1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Diagnostics;
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4 | using System.Linq;
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5 | using System.Text;
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6 | using System.Threading.Tasks;
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7 |
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8 | namespace HeuristicLab.Algorithms.Bandits {
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9 | /* see: Streeter and Smith: A simple distribution-free approach to the max k-armed bandit problem, Proceedings of the 12th
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10 | International Conference, CP 2006, Nantes, France, September 25-29, 2006. pp 560-574 */
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11 |
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12 | public class ChernoffIntervalEstimationPolicy : IPolicy {
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13 | private readonly double delta;
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14 |
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15 | public ChernoffIntervalEstimationPolicy(double delta = 0.01) {
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16 | this.delta = delta;
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17 | }
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18 | public int SelectAction(Random random, IEnumerable<IPolicyActionInfo> actionInfos) {
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19 | Debug.Assert(actionInfos.Any());
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20 | // select best
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21 | var myActionInfos = actionInfos.OfType<DefaultPolicyActionInfo>().ToArray(); // TODO: performance
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22 | int k = myActionInfos.Length;
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23 | int totalTries = myActionInfos.Where(a => !a.Disabled).Sum(a => a.Tries);
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24 | int bestAction = -1;
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25 | double bestQ = double.NegativeInfinity;
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26 | for (int a = 0; a < myActionInfos.Length; a++) {
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27 | if (myActionInfos[a].Disabled) continue;
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28 | if (myActionInfos[a].Tries == 0) return a;
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29 |
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30 | var sumReward = myActionInfos[a].SumReward;
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31 | var tries = myActionInfos[a].Tries;
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32 |
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33 | var avgReward = sumReward / tries;
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34 |
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35 | // page 5 of "A simple distribution-free appraoch to the max k-armed bandit problem"
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36 | // var alpha = Math.Log(2 * totalTries * k / delta);
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37 | double alpha = Math.Log(2) + Math.Log(totalTries) + Math.Log(k) - Math.Log(delta); // total tries is max tries in the original paper
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38 | var q = avgReward + (alpha + Math.Sqrt(2 * tries * avgReward * alpha + alpha * alpha)) / tries;
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39 | if (q > bestQ) {
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40 | bestQ = q;
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41 | bestAction = a;
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42 | }
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43 | }
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44 | Debug.Assert(bestAction >= 0);
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45 | return bestAction;
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46 | }
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47 |
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48 | public IPolicyActionInfo CreateActionInfo() {
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49 | return new DefaultPolicyActionInfo();
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50 | }
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51 |
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52 | public override string ToString() {
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53 | return string.Format("ChernoffIntervalEstimationPolicy({0:F2})", delta);
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54 | }
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55 | }
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56 | }
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