqa2p0f7k3dqfvFu/fLRa\nkuTg6KjOEd0VOqBv/R65flGNvj+urrZWOfsydWB3qrJ2p+rA7jQd2J2qggOcJwcAaHsobWg3Js29\nWa4e7vrkX8+ZHQVACzPq6nRwz14d3LNXmz5ZK6n+IkSBod0U2j9KXaP6qFtUb4UP6q+hUybaf66i\npFQHdqfqQEpaQ5lLVXbKHlWVl5v1UQAAaBKlDe1Cp4juOvPKSxW//GMdSt9ndhwAJjAMQ3m2/cqz\n7de2L76xL3fz8lTXPr3VNaqPukb1VreoPhp+4RSN8fayz8nNtNn3xmWnpSs7dY9y92WqtqbGjI8C\nAEAjlDa0CxfedYeqq6q07oVXzI4CwGKqysq1d+t27d26vdHygG4h6hbVp6HM9VG3qD4aeO7ZcnRy\nklR/WGZuhk3ZqXvq9+qlpSs7LV05ezNUW11txkcBAHRQlDa0ed0HD9Sg88Zpzb9fVGl+gdlxALQR\nBVnZKsjKbvQVBM5ubuoc0V0hfXqqS6+eCunTU92i+uiMCeMalbm8zP3KTkvXwT3pOpj6a5mrOXzY\nrI8DAGjHKG1o86b9ca5K8vL1w9vLzI4CoI2rqapS1q4UZe1KabTc2dVVnSK6K6R3T3VpGCG9e2rg\nuWfLybn+f6V1tbXKy9yvQ+n7dGhvhnL2HrnN4A9KAIDTQmlDm9Zn5HBFjh6hlYue0eGKCrPjAGin\nag4frr+Aye7URsudXFzqy1yvCHuZ69yzh/qOGSVnV1f7vPLiYuWkZ9hL3KG9+5SzN0O5GTb2zgEA\nmkRpQ5s2df5tKsw+qJ+XfWR2FAAdUG11tbJT0pSdktZouYOjowK6hahzRHd1iujRcNtdUaNjFDN9\nmn1eXV2dCrIO1Je59F/LXM6+DBUfyuX7JgEAkihtaMP6nzNGEUPO0AcLH+cv1QAsxairU74tS/m2\nLCX/GN/oOTdPT3WKCFenHvVF7kix6zVsiNw8Pe3zqiurlJtpU16mTbkZ+5WbYVOezabcDJsKDhyU\nUVfX2h8LAGASShvaHC9/Px3a3Cv3AAAY30lEQVSurNTUP85RboZNv6z8xOxIAHDSqsrLZUvcJVvi\nrmOe8+vSSZ0jeii4R7iCw8MU3D1UQeFh6nvWaLm4u9nn1VRXK9+WpdzM+hKXl7nffr9g/wG+qgAA\n2hlKG9oUD19fLVgVJ0cnJ3n4+uidvzysuppas2MBQLMoOpijooM5Slm/odFyBwcH+XQKVnD3sIYy\nF2a/32v4ULl7/fqdc3W1tSo4kF1f5DJsyt+fpbz9B+r3/O3PUnlRcWt/LADAaaK0oU3oPSJaE2+7\nSVVl5fLw85VtZ7Jqa2q0ec0XZkcDgBZnGIaKD+Wo+FCO9mzYfMzz3kEBCg4LU1D3xoVu6JSJ8vTz\nbTS3srRM+VkHlL8/S/m2htv9WfXLbAdUVV7eWh8LAHCSTqq0TZ48WUuWLJGTk5NefvllLVq0qNHz\nd911l2699VbV1NQoJydHN998szIyMlokMDqmi+6dr/AB/SRJv6z8RO//7TGTEwGAdZTmFag0r+CY\nLxCXJHdvLwV066qgsG4KDO2mwNCuCuzWVUFhoYocNaLReXSSVFZQqLz9Wcrff6TQHbDfL8jK5hxi\nADBBk6XN0dFRS5cu1fnnny+bzaaEhAStWrVKSUlJ9jmbN2/WiBEjVFFRoblz52rx4sWaMWNGiwZH\nxxF15kiFD+in5f9YrNL8/GMOGwIAnFhladlxv67gCK8AfwWGdlNQaFcFhHa13w/tG6lB48c2+uoC\nSSrJy1fBgWwVHjioggPZKjhwUIVHbrMP8p10ANACmixtI0eOVGpqqtLT0yVJcXFxmj59eqPS9u23\n39rvx8fHa+bMmc2fFB3WhFtnqfDgIf3y0WpOrgeAZlZWUKiygkJl7kg85rkj59IFNZS5gG4h8u/a\nRQEhIercK0J9x4yWm6dHo5+prqxSYfZBFWQftBe7XwtetgqzD7G3DgBOUZOlLTQ0VJmZmfbHNptN\no0aNOuH8W265RZ999tlxn5s9e7bmzJkjSQoODj7VrOiA7nj9efUeHq2PFy+hsAFAKzv6XLr0zduO\nO8fD11eBR8pc1y7yDwmpv+3aRX3PGiWfTkFydHRs9DNH760rPHio/gIsh3JUdNR9ih0A/KrJ0ubg\n4HDMshN92ed1112nESNGaNy4ccd9PjY2VrGxsZKkhISEU8mJDmjYBZPUe3i0DldUKn75x2bHAQAc\nR0VxsfYXF2t/8u7jPu/k7Cy/Lp0U0DVE/l1/LXQBISHq0runos4a2ejql0eUFRTWF7pDOUeVuoZi\ndyhHhQcPqbKktKU/HgBYQpOlzWazKTw83P44LCxMWVlZx8ybMGGCHnzwQY0bN06H+esYmsE519ef\nF/m3syfzF1cAaKNqa2rsFzM5ETcvT/l17iT/kM7y69xJfl0a34YP7C+foMBjfq6qvMJe4uzF7qg9\ndsW5uSrJy+erYQC0eU2WtoSEBEVGRioiIkL79+/XjBkzdO211zaaM3ToUL300kuaMmWKcnJyWiws\nOo6ew4YofGB/LX9kMYUNANq5qrJyHUrfp0Pp+044x8nFRb6dguR/dKHr8mux6zV8qPw6d5KTS+Nf\nberq6lRWUKiS3DwV5+SpODdXxTl5Kmm4PXpZTVVVS39UAPhdmixttbW1mjdvntauXSsnJye9+uqr\nSkxM1MKFC7VhwwatXr1aTzzxhLy9vfXBBx9IkjIyMjR9+vQWD4/265zrZ6i8qFgbVx///EgAQMdS\nW12tgqxsFWRln3COg4ODvAL95d+ls3w7dZJvpyD5BgfJt3Mn+QYHyadTkEIie8knMPCYcidJ5cXF\n9YXuqCJXnJtb/zgnV8W59bdVZXyXHYDW5SDp+CeotbCEhATFxMSY8dawuMCwbvrLpx/om1ff1pol\nL5gdBwDQzjg4OMgrwF8+wUHy7RTcUO7qb/93mYu72zE/X1VeoZLcPJXmF6gkL18lefkqzctv9PjI\nssrSMhM+IYC24mQ70Ul9uTbQmsZee5WM2jr9+N5ys6MAANohwzBUml+g0vyCE35/3REevj71e+s6\nBcvnf8qdd2CAgruHKWLoGfIK8D/mKpmSVF1VZS9zpXkNt/bH+Y0elxcWnfBibwA6NkobLMXd20sj\nL7tQW9d9peJDnB8JADBXRXGJKopLdHDP3t+c5+jkJC9/P3kHBcgnKFDeQYHyCQxsuB8g76BA+XYK\nVmi/KHkHBhz38Mzampr68++OKnJlBYUqzS9UWUGBygqLVJpfqNKCApUVFKqypJSSB3QQlDZYysjL\nLpK7l5e+ezPO7CgAAJy0utpa+2GRB5T2m3MdHBzk4esj78D6gmcveUGB9mXeQYHq1KO7vAL8j/kC\n8yNqa2pUVlhk/4L00oZb+/38gvrbwobiV1jIlTSBNorSBstwcHTU2ddcqT0bt8iWmGx2HAAAWoRh\nGCovKlZ5UfFvXjHzCBd3N3n5+8s70F9e/v7yCvSXd0CAvPz9Gt3vFtVHXgH+8vL3O+FrVRSXHFvu\nCgpUVlCk0oLC+lyFRSorKlJ5YZHKi0tk1NU158cH8DtQ2mAZ/ceepaCwbvrk6aVmRwEAwDKqK6tU\nmH1QhdkHT2q+o5OTPP185RXgL+8A//oiF+Av78D6cucd4C+vwAD5d+2isAH95BXoL2cXlxO+Xnlx\nscoLi1VWWNRwv6j+fkPx/PVx/bKywiKusAk0M0obLOOsqy9V0aEc7fj6O7OjAADQZtXV1tovtHJy\nNa/+C869AwLk6ecrT38/efn7ytPPr778+fvVL/PzlXeAvzpHdJenn588fLxP+Ho11dWNSl19oSux\nlzt76WsoghXFpaooKdHh8grO0wOOg9IGSwgM7aq+Y0bry5de43h7AABaWVVZuarKypVn23/SP+Po\nXL9Hz9P36GLnZy9+nv6+9seBYaEKH1i/zMXt2K9ROKKutlaVpWWqKCmxF7mKklJVlpTWl7uSUlVX\nVKqyrKxheYnKi0rs9ytKS/k9Au0SpQ2WcOaVl8ioq1P8io/NjgIAAE5CXU2tSvMKVJpXcEo/5+rh\nLk/fI3v0/OTu4y0PHx95+HjLw/fo2/r7nXqE25e7eXo2+fpV5eWqKClVRXGJKktK6++X1F8F9Mjy\nI8sq7c81PC4tU10tpQ/WQ2mD6ZxcXDTy0ouU+N1PKjrIZf4BAGjPDldU6nBFpQoPHjrln3V0dpKr\nu7vcvDzrS91R5c7D11vuR+4fdevbKVhdekfIw8dH7j7ex/0+vaPZ9/TZi12ZKktLG5aX1t9vWFZx\n1P3KklJVlpWpqqycQzzR7ChtMN2QSePlHRig/76/wuwoAADAwupq6g+frCwt+11/6HVwcJCrp0dD\n4fM+tvj5eMvdt3Hx8w/pLHfvnnL39pa7t5ecnH/71+e6ujpVlZXbi15lSUO5a7hfWVqqCnsRbHz/\nyGerLC3r0FftdHZzk6u7m5ycnVVXV6fqyipVV1XZ/008fH3k7Oqq6spKHa6sPO4hsa4e7uodM1z9\nxoxS1JkjVXAgW/+57c7W/ijNhtIG05111WXK2ZeplPgNZkcBAADtmGEY9vP3TvZqnP/L1cPdXuDc\nfbzl4e0tdx9vuXt51i/3qX/Ow8fbPs8nOEidI3rYf+a3rtZ5RGVZ2VFFr6xhr15pfSFs2KN39P3j\nListU2119e/6nK0tKDxMA889WwPOGaNew4ce9wvoa6qrVVN1WO7eXscsr66oL3BHCl6nHuFydnVV\nVXmF0jZsUsr6tv17JqUNpgqJ7K2ew4Zo1RP/5lACAABgeUcO7yzOyf3dr+Hs6ip3Hy+5ex9V+ry9\nGt2vL4Je9gLo5eenoNBucvPylJuXp9y9vJp+I9UXmiMFrqq8XFWlZapsuK0qK298314Ay1V1VPGr\nKq9fVlNV9bs/s1R/eGvE0MEK7RspRycn1dXVKaBrF/U7+0x16RUhSTqQkqbv3nxXRYdyVFdbJwdH\nR7m4ucnF3a3+1s1Nxbm5qigplau7u1zc3eTq7i5XDw+5eLg1LHNX8o/x2vVTvPZs2tpmiutvobTB\nVKMvv1jVVVVK+PhTs6MAAAC0iprDh1Wad/iUL+JytCOHerp5ecndy7P+1ttLbp6e9bdeno3uu3t5\n2Qufl5+fArt1tS9z9fRo8lw/SaqtrqkvcEcK4FGl7nBFpf1wxerKqvrHVVWqrqyUJPWJGaa+Z4+W\np6/vMf8WezZu0X/f/1CJ3/2o/P0Hfve/SXtGaYNpnF1dNfzCKdrx1XcqLyo2Ow4AAECbcfShnqf7\nW5SDg4NcPTzqy11D8Tv6/vFK4JGyeOS8Pxd3d7l6/Lrny9HJqdF7lOTla8dX3yvxux+1Z9NW1Rw+\nLEcnpw5//t7JorTBNAPHj5Wnn69+WfmJ2VEAAAA6LMMw6veclZef1mGfR3NycWkoce5ydnFWQVY2\np8KcBkobTDPykguVn3VAKes3mh0FAAAAzai2uloV1dWqKC4xO0q70PTBq0AL8O/SWVFnjdSGj9ew\nSxwAAAD4DZQ2mGLE9GlydHTkAiQAAABAEyhtaHUODg6KueQCpcRv4ApBAAAAQBMobWh1vYYPVXB4\nmH5ZudrsKAAAAIDlUdrQ6mIuuVAVxSXa9uV3ZkcBAAAALI/Shlbl6uGuweefqy3rvlJNVZXZcQAA\nAADLo7ShVQ08d6zcPD216dN1ZkcBAAAA2gRKG1rVsAsmq+BAttI3bjE7CgAAANAmUNrQarz8/dT3\nrFHa/NkXMgzD7DgAAABAm0BpQ6sZMnmCnFyctenTtWZHAQAAANoMShtazbALJutASpoO7E4zOwoA\nAADQZlDa0CoCQ7uqZ/RgLkACAAAAnCJKG1pF9LRJkqTNayhtAAAAwKmgtKFVDLtgsvZs3KKCA9lm\nRwEAAADaFEobWly3vpEK6d1Tm9jLBgAAAJwyShta3LBpk1RbXaNt6742OwoAAADQ5lDa0KIcHBwU\nPe187frvepUVFpkdBwAAAGhzKG1oURHRg+Uf0oVDIwEAAIDfydnsAGifxsy4XF2j+qhTj3BVlVdo\n5zc/mB0JAAAAaJMobWh2bl6euuieP8rB0VHOLi76ZeUnOlxRYXYsAAAAoE2itKHZDRh3tlzc3PTs\n9bcpZ+8+VZSWmh0JAAAAaLMobWh2Qyefp8KDh7Rv63YZhmF2HAAAAKBN40IkaFbuPt4adN44bfvi\nGwobAAAA0AwobWhWlyy4S5K0dS3fyQYAAAA0B0obmo2Ts7OGTpmgAylp2rtlm9lxAAAAgHaB0oZm\nc/a1V8rFzU2f/ftFs6MAAAAA7QalDc3mjAnjVFFcop3f/mh2FAAAAKDd4OqROC0Dxp2ts2Zcprqa\nWvUcNkSfPfuS2ZEAAACAdoXSht/NydlZMxcvlJunp4oO5mh/8m5tXP252bEAAACAduWkDo+cPHmy\nkpOTlZKSogULFhzzvKurq+Li4pSSkqL4+Hj16NGj2YPCenqNiJabp6denX+f/jHxYv3ryhtUcCDb\n7FgAAABAu9JkaXN0dNTSpUs1depUDRgwQNdcc4369+/faM4tt9yigoICRUZG6umnn9aiRYtaLDCs\nY8A5Y1RdWaXdP/9idhQAAACg3WqytI0cOVKpqalKT09XdXW14uLiNH369EZzpk+frjfeeEOStHz5\nck2YMKFl0sJSBpw7Rim/bFB1ZZXZUQAAAIB2q8lz2kJDQ5WZmWl/bLPZNGrUqBPOqa2tVVFRkYKC\ngpSXl9fMcVvWFX9foOhp55sdo01wcHCQm6envn3tXbOjAAAAAO1ak6XNwcHhmGWGYZzyHEmaPXu2\n5syZI0nq27evEhISTjpoawkODlZubq7ZMdqGSumc+x6Q7nvA7CRtBusXWhrrGFoS6xdaEusXWpJV\n16+TvRZIk6XNZrMpPDzc/jgsLExZWVnHnbN//345OTnJz89P+fn5x7xWbGysYmNjTyqYWRISEhQT\nE2N2DLRTrF9oaaxjaEmsX2hJrF9oSW19/WrynLaEhARFRkYqIiJCLi4umjFjhlatWtVozqpVq3TD\nDTdIkq644gp9/fXXLZMWAAAAADqYJve01dbWat68eVq7dq2cnJz06quvKjExUQsXLtSGDRu0evVq\nvfLKK3rrrbeUkpKi/Px8zZgxozWyAwAAAECHYDB+HbNnzzY9A6P9DtYvRksP1jFGSw7WL0ZLDtYv\nRkuOtr5+OTTcAQAAAABYUJPntAEAAAAAzENpO8rkyZOVnJyslJQULViwwOw4aCPCwsL09ddfKzEx\nUTt27ND8+fMlSQEBAVq3bp12796tdevWyd/f3/4zS5YsUUpKirZu3aro6Gj78lmzZmn37t3avXu3\nZs2a1eqfBdbk6OioTZs2afXq1ZKkiIgIxcfHa/fu3YqLi5OLi4skydXVVXFxcUpJSVF8fHyjywjf\nf//9SklJUXJysiZNmmTK54A1+fn56YMPPlBSUpISExM1evRotl9oNnfeead27Nih7du3691335Wb\nmxvbMJyWV155RQcPHtT27dvty5pzmzVs2DBt27ZNKSkpWrJkSet8qJNk+jGaVhiOjo5Gamqq0bNn\nT8PFxcXYsmWL0b9/f9NzMaw/QkJCjOjoaEOS4e3tbezatcvo37+/sWjRImPBggWGJGPBggXG448/\nbkgypk6daqxZs8aQZIwaNcqIj483JBkBAQFGWlqaERAQYPj7+xtpaWmGv7+/6Z+PYf646667jHfe\necdYvXq1Icl4//33jauvvtqQZLzwwgvG3LlzDUnG7bffbrzwwguGJOPqq6824uLiDElG//79jS1b\nthiurq5GRESEkZqaajg6Opr+uRjWGK+//rpxyy23GJIMFxcXw8/Pj+0Xo1lGt27djD179hju7u6G\nVL/tuuGGG9iGMU5rjB071oiOjja2b99uX9ac26z169cbo0ePNiQZa9asMaZMmWL6Z24YpgewxBg9\nerTx+eef2x/ff//9xv333296LkbbGytXrjQmTpxoJCcnGyEhIYZUX+ySk5MNScaLL75ozJgxwz7/\nyLwZM2YYL774on35/85jdMwRGhpqfPnll8b48ePtpS0nJ8dwcnIypMbbrs8//9z+PxonJycjJyfH\nkI7dnh09j9Gxh4+Pj7Fnz55jlrP9YjTH6Natm5GRkWEEBAQYTk5OxurVq41JkyaxDWOc9ujRo0ej\n0tZc26yQkBAjKSnJvvx/55k5ODyyQWhoqDIzM+2PbTabQkNDTUyEtqhHjx6Kjo7W+vXr1aVLF2Vn\nZ0uSsrOz1blzZ0knXtdYB3E8zzzzjO677z7V1dVJkoKCglRYWKja2lpJjdeTo9eh2tpaFRUVKSgo\niHULJ9SrVy/l5OTotdde06ZNmxQbGytPT0+2X2gWWVlZevLJJ5WRkaEDBw6oqKhIGzduZBuGZtdc\n26zQ0FDZbLZjllsBpa2Bg4PDMcsMwzAhCdoqLy8vrVixQnfeeadKSkpOOO9E6xrrIP7XBRdcoEOH\nDmnTpk32Zb+1nrBu4VQ5Oztr2LBheuGFFzRs2DCVlZXp/vvvP+F81jGcCn9/f02fPl09e/ZUt27d\n5OXlpalTpx4zj20YWsqprlNWXtcobQ1sNpvCw8Ptj8PCwpSVlWViIrQlzs7OWrFihd555x199NFH\nkqSDBw8qJCREkhQSEqJDhw5JOvG6xjqI/zVmzBhdfPHFSk9PV1xcnM477zw988wz8vf3l5OTk6TG\n68nR65CTk5P8/PyUn5/PuoUTstlsstls+uWXXyRJy5cv17Bhw9h+oVlMnDhR6enpys3NVU1NjT78\n8EOdddZZbMPQ7Jprm2Wz2RQWFnbMcqsw/RhNKwwnJycjLS3NiIiIsF+IZMCAAabnYrSN8cYbbxhP\nP/10o2WLFy9udFLsokWLDEnGtGnTGp0Uu379ekOqPyl2z549hr+/v+Hv72/s2bPHCAgIMP2zMawx\nxo0bZz+nbdmyZY1O4r/99tsNScYdd9zR6CT+999/35BkDBgwoNFJ/GlpaZzEz7CP77//3oiKijIk\nGQ899JCxePFitl+MZhkjR440duzYYXh4eBhS/UVv5s2bxzaMcdrjf89pa85t1i+//GKMGjXKkOov\nRDJ16lTTP2/DMD2AZcbUqVONXbt2GampqcYDDzxgeh5G2xhjxowxDMMwtm7damzevNnYvHmzMXXq\nVCMwMND48ssvjd27dxtffvllo19gnnvuOSM1NdXYtm2bMXz4cPvym266yUhJSTFSUlKMG2+80fTP\nxrDOOLq09ezZ01i/fr2RkpJiLFu2zHB1dTUkGW5ubsayZcuMlJQUY/369UbPnj3tP//AAw8Yqamp\nRnJyspWuhMWwwBgyZIiRkJBgbN261fjoo48Mf39/tl+MZhsPP/ywkZSUZGzfvt148803DVdXV7Zh\njNMa7777rpGVlWUcPnzYyMzMNG6++eZm3WYNHz7c2L59u5Gammo8++yzpn/eI8Oh4Q4AAAAAwII4\npw0AAAAALIzSBgAAAAAWRmkDAAAAAAujtAEAAACAhVHaAAAAAMDCKG0AAAAAYGGUNgAAAACwMEob\nAAAAAFjY/wO0kOWk/ErtmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(sample_average)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.23236940748\n",
      "0.414776\n"
     ]
    }
   ],
   "source": [
    "test_method(sample_average)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constant step-size method with drift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "const_step_size = lambda timesteps: sample_average(timesteps, alpha=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kacv6V1NcCQAAAAB8yJHqAjJJYHBI/+fCy+UfGEx1KQAAAAAQR7A7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\nAAAAMhzBDgAAAAAy3P8HwwLQG5612IAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GzZ6uUbNnaNJti9XU1KTMs0lKOnBYyQcO6cLnp9TY0GB02TAQnTY4HA9fHz32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\n4akxNwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(const_step_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.83689007043\n",
      "0.59682\n"
     ]
    }
   ],
   "source": [
    "test_method(const_step_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eps-greedy sample-average method with drift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [],
   "source": [
    "method = lambda timesteps: sample_average(timesteps, eps=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FdrtDCckeDfX3y+50KqMgX7Mumh8ZCTt+8D2FAgEN9fcrMDSsjMLZypidL0fc2NG0YCCg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\ny0/b7+abb1ZFRYWqqqp0991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      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kTGgDAADImNAGAACQMaENAAAgY0IbAABAxoQ2AACAjAltAAAAGRPaAAAAMia0AQAAZExo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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(method)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.998884171544\n",
      "0.284724\n"
     ]
    }
   ],
   "source": [
    "test_method(method)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eps-greedy, constant step size sample-average method with drift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "method = lambda timesteps: sample_average(timesteps, eps=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A2RDaMqHVBgAAAMAkCG3paLQBAAAAMBlCWwasHgkAAADALAhtabimDQAAAIDZENoyotMG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\nPQL4j1gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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88r8UN3OaZt9xm4qzTNr19iZ7lwUAQDtGFxeNmT1LU65drJGzZsjN00OVJaVK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\ngg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(method)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.22504348014\n",
      "0.4686\n"
     ]
    }
   ],
   "source": [
    "test_method(method)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basically constant step size makes recent experiences more important thus it performs better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}