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.BanditPolicies {
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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 : IBanditPolicy {
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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<IBanditPolicyActionInfo> 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>();
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22 | int k = myActionInfos.Count(a => !a.Disabled);
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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 | var aIdx = -1;
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27 | foreach (var aInfo in myActionInfos) {
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28 | aIdx++;
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29 | if (aInfo.Disabled) continue;
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30 | if (aInfo.Tries == 0) return aIdx;
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31 |
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32 | var avgReward = aInfo.SumReward / aInfo.Tries;
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33 |
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34 | // page 5 of "A simple distribution-free appraoch to the max k-armed bandit problem"
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35 | // var alpha = Math.Log(2 * totalTries * k / delta);
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36 | double alpha = Math.Log(2.0) + Math.Log(totalTries) + Math.Log(k) - Math.Log(delta); // total tries is max tries in the original paper
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37 | var q = avgReward + (alpha + Math.Sqrt(2 * aInfo.Tries * avgReward * alpha + alpha * alpha)) / aInfo.Tries;
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38 | if (q > bestQ) {
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39 | bestQ = q;
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40 | bestAction = aIdx;
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41 | }
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42 | }
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43 | Debug.Assert(bestAction >= 0);
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44 | return bestAction;
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45 | }
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46 |
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47 | public IBanditPolicyActionInfo CreateActionInfo() {
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48 | return new DefaultPolicyActionInfo();
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49 | }
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50 |
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51 | public override string ToString() {
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52 | return string.Format("ChernoffIntervalEstimationPolicy({0:F2})", delta);
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53 | }
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54 | }
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55 | }
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