{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "First, we define the basic building blocks for the FTL and multiplicative weights updates." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "\n", "def FTL(rewards):\n", " \"\"\"\n", " Code that follows the leader. Returns index of largest reward.\n", " \"\"\"\n", " if rewards[0] == rewards[1]:\n", " return [0,1]\n", " else:\n", " return [np.argmax(rewards)]\n", "\n", "def MultiplicativeWeights(rewards, eta):\n", " \"\"\"\n", " Code that implements the randomized multiplicative weights algorithm.\n", " \"\"\"\n", " \n", " weights = np.exp(eta*rewards)\n", " return weights/sum(weights)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define code to generate our example sequences -- iid Bernoulli 0.7, 1-periodic and 2-periodic. *Feel free to create your own sequences here to play around with*!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def GenerateIIDSequence(T, p):\n", " \"\"\"\n", " Code that generates an iid sequence of length T with Bernoulli parameter p.\n", " \"\"\"\n", " \n", " return np.random.binomial(1, p, T)\n", "\n", "def GenerateOnePeriodicSequence(T):\n", " \"\"\"\n", " Code that generates a 1-periodic sequence of length T.\n", " \"\"\"\n", " \n", " sequence_list = [0,1]*int(T/2)\n", " return np.array(sequence_list)\n", " \n", "def GenerateTwoPeriodicSequence(T):\n", " \"\"\"\n", " Code that generates a 2-periodic sequence of length T.\n", " \"\"\"\n", " \n", " sequence_list = [0,0,1,1]*int(T/4)\n", " return np.array(sequence_list)\n", "\n", "T = 1000\n", "p = 0.7\n", "sequence_iid = GenerateIIDSequence(T,p)\n", "sequence_oneperiod = GenerateOnePeriodicSequence(T)\n", "sequence_twoperiod = GenerateTwoPeriodicSequence(T)\n", "\n", "#print(sequence_iid)\n", "#print(sequence_oneperiod)\n", "#print(sequence_twoperiod)\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Space for creating own sequences." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, define code to evaluate cumulative rewards and regret for each algorithm on ANY sequence.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def getRewardAndRegretFTL(sequence):\n", " T = len(sequence)\n", " \n", " rewards_actual = np.zeros(2)\n", " reward_cum = 0\n", " rewards_alg = []\n", " regrets_alg = []\n", " for t in range(T):\n", " inds = FTL(rewards_actual)\n", "# print(inds)\n", " if len(inds) > 1:\n", " reward_cum += 0.5\n", " else:\n", " reward_cum += (inds[0] == sequence[t])\n", " rewards_alg.append(reward_cum)\n", " rewards_actual[0] += (sequence[t] == 0)\n", " rewards_actual[1] += (sequence[t] == 1)\n", " regrets_alg.append(max(rewards_actual) - reward_cum)\n", " \n", " return rewards_alg, regrets_alg\n", "\n", "def getRewardAndRegretOneMemoryFTL(sequence):\n", " T = len(sequence)\n", " rewards_actual = np.zeros((2,2))\n", " reward_cum = 0\n", " rewards_alg = []\n", " regrets_alg = []\n", " for t in range(T):\n", " if t == 0:\n", " inds = [0,1]\n", " reward_cum += 0.5\n", " rewards_alg.append(reward_cum)\n", " regrets_alg.append(0.5)\n", " else:\n", " inds = FTL(rewards_actual[sequence[t-1]])\n", " if len(inds) > 1:\n", " reward_cum += 0.5\n", " else:\n", " reward_cum += (inds[0] == sequence[t])\n", " rewards_alg.append(reward_cum)\n", " rewards_actual[sequence[t-1]][0] += (sequence[t] == 0)\n", " rewards_actual[sequence[t-1]][1] += (sequence[t] == 1)\n", " regrets_alg.append(max(rewards_actual[0][0] + rewards_actual[1][0], \n", " rewards_actual[0][1] + rewards_actual[1][1]) - reward_cum)\n", " \n", " return rewards_alg, regrets_alg\n", " \n", "def getRewardAndRegretMW(sequence, eta):\n", " T = len(sequence)\n", " rewards_actual = np.zeros(2)\n", " reward_cum = 0\n", " for t in range(T):\n", " inds = MultiplicativeWeights(rewards_actual, eta)\n", " reward_cum += inds[sequence[t]]\n", " rewards_actual[0] += (sequence[t] == 0)\n", " rewards_actual[1] += (sequence[t] == 1)\n", " return reward_cum, max(rewards_actual) - reward_cum\n", "\n", "def getAllRewardsAndRegretsMW(sequence, etas):\n", " T = len(sequence)\n", " rewards = []\n", " regrets = []\n", " for t in range(T):\n", " eta = etas[t]\n", " #eta = 8*np.log(2)/np.sqrt(t)\n", " reward, regret = getRewardAndRegretMW(sequence[0:t], eta)\n", " rewards.append(reward)\n", " regrets.append(regret)\n", " return rewards, regrets\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we evaluate the greedy FTL against an iid Bernoulli (0.7) sequence. We see that it does really well, in fact as well as possible!" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wV14JYWHw9NNPs3btWrp37x6wicSXspNM/g/oDOx1X53deTlVDdgvIhNFZKWI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\n25271qdMgZiYBI4dO3jG+iJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "Ts = np.arange(T)\n", "\n", "rewards_iid, regrets_iid = getRewardAndRegretFTL(sequence_iid)\n", "\n", "plt.plot(Ts, rewards_iid,label=\"FTL\")\n", "plt.plot(Ts, 0.7*Ts, 'k--',label=\"Single alphabet benchmark\")\n", "plt.ylim(0,1000)\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Total reward\")\n", "plt.title(\"iid Bernoulli (0.7) sequence\")\n", "plt.legend(loc=2)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we see an example where greedy FTL does badly -- a periodic sequence of 010101 designed to fool FTL. One way of solving this problem is to now try and do well on the adversary -- one way to do this would be to use the previous memory of the sequence to predict. *We see that this does really well for this sequence!*" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VaNv70ksvabNmzYLuu+OOO/T88893bzfW+1pVvV9Cqlphy9pAKtsO9pFHHlHV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\nUmvJkiU8+eSTzJ49m8zMTAYPHsx9991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3hl8bqRVaRLwyCRXOOusshgwZQmJiYpHPbdiwIb///rt73fOzN7Gxsbz++uuk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\nw4YNc+0rV64cd999d5B6ZhhFw2ImRp5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rewards_oneperiod, regrets_oneperiod = getRewardAndRegretFTL(sequence_oneperiod)\n", "plt.plot(Ts, rewards_oneperiod,label=\"FTL\")\n", "plt.plot(Ts, 0.5*Ts, 'k--',label=\"Single alphabet benchmark\")\n", "plt.plot(Ts, Ts, 'r--', label=\"One-memory benchmark\")\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Total reward\")\n", "plt.title(\"1-periodic sequence 010101...\")\n", "plt.legend(loc=2)\n", "plt.grid()\n", "plt.show()\n", "\n", "rewards_oneperiod_oneFTL, regrets_oneperiod_oneFTL = getRewardAndRegretOneMemoryFTL(sequence_oneperiod)\n", "plt.plot(Ts, rewards_oneperiod,label=\"FTL\")\n", "plt.plot(Ts, rewards_oneperiod_oneFTL,label=\"One memory FTL\")\n", "plt.plot(Ts, 0.5*Ts, 'k--',label=\"Single alphabet benchmark\")\n", "plt.plot(Ts, Ts, 'r--', label=\"One-memory benchmark\")\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Total reward\")\n", "plt.title(\"1-periodic sequence 010101...\")\n", "plt.grid()\n", "plt.legend(loc=2)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we can construct a new adversary that makes both FTL and \"one-memory-FTL\" fail! In fact, this adversary looks like a 2-periodic sequence of the form 00110011..." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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89ddfZ+jQobRs2TLocy1evJjjjjuOnTt38uCDD3LBBRd4O+dW5TkqWnb3iiuu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\nn/4E+/Zl07BhaO+/YsUKb2lztJ8/XNs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rewards_twoperiod_FTL, regrets_twoperiod_FTL = getRewardAndRegretFTL(sequence_twoperiod)\n", "rewards_twoperiod_oneFTL, regrets_twoperiod_oneFTL = getRewardAndRegretOneMemoryFTL(sequence_twoperiod)\n", "\n", "plt.plot(Ts, rewards_twoperiod_FTL,label=\"FTL\")\n", "plt.plot(Ts, rewards_twoperiod_oneFTL, label=\"One memory FTL\")\n", "plt.plot(Ts, 0.5*Ts, 'k--', label=\"One memory benchmark\")\n", "plt.plot(Ts, Ts, 'r--', label=\"Two memory benchmark\")\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Total reward\")\n", "plt.title(\"2-periodic sequence 00110011...\")\n", "plt.legend(loc=2)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We showed in class that any deterministic algorithm (like FTL, one-memory FTL) is doomed to fail against some adversary. Now, we see the benefits of randomization in the multiplicative weights algorithm with an appropriately set learning rate. *Feel free to play around with the sequence of learning rates!* \n", "We measure performance by *regret* with respect to the benchmark of always predicting the alphabet that appeared the most often. We see that multiplicative weights always has a low regret against each of the adversaries we considered! " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NiXD5eNw8ZWZWo2aOPbVI0oiyA28OLBrogc3MbOgpUmmcAFwPbCLp18AtwNcb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\nimEn4Phe/sovP34AiyJiR+B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LXaRaN9p4rhHeoKozVPXvqvqWd0tIhWFMJNaOH2SxCIpWLIqL4Ygj3HoX27alXoURTREr\nDRHpIyJ9gcUicruIDPL29RGRPnEsY0orKioiNzeX3bt3H7B/7NixZGRk8Prrr1NYWHjAVcKNN95I\njx49Dtp36623xq3cxpjgano33ODW6l60CPr2TXSpEqutK41/4OadugaX0/grbj6qt739xgcRYeTI\nkSxcuLBl39q1a6mpqUFE6NevH6rK228HL95effVVhg0bdtC+iRMnxrXsqSQZ5hhKFhaLoM7EoqzM\nraZXUwMffOAqD9NGpaGqRao6IsJtZDwLmeqmTZvGggULWrbnz5/P1VdfjaqSnZ3NuHHjeOWVVwD4\n8ssvaWhoYPLkyQfs27BhAxMmTEhI+Y1JJ+XlcMUVrvvsb34DpaWpk+yOBz9zT+WJyPdEpFhEFonI\nd0SkWzwK11WMGzeOqqoq1q9fT1NTE08//TTTpk1reXzChAktFcQrr7zC+PHjOfPMMw/YN2LECAYP\nHpyQ8qcCa8cPslgEdTQWJSUwcqTLXWzdmt65i0j8jAhfAFQBjwACXAH8FrgshuWKOvnPTncaAEDv\nP7QeSldddRULFixgwoQJjB49miFDhrhyiTBhwgQeeeQRwDVDTZgwgdNPP72lYnn11VetycGYGCov\nh1tvhRdegJkzrSmqLX4qjeNUdXTI9ksisi5WBYqVQ/2yjwYR4aqrruKss85i8+bNLU1TAePGjWPv\n3r289957vPrqq9x+++0UFBQwbNiwln133XVXwsqfCqxSDbJYBPmJRWkp3HgjnH66y11YU1Tb/HS5\n/YeInB7YEJFxuGS46YDhw4czcuRIli5dyiWXXHLAY926dePUU0+lrKyML774glGjRgFw1llnUVZW\nxpo1ayyfYUyUVVS43MXll8Mjj7imKasw2uen0jgF+IuIfCIiW3C9qE4RkbXewD/j05w5c3jppZfI\ny8s76LEJEybw8MMPc+aZZ7bsGz9+PA8//DCDBw9mxIgR8SxqyrF2/CCLRVCkWBQXw+GHu9zFJ5+4\n5qgIi2iaVvw0T10Q81KkiZEjD+x0FrrU68SJE3nwwQcZP358y74zzzyTnTt3cnk6TWxjTAyF5i5m\nzbJE96GIOI1IewP4VLW8zRcWGYZLog/ArSn+pKo+4r3u08DhwBZgsqpWesfcC1yHm67kTlVdEeZ1\nbRqRMNL9/RvTnpISuOkml7uYNSv9mqJiPveU1xQV8VtIVdtsLxGRgcBAVV0tIt1xeZBv4Vb+26Wq\nvxSRHwC9VfUeERkN/AE4FRgCvACMUtXmVq9rlUYY6f7+jYmkosLNGVVaCnPnuvEX6dgUFfO5p9oZ\n3NduA7uqblfV1d79vcAHuMrgImC+97T5uIoE4GJgoao2qOoWYCNw2iG/M5NWrB0/yGIR9LOfrWL4\ncJe72LzZNUelY4URTX5yGohIb+AooGVQn6q+4vckIlIEjAX+Dhymqju8h3YAh3n3BwOvhxy2FVfJ\nGGNMhwRyF0uWwOzZlruIpnYrDRG5Ebdq3zDgHWAc8DfA13oaXtPUs8BdqlodmvxVVRWRttpUwj42\nffp0ioqKAOjVqxdjxozxU5S0EPiVGeifbtvpuR2QLOWJ5/Zrr8Gjj05i3Dg3hXnv3quA5ClfvLZX\nrVrFvHnzAFq+L6PBz3oa7+HyDH9T1TEicgzwgKr+S7svLpINPAcsVdWHvH3rgUmqul1EBgEvq+ox\nInIPgKo+6D1vGXC/qv691WtaTiOMdH//xlRWutX0ysqCVxfWFBUUz/U0alW1xjtpN1VdDxzto4AC\nzAHWBSoMTxnBNcavAUpC9k8VkRwRGYFrDnsDY3xo/Qs7naVjLEpKYOhQl7vYtCk47iIdYxFrfnIa\nn3k5jRJgpYhU4LrKtudMYBqwRkTe8fbdCzwIPCMi13uvMxlAVdeJyDPAOqARuC3sJUUbxH5WGJNW\nArmLlSuDPaNMbLXbPHXAk0UmAT2AZapaH6tCtVOGjtYlxpguqKQEbr4Zxo1zzVH9+ye6RMktbmuE\nJxurNIxJb5a7ODTxzGmYJGXttUEWi6CuHIvSUhgy5ODcRSRdORaJ4muchjHGJFIgd7FiBcybB5el\n1Go+XYuv5ilvcN6RqvqCiOQDWapaFeOyRSqLNU8Zk0aKi+GWW4JzRlnu4tDErXlKRG4C/g94wts1\nFCju7ImNMaYtlZVuvYtrroGHHnKVh1UYiecnp3E7MB635CuqugE3c61JMGuvDbJYBHWFWARyF7W1\nsHGjWyjpUJLdXSEWycZPTqNOVesCYyBEJIs2Zr81xphDFchdLF9uuYtk5Wcakf8GKoGrgTuA23Cj\nvP8j9sULWx7LaRjTBRUXu3EXZ5xhuYtYiNs4DRHJBK4Hzvd2LQdmJ+qb2yoNY7qWwLiL55+HJ56w\ncRexErdEuKo2qeqTqnqpd5tl39rJwdprgywWQakUi7IyGDYMampgw4bor9WdSrFIFRFzGiKyto3j\nVFVPjEF5jDFpIJC7WLrUzRlluYvU0dZyr0VtHeitrhd31jxlTGoL5C7OPBOefNJyF/Fic08ZY1JK\nYK3uJUtgxgzXjdbETzwH91WHuW0VkWIRGdnZAphDZ+21QRaLoGSMRVkZFBUFcxfxqjCSMRapzs84\njYeBz4CF3vZU4Ajc0q9zCayjaIwxrZSXB3tGzZlj6110BX663K5pnfQWkdXe0q/vqupJMS3hweWx\n5iljUkBxMdx0E4wfb7mLZBDPqdH3i8gUEcnwbpOBWu8x+/Y2xhygosLNGXXttfDIIzZnVFfjp9K4\nErgK+NK7XQ1ME5E83AhxkyDWXhtksQhKZCzKymDEiPjnLiKxz0X0tZvTUNWPgQsjPPxadItjjElF\nu3e7nlGLF8NTT1nuoivzk9MYANwIFBGsZFRVr4tt0SKWx3IaxiSRRYtc7mLCBJe76Ncv0SUy4UQr\np+Gn91Qp8AqwEmj29tm3tjFpLjDuYulSePzxxDdFmfjwk9PIU9UfqOozqvon7/ZszEtm2mXttUEW\ni6B4xKKsDEaOhP374cMPk7fCsM9F9PmpNJ4TkW/EvCTGmKRXXu4qiKlT3Yy0JSUwwJZkSyt+chp7\ngXygHmjwdquq9ohx2SKVx3IaxiRAcTHccANMnGi5i1QUt5yGqnbv7EmMMamrvNzlLpYvd7mLqVMT\nXSKTSBGbp0TkWO/fr4S7xa+IJhJrrw2yWARFMxaLF8ORR7pxFx98kHoVhn0uoq+tK43v4rra/prw\nvaXOjkmJjDEJF5gzqqQE5s93q+kZAzY1ujGmleJiuP56OPtsl7vo2zfRJTLREM+p0S8TkR7e/f8n\nIousecqYrifQM+r66+Gxx+DZZ63CMAfz0+X2R6paJSLjgXNx06HPjG2xjB/WXhtksQg6lFgsXgyj\nRrncxfr1yTvuoqPscxF9fiqNJu/fC4FZqvockB27Ihlj4iVwdXHppe7qwsZdmPb4GafxPPA58DVg\nLG5a9L/Hex2NkPJYTsOYKCguhuuuc7mLWbOsKaqri9sa4SJSAFwArFHVj0RkEHCCqq7o7MkPhVUa\nxnROoGfUihU27iKdxC0Rrqr7VPVZVf3I2/4iURWGOZC11wZZLILaikVZGRx9NNTWutxFV68w7HMR\nfX5muTXGpLjycrjjDjeNuY27MJ0R03EaIjIX+Abwpaqe4O37MXADsNN72n2qutR77F7gOlzy/c5w\nVzTWPGVMxxQXu6VXzz3XTTJoc0alp3iO0/iFn30RPIXLh4RS4NeqOta7BSqM0cAUYLR3zOMi4qd3\nlzEmjPJy1/x0ww0wc6Ybd2EVhuksP1/K54fZ989+XlxVXwUqwjwUrra7GFioqg2qugXYCJzm5zzp\nytprgywWQatWraK0FI45JnXnjIoW+1xEX8SchojcCtwGHCEia0MeKgT+0snzfltErgbeAr6nqpXA\nYOD1kOdsBYZ08jzGpJXycvjpT+Gvf3VrdU+ZAtLpBgljgiLmNESkJ9AbeBD4AcGrgypVLfd9ApEi\nYHFITmMAwXzGT4FBqnq9iDwKvK6qv/eeNxtYoqqLWr2e5TSMCaOkBK65Jpi76N8/0SUyySTm62mo\n6h5gj4j8ENihqrUicjZwgogs8K4OOkxVvwzc9yqGxd7m58CwkKcO9fYdZPr06RQVFQHQq1cvxowZ\nw6RJk4Dg5aht23a6bFdVwe9/P4kXXoC77lrFOedA//7JUz7bTsz2qlWrmDdvHkDL92VUqGqbN2A1\nrnI5EtgA/DfuCqDdY73ji4C1IduDQu5/B/iDd3+0d64cYATwMd6VUKvXU+O8/PLLiS5C0kjXWJSU\nqPbvr3rRRao7drh96RqLcCwWQd53p6/v7bZufsZpqKo2isglwKOq+qiIvOOnQhKRhcBEoJ+IfAbc\nD0wSkTG4XlSbgZu9k6wTkWeAdUAjcJv3Ro0xrVRUuNX0Skpc7mLyZMtdmPjwM43I34GHgfuAb6rq\nZhF5T1WPj0cBw5TH6hKT1kpK4Kqr4PzzXVday10YP+K2RjhusN3NwM+9CmME8NvOntgY0zHl5XDr\nrbByJcyebaO6TWL4mXvqfeAe4B1ve7Oq+h3cZ2IokPQyXT8WJSVw7LHBOaPaqjC6eiw6wmIRfX5G\nhF+EqzCWedtjRaQs1gUzxrjcxZVXutsjj9h6Fybx/OQ0/gGcA7ysqmO9fZbTMCbGSkpg2jT4+tdh\nxgyrLEznxDOn0aCqlXJg14zmzp7YGBNeaO5i7lzXM8qYZOFn7qn3ReRKIEtEjvJGbv81xuUyPlh7\nbVBXiUVo7uLDDw+twugqsYgGi0X0+ak0vg0cB9QBC4Eq4O5YFsqYdFNZCVdc4ZqjHn7YVR7WldYk\nI9/raXhzUamqVsW2SO2Ww3IapkspKXGJ7gsusNyFiZ245TRE5FRgLtDD264ErlfVtzp7cmPSWSB3\nsWJFcFS3McnOT/PUXNyUHoer6uHA7d4+k2DWXhuUarEoLnbrXdTVwYYN0a0wUi0WsWSxiD4/vaca\n1S2mBICqviYijTEskzFdVmUl3HYbPPccPPmkrXdhUk9b62mc7N29CsjDJcHBLclaq6rfiX3xwpbL\nchomJZWWwuWXu9zFzJmWuzDxFa2cRluVxircTLQHPYRLiJ/d2ZMfCqs0TKoJ5C6WL4dZs+CyyxJd\nIpOOolVpRMxpqOokVT07zG1SoioMcyBrrw1K1liE5i4++ig+FUayxiIRLBbR5yenYYzpIMtdmK7K\n9ziNZGHNUybZlZa6QXpf+5rlLkzyiOfcU8YYHwK5i2XLYM4cG3dhuiY/U6PniMhdIvKsd/u2iGTH\no3CmbdZeG5ToWCxa5HIX9fWwcWNiK4xExyKZWCyiz8+VxgzveY/hek5d5e27IYblMiYlBNbqfv55\n1xR1+eWJLpExseVnPY01qnpie/vixXIaJlmUlbncxbnnwhNPWO7CJLeYd7kN0SgiR4ac+AjARoSb\ntLV7N0yd6iYZnD3bdau1CsOkCz+VxveBl0TkzyLyZ+Al4N9iWyzjh7XXBsUrFqHjLjZtSs5kt30u\ngiwW0ecnp/EXYBRwtLf9YeyKY0xyCuQulixx05db7sKkK19rhKvqV9rbFy+W0zDxVlYGV18NZ59t\nuQuTumI+TkNEBgGDgXwR+QrenFO4dTXyO3tiY5JdeXlwVLet1W2M01ZO43zgf4AhwK+8+78Cvgvc\nF/uimfZYe21QtGNRXAyjRrlxF1u2pFaFYZ+LIItF9EW80lDV+cB8EblUVf8UxzIZkzDl5S53sWwZ\nPP645S6Mac3mnjLGs3ixy11MnOgmGbTchelKbO4pY6IkkLsoK4N581KrKcqYePMz91Q3P/tM/Fl7\nbdChxqK4GI46yuUuPv20a1QY9rkIslhEn5/BfX/1uc+YlFFe7vIV110Hv/mNm3CwX79El8qY5NfW\ncq+BLre/B67gwC63M1X1mHgVslW5LKdhOmXxYpg+Hc46y3IXJn3EI6dxPjCdYJfbgGqsy61JQYHc\nRWmpy11MmZLoEhmTetpaI3y+txb49FZrhF+kqoviWEYTgbXXBrUXi9DcxdatXbvCsM9FkMUi+vzk\nNE4RkV6BDRHpLSI/i2GZjImaQO7i+uuDuYu+fRNdKmNSl5+5p1ar6phW+95R1bExLVnk8lhOw/gS\nyF2MHw//Dbe7AAAd9ElEQVSzZlnuwqS3eK6nkRHaxVZE8oAcPy8uInNFZIeIrA3Z10dEVorIBhFZ\n0eoq5l4R+UhE1ovI+R15I8YEBK4uLr3UjeouLbUKw5ho8VNp/B54UUSuF5EbgBeABT5f/yngglb7\n7gFWquoo4EVvGxEZDUwBRnvHPC4ifsqXtqy9NigQi+JiOOIIl7vYtq1r5y4isc9FkMUi+todEa6q\nvxCRNcC53q6fqOpyPy+uqq+KSFGr3RcBE73784FVuIrjYmChqjYAW0RkI3Aa8Lqfc5n0VlXlVtNb\nscKtdzF1aqJLZEzX5HcakQ+ARlVdKSL5IlKoqtWHeM7DVHWHd38HcJh3fzAHVhBbcd19TQSTJk1K\ndBGSQlkZXH/9JM48E9avt6Yo+1wEWSyiz880IjcB/wfM9HYNBUqicXIvo91WVtsy3iaiQO5i8mTX\nM6qkxCoMY2LNz5XG7YQ0E6nqBhHpzJ/mDhEZqKrbvVHnX3r7PweGhTxvqLfvINOnT6eoqAiAXr16\nMWbMmJZfFIE2zHTYDm2vTYbyxHO7omIS114LJ564iqefhp49ASYlTfkSub169WruvvvupClPIrcf\neuihtP5+mDdvHkDL92VUqGqbN+AN7993vH+zgDXtHRdyfBGwNmT7l8APvPv3AA9690cDq3E9s0YA\nH+N1CW71emqcl19+OdFFiLvdu1WnTFHt00d14cLg/nSMRSQWiyCLRZD33enre7utm59xGv8NVAJX\nA3cAtwHrVPU/2quQRGQhLundD5e/+BFQCjwDDAe2AJNVtdJ7/n3AdUAjcJeGSbjbOI30VVoKN9wA\nZ5xh4y6M6ahojdPwU2lkAtfj5qICWA7MTtQ3t1Ua6ae8HO64w3WnDax3IZ3+6BuTXuI2uE9Vm3Bd\nY38K/ASYb9/aySHQftmVlZTAiBFQV+fWu5gyJXyFkQ6x8MtiEWSxiL52E+Ei8g1cz6lN3q6RInKz\nqi6JaclMWisvh1tvhRdecNOXp+MgPWOSkZ/mqQ+Bb6jqRm/7CGCJqh4dh/KFK49d6HRxpaVw441w\n+umWuzAmWuK5RnhVoMLwbAKqOntiY1qrqIDbb3dNUnPnRm6KMsYkjp+5nd4WkSUiMl1EpgPPAW+J\nyCUicklsi2fa0pXaa0tK4PDDXe7ik0/cNCAdqTC6Uiw6y2IRZLGIPj9XGt1w3WUD80Xt9PZ909u2\nBZnMIQvNXcyaZbkLY5JduzmNZGM5ja6jpARuuslyF8bEQ9y63IrIL0Wkh4hki8iLIrJLRK7q7IlN\n+qqogCuvdLdHHrE5o4xJJX5yGl9X1SrgQtwI7iOA78eyUMafVGyvLSmB4cOhthY2b+547iKSVIxF\nrFgsgiwW0ecnpxF4zoXAn1R1j4hY+5DpkEDuYuVKmDPHjeo2xqQeP+M0HgS+BdTiZrvtBSxW1a/G\nvnhhy2M5jRRTUgI33wzjxlnuwphEidvcU97J+gB7VLVJRAqAQlXd3tmTHwqrNFJHZSXcdptbJGn2\nbBt3YUwixTMRXoBbUyOwCNNg4JTOnth0XjK315aWwpAhbtzFpk3Ry11EksyxiDeLRZDFIvr8JMKf\nAuqBM7ztbcDPY1Yik9LKy90VxbXXwlNPwbPPWnOUMV2Jn5zG26p6soi8o6pjvX3vqupJcSnhweWx\n5qkkVVwMt9zichezZ0P//okukTEmIJ5zT9WJSF7IiY8A6jp7YtN17NkTzF0ERnVb7sKYrslP89SP\ngWXAUBH5A/AS8INYFsr4kwzttaWlMGgQ1NTAxo2xz11EkgyxSBYWiyCLRfS1eaUhIhlAb+BfgXHe\n7rtUdWesC2aSW2DcxfLlMH8+XHZZoktkjIkH3zmNOJWnXZbTSLxA7iIwZ5TlLoxJfvFcI/xBYBfw\nNLAvsF9Vyzt78kNhlUbiBMZdPPccPPFE4pqijDEdF7dxGsBU3DiNV4C3vdtbnT2x6bx4tteWlsLQ\noW7OqI0b4fLLk6vCsLbrIItFkMUi+trtPaWqRXEoh0lSgdzFsmVu3IXlLoxJb7aeholo0SKXuzjj\nDMtdGJPq4jlOw6SZwFrdS5bAjBmuKcoYY8BfTsMkqVi015aVubW6a2pgw4bUqTCs7TrIYhFksYg+\nX1caIjIEKAIyAQFUVV+JYblMnJWXu55RS5a49S4sd2GMCcdPl9tfAFOAdUBTYL+qfjO2RYtYHstp\nRFlxsVure/x4ePJJy10Y0xXFc5zGBuAEVU2K+aas0ogey10Ykz7iOU7jYyCnsycy0deZ9tqyMigq\ngv37Uyt3EYm1XQdZLIIsFtEXMachIo96d/cDq0XkRYKz26qq3hnrwpnoC+QunnsO5s61tbqNMR0T\nsXlKRKYDgQel9X1VnR/z0oUvlzVPHaJFi9xa3ePHu3EX/folukTGmHiJ+TgNVZ3nnehuVX2o1cnv\n7uyJTfxUVLiri2XL4PHHU78pyhiTOH5yGteE2Tc9yuUwh8BPe+3ixTBypBt38eGHXbfCsLbrIItF\nkMUi+trKaVwOXAGMEJHFIQ8VArtjXTDTOYHcRVkZzJtnuQtjTHS0ldM4HBgBPIhbqS/QFlYNvKuq\njXEp4cHlspxGO4qL4cYbYcIEN+7CchfGmLiN00g2VmlEVl7uxl1Y7sIY01rMx2mIyF+8f/eKSHWr\nW1VnTywiW0RkjYi8IyJvePv6iMhKEdkgIitEpFdnz9OVhbbXLl4MRx7Z9XMXkVjbdZDFIshiEX0R\nKw1VPdP7t7uqFra69YjCuRWYpKpjVfU0b989wEpVHQW86G2bNpSXuwpi8mQ3qrukBAYMSHSpjDFd\nlZ9pRH4G/Bn4q6rua/PJHTmxyGbgFFXdHbJvPTBRVXeIyEBglaoe0+o4a57yLFrkchcTJ7pxF337\nJrpExphkFc+5p64DzgLGAXtxy76+qqolnTqxyCZgD24SxCdUdZaIVKhqb+9xAcoD2yHHpX2lEchd\nLF/uchdTpya6RMaYZBe3RZhUdS4w1/vlPwX4N+BmoHsnz32mqn4hIv2Bld5VRuh5VUTC1g7Tp0+n\nqKgIgF69ejFmzBgmTZoEBNswu+r2Aw+s4oEH4JxzJjFnzip694ZVq5KnfInaDuxLlvIkcnv16tXc\nfffdSVOeRG4/9NBDafX9ELq9atUq5s2bB9DyfRkNfq405gDHAjuA14BXgXdUtSFqhRC5H3cVcyMu\nz7FdRAYBL1vzlBO4uli0CBYsgClT3Ack8GFJdxaLIItFkMUiKJ7NU8XAEOB9XNPUn1V1U6dOKpIP\nZKpqtYgUACuA/wTOA3ar6i9E5B6gl6re0+rYtKs0iovh+uvh7LPduAvLXRhjOiru4zRE5FjgAuBu\n3Bf+0EM+qcgIoNjbzAJ+r6oPiEgf4BlgOLAFmKyqla2OTZtKIzCqe+VKeOwxy10YYw5d3NbTEJFv\nisgvgbnATcBLwI86c1JV3ayqY7zb8ar6gLe/XFXPU9VRqnp+6wojnSxeDKNGQW0tfPBB+AojtD0/\n3VksgiwWQRaL6POzRvjXcXmMh1R1W4zLk/bKy+GOO1zuYv58l7swxphkYdOIJJHiYrjuOpe7sHEX\nxphoiluXWxN7obmLGTMsd2GMSV5+1tMwMVRWBkcf7eaMipS7iMTaa4MsFkEWiyCLRfT5SYTf5Wef\n6ZjycrjiCpez+M1vbM4oY0xq8DNO4x1VHdtq32pVHRPTkkUuT8rnNEpKYPp0OPdceOIJW+/CGBN7\nMc9p2Mp90VdeDrfeCi+8ADNnWu7CGJN62mqe+ivwK2A98D/e/V8B38V1wzUdUFoKxxzT9riLjrL2\n2iCLRZDFIshiEX0RrzRU9RPgE2CciBQBR6rqC94UIHm4ZV9NOyoq3LiL4mKYO9flMKTTF4jGGJMY\nfnIaN+EmEuyjqkeIyChghqqeG48ChilPyuQ0Skrg6qvha19zzVH9+ye6RMaYdBXPcRq3A6cBrwOo\n6gYRsX4+bQjNXcyaZaO6jTFdh59xGnWqWhfYEJEs3FKtJoySkgNzF7GsMKy9NshiEWSxCLJYRJ+f\nK40/i8h/APki8jXgNmBxO8eknYoKt95FaanLXUyebLkLY0zX4yenkQHcAJzv7VoOzE5UYiEZcxql\npTBtGpx/vpsGxAbpGWOSTVzW0/Caot5rvXpeIiVTpVFeDrfc4nIXM2ZY7sIYk7zisp6GqjYCH4rI\n4Z09UVdTUgLHHgt1dfDhh4mpMKy9NshiEWSxCLJYRJ+fnEYf4H0ReQPY5+1TVb0odsVKXpWVwdzF\n7Nk27sIYk1785DQmhduvqqtiUJ52JbJ5qqQkmLuYOdNyF8aY1BH3NcKTRSIqjcC4i5UrXWUxeXJc\nT2+MMZ0Wt8F9IhJuupA9wJvA91R1U2cLkcyKi12ye9w4WL8+ua4uVq1axaRJkxJdjKRgsQiyWASl\nYixUFUVRVeqa3BC56rpqmrWZPXV7qG+qZ2/9XvY37Gdf/T721O2htrGWipoKahtr2bV/F7WNtezc\nv5Oaxhq2793OKYNOiVr5/OQ0HgY+AxZ621OBI4B3gLnApKiVJolUVrrV9BYvdrkLG3dhTHoIfGk3\nazN1jXU0aRP76vfR0NxAVV0VtY217K3fS3VdNfsb9lNZW0lNYw079+2kvqmeL/Z+QUNzA59XfU59\nUz279u9CRKioqUBEqKytRBCatClu7+nbp32bucyNymv5yWmsUdUTW+1brapjRORdVT0pKiXxKR7N\nU6WlboGkr3/dchfGJErgy7u+qZ6m5ib2Neyjvqme6rpqahprqK6rZm/9XvbW72VP3R6q66qpqK2g\nqq6KitoKKmsrKa8pZ0/tHmoaa6hpqKGuqY79Dfupb6qnWZvj8j6yM7Jp1mb65PWhSZvok9eHZm1m\nQMEAcjNzGVw4mKyMLAYXDiY7I5t++f3oltWN3nm9ycvKoyCngMKcQnKzcumR24NMyaQwt5AMySAv\nKw8RIVMyAdcEFUk8557aLyJTgP/zti8Far37qZUQaUcgd7F8OcybB5ddlugSGZMcVN0vb0XZ37Cf\nZm2msraShqYGKmsr2dewr+VLu6ahhh37dlDXWMfn1Z9T11TH1qqtLU0nABU1FShKVV1VXMqflZFF\nXlYeuVm5DCgYQE5mDj1ye9Ajtwf98/tTkFNA//z+5Gfn0yevDwXZBfTs1pOC7IIDvrR75vYkMyOT\nwpxCRITczFxEBEHa/MLuSvxUGlfimqge87ZfB6aJSB5wR6wKFm/FxXDzzXDGGfDRR6kxI20qttfG\nSjrGIvBLvLG5kfqmemoaaqhprOHFl15k9KmjqaqrYk/dHqrqqiivKaeqroov931JdX0126q3sbd+\nL+U15TQ1N1FZW0mzNlNdH9sVD3IycxCE3nm9EYShPYaSlZHFoO6DyM/Ob/m3X34/CnIK6N2tN91z\nulOYW0hhTiH52fl0z+lOt6xu5GXnkZ2RTXZmdsRf2un4uYi1disNVf0YuDDCw69FtzjxFxh3sXix\nW3p16lTLXZjOC3yhB9rE99S6ZGVlbSXV9dUHfZHvqd3D9n3bqaipYMe+HdQ21rKvfh81jTXsrd9L\nY3Oj/5NvBtb4e2puZi4ZktHyJV7Uq4jszGyG9xxOt6xuDCkcQl5WHgO7D6RbVjf65vele053uud0\np2duT3Iyc+jVrRcZkkFBTgEZkkGmZKbNr+505CencTTwODBQVY8TkROBi1T1Z/EoYJjyRC2nUVoK\nV15p4y7SlarS0NxAU3NTS6+U3ft3U11fzZ7aPezcv5O99XvZWrWVffX72LJnC3vr9/JF9Rc0azO7\na3bT1NwUk1/nOZk5FGQXkJed19JE0jevL/0L+tOnWx/65veld7fe9M7rTc/cnvTI7UHPbj3Jz86n\nZ25PcrNyKcguIDMjk+yMbKDt9m7T9cVtnIaIvAJ8H5ipqmPFffLeU9XjOnvyQxGNSiOQu1i2zPWM\nstxFcgu0p9c31bOvYR/76ve1JDorairYuX8nFTUVbKveRkVtBZ/s+YTqump21+ymsbmRXft30dTc\nFLXeKjmZOWRIBv3y+5EhGfTN60tBTgHDew6nMKeQwYWDKcwppH9Bf3rm9qRnt5706tar5Qs9JzOH\nvOw8sjKy0qot3CRWPBPh+ar698AHW1VVRBo6e+JECc1dbNyYGrmLSJK1vTbQNFPTUENtY63rwVK3\nh937d7Nz/0527d/F9r3b2bFvB1urtrJz306q66tbesPUNNZ0/KSbgREH7go0m4zoNYLMjMyWL/Wi\nXkV0z+nO4MLB9MjtQZ+8PvTJ60N+dj598/qSlZFF95zurqklIzMqMYmnZP1cJILFIvr8VBo7ReTI\nwIaIXAp8EbsixUZgvYvnn3e5C5sz6mCBX/TV9dXUNtayY+8OKmor2LV/F1urtlJeU87HFR+3bIcO\nJKpvqu/UubvndKcwp5ChPYbSq1svBhQMYGiPofTN68vgwsH0yQs2yRTmFtI3ry+5WbnkZ+eTIRm8\n8udX7MvBmDjw0zx1BPAkcDpQiftNd6Wqbol56cKXp8PNU2VlLndx3nkud3HYYTEqXII1azMNTQ2U\n15RTXV/N9r3b+aL6C3bu38nG8o3s3L+TDbs3UNPgRonWN9Ufcnt8t6xu5GbmtvQpH1Q4iIHdBzKs\nxzAGFAzgsILD6Jffr+VXfI/cHuRn57c07ViTjDHxFfe5p0SkOyDAXmCyqj7d2ZMfio5UGoHcxdKl\nMGdOauQuVLVlmoAd+3awY+8OPq/+nM0Vm9lWvY11u9ZRVVfFF9VfUNNY0+F+7oKQm5XLoO6DyMnM\nYVjPYfTP78+RfY6kX34/hvYYSv/8/vTO682AggF0y+pGQXaBfdEbk+JintPwKombcVOGvAfMBC4G\nfg5sBBJSafi1aJGbM+rMM+HjjxOTuwhUABW1FWzfu53P9nzG5srNbCzfyAe7Pmhp2w+MWPUrMIo0\n57MczjjtDAZ2H8jRfY9uadIZ1H2QG7RU0L+lH3tXZ23XQRaLIItF9LWV01gAVAF/wy31Oh03EvwK\nVV0d+6IdmkDuYskSt5re5ZdH9/WbtZnaxlq2Vm3lk8pP2FSxiTU71rChfAPbqrfx5b4vW0a9tqcg\nu6ClWeeoPkdxeM/DGdV3FIMLBzOocBCDCwe3dLfMkIPXy7I/CGNMvEVsngqdc0pEMnHJ78NV9RC6\ntkRPW81TZWVw1VVwzjku2d3RcReNzY1srdrKx+Uf88GuD3h96+tsqdzClsotbN+7vd0umwMKBjCw\n+0AOKziM4wccz5F9jmRk75EM7zm8pcnHBj4ZYxIhHl1uW74hVbVJRD5PdIURSXm5m5H2+edd7iLS\nehfN2syWyi2s3bGWN7e9yWufvsYXe79gw+4NEV+7R24Phvcczuj+oznxsBM5fsDxHNXnKIb3HN4y\nh41VAsaYdNHWlUYTsD9kVx4QqDRUVXvEpEAiFwAPAZnAbFX9RavHD7jSWLTIjbsYPx5mzYJ+/aC+\nqZ41O9aw9KOlvLHtDf7xxT/YVr3toHP16taLIYVDOLrf0YwdOJaTB53MMf2OYVDhoJaJyJKZNU8F\nWSyCLBZBFougmF9pqGrcRzV5zWC/Ac4DPgfeFJEyVf2g9XNbchdLlR8+9CF7D/8j/1y8hDe3vXnA\n8/rk9eGkw07iX4/9V84dcS5jB41lUPdBXSI5vHr1avuD8FgsgiwWQRaL6PMzuC+eTgM2BsaAiMgf\ncT22Dqg0ikubmPbjZXQ/5xH23L2C728BtsBXh3yV2065jUuOvYTThpxGYW5hnIsfX5WVlYkuQtKw\nWARZLIIsFtGXbJXGENwqgQFbga+2ftIlrw2Bb+3glMMn8IOjf8W0E6cxoMBmGzTGmFhLtkrD16i9\nB/7ph3xnwo3kZuXGujxJbcuWLYkuQtKwWARZLIIsFtHne0R4PIjIOODHqnqBt30v0ByaDBeR5Cmw\nMcakkLhOIxIPIpIFfAicC2wD3gAuD5cIN8YYE39J1Tylqo0icgewHNfldo5VGMYYkzyS6krDGGNM\ncjt4QqMkJSIXiMh6EflIRH6Q6PLEmogME5GXReR9EXlPRO709vcRkZUiskFEVohIr5Bj7vXis15E\nzk9c6WNDRDJF5B0RWextp2UsRKSXiPxJRD4QkXUi8tU0jsW93t/IWhH5g4jkpkssRGSuiOwQkbUh\n+zr83kXkZC9+H4nIw+2eWFWT/oZrqtoIFAHZwGrg2ESXK8bveSAwxrvfHZfrORb4JfDv3v4fAA96\n90d7ccn24rQRyEj0+4hyTL4L/B4o87bTMhbAfOA6734W0DMdY+G9n01Arrf9NHBNusQCOAsYC6wN\n2deR9x5oaXoDOM27vwS4oK3zpsqVRsugP1VtAAKD/rosVd2u3mzCqroXN8BxCHAR7ksD799vefcv\nBhaqaoO6wZEbcXHrEkRkKPDPwGzcui6QhrEQkZ7AWao6F1weUFX3kIaxwM3C3QDke51o8nEdaNIi\nFqr6KlDRandH3vtXRWQQUKiqb3jPWxB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AFWG0bbfxj+O3xZaeLvFA1OP4JSUwbpzTLj75xIndUSLqbRGH7FLTUNXPgZO7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\n5v+WjVfqVYEaoAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "etas = 8*np.log(2)/np.sqrt(np.arange(1,T+1))\n", "rewards_iid_MW, regrets_iid_MW = getAllRewardsAndRegretsMW(sequence_iid, etas)\n", "rewards_oneperiod_MW, regrets_oneperiod_MW = getAllRewardsAndRegretsMW(sequence_oneperiod, etas)\n", "rewards_twoperiod_MW, regrets_twoperiod_MW = getAllRewardsAndRegretsMW(sequence_twoperiod, etas)\n", "\n", "plt.plot(Ts, regrets_iid, label=\"FTL\")\n", "plt.plot(Ts, regrets_iid_MW, label=\"MW\")\n", "plt.ylim(0,250)\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Regret with respect to best single alphabet\")\n", "plt.grid()\n", "plt.title(\"iid Bernoulli (0.7) sequence\")\n", "plt.legend(loc=2)\n", "plt.show()\n", "\n", "plt.plot(Ts, regrets_oneperiod,label=\"FTL\")\n", "plt.plot(Ts, regrets_oneperiod_MW, label=\"MW\")\n", "plt.ylim(0,250)\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Regret with respect to best single alphabet\")\n", "plt.grid()\n", "plt.title(\"1-periodic sequence 010101...\")\n", "plt.legend(loc=2)\n", "plt.show()\n", "\n", "plt.plot(Ts, regrets_twoperiod_FTL,label=\"FTL\")\n", "plt.plot(Ts, regrets_twoperiod_MW, label=\"MW\")\n", "plt.plot(Ts, regrets_twoperiod_oneFTL, label=\"One memory FTL\")\n", "plt.ylim(0,250)\n", "plt.xlabel(\"Round number\")\n", "plt.ylabel(\"Regret with respect to best single alphabet\")\n", "plt.grid()\n", "plt.title(\"2-periodic sequence 00110011...\")\n", "plt.legend(loc=2)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Place to play around with learning rates in multiplicative weights updates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, we will prove that the \"low-regret\" property of multiplicative weights holds in general for *any sequence* of 0's and 1's." ] } ], "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": "3.4.5" } }, "nbformat": 4, "nbformat_minor": 0 }