source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Algorithms.Bandits/BanditPolicies/UCB1TunedPolicy.cs @ 11832

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using HeuristicLab.Common;

namespace HeuristicLab.Algorithms.Bandits.BanditPolicies {
  // policy for k-armed bandit (see Auer et al. 2002)
  public class UCB1TunedPolicy : IBanditPolicy {

    public int SelectAction(Random random, IEnumerable<IBanditPolicyActionInfo> actionInfos) {
      var myActionInfos = actionInfos.OfType<MeanAndVariancePolicyActionInfo>();

      int totalTries = myActionInfos.Sum(a => a.Tries);

      int aIdx = -1;
      double bestQ = double.NegativeInfinity;
      var bestActions = new List<int>();
      foreach (var aInfo in myActionInfos) {
        aIdx++;
        double q;
        if (aInfo.Tries == 0) {
          q = double.PositiveInfinity;
        } else {
          var sumReward = aInfo.SumReward;
          var tries = aInfo.Tries;

          var avgReward = sumReward / tries;
          q = avgReward + Math.Sqrt((Math.Log(totalTries) / tries) * Math.Min(1.0 / 4, V(aInfo, totalTries)));
          // 1/4 is upper bound of bernoulli distributed variable
        }
        if (q > bestQ) {
          bestQ = q;
          bestActions.Clear();
          bestActions.Add(aIdx);
        } else if (q.IsAlmost(bestQ)) {
          bestActions.Add(aIdx);
        }
      }
      Debug.Assert(bestActions.Any());

      return bestActions.SelectRandom(random);
    }

    public IBanditPolicyActionInfo CreateActionInfo() {
      return new MeanAndVariancePolicyActionInfo();
    }

    private double V(MeanAndVariancePolicyActionInfo actionInfo, int totalTries) {
      var s = actionInfo.Tries;
      return actionInfo.RewardVariance + Math.Sqrt(2 * Math.Log(totalTries) / s);
    }

    public override string ToString() {
      return "UCB1TunedPolicy";
    }
  }
}