10-ExplorationExploitation.ipynb

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     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Exploration and Exploitation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "using PGFPlots\n",
      "using Interact\n",
      "using Reactive\n",
      "using Distributions\n",
      "include(\"helpers.jl\")\n",
      "include(\"bandits.jl\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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     "source": [
      "Multi-Armed Bandit Problems"
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     "collapsed": false,
     "input": [
      "srand(0)\n",
      "arms = 3\n",
      "b = Bandit(arms)\n",
      "banditTrial(b)"
     ],
     "language": "python",
     "metadata": {},
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     "source": [
      "Bayesian Model Estimation"
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     "input": [
      "srand(0)\n",
      "arms = 2\n",
      "b = Bandit(arms)\n",
      "banditEstimation(b)"
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    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ad Hoc Exploration Strategies"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Select random action with probability eps, otherwise greedy\n",
      "type EpsGreedy <: BanditPolicy\n",
      "    eps::Real \n",
      "end\n",
      "function arm(b::EpsGreedy, s::BanditStatistics)\n",
      "    if rand() < b.eps\n",
      "        D = DiscreteUniform(1, numArms(s))\n",
      "        return rand(D)\n",
      "    else\n",
      "        return indmax(winProbabilities(s))\n",
      "    end\n",
      "end;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Select arm with probability proportional to exp(precision*winprobability)\n",
      "type SoftMax <: BanditPolicy\n",
      "    precision::Real \n",
      "end\n",
      "function arm(b::SoftMax, s::BanditStatistics)\n",
      "    p = exp(b.precision * winProbabilities(s))\n",
      "    p = p / sum(p)\n",
      "    D = Categorical(p)\n",
      "    return rand(D)\n",
      "end;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Select arm with highest alpha upper confidence bound\n",
      "type IntervalExploration <: BanditPolicy\n",
      "    alpha::Real\n",
      "end\n",
      "function arm(b::IntervalExploration, s::BanditStatistics)\n",
      "    i = @argmax (i in 1:length(s.numWins)) quantile(Beta(s.numWins[i] + 1, s.numTries[i] - s.numWins[i] + 1), b.alpha)    \n",
      "end;"
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     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "steps = 50\n",
      "iterations = 1000\n",
      "bandit = Bandit([0.1:0.2:1])\n",
      "@manipulate for epsgreedy = 0:0.1:1, softmax = 0:2:40, interval = 0.5:0.05:1\n",
      "    epsGreedyResults = simulateAverage(bandit, EpsGreedy(epsgreedy), steps=steps, iterations = iterations)./[1:steps]\n",
      "    softMaxResults = simulateAverage(bandit, SoftMax(softmax), steps=steps, iterations = iterations)./[1:steps]\n",
      "    intervalResults = simulateAverage(bandit, IntervalExploration(interval), steps=steps, iterations = iterations)./[1:steps]\n",
      "    Axis([\n",
      "        Plots.Linear(epsGreedyResults, legendentry=\"eps greedy\", style=\"very thick\", mark=\"none\"),\n",
      "        Plots.Linear(softMaxResults, legendentry=\"softmax\", style=\"very thick\", mark=\"none\"),  \n",
      "        Plots.Linear(intervalResults, legendentry=\"interval\", style=\"very thick\", mark=\"none\")  \n",
      "        ], style=\"legend pos=south east\", ymin=0, ymax=1, xmin=0, xmax=steps, xlabel=\"Pulls\", ylabel=\"Average success\")\n",
      "end"
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     "language": "python",
     "metadata": {},
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