source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Algorithms.Bandits/Policies/UCBNormalPolicy.cs @ 11732

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

namespace HeuristicLab.Algorithms.Bandits {
  public class UCBNormalPolicy : IPolicy {

    public int SelectAction(Random random, IEnumerable<IPolicyActionInfo> actionInfos) {
      var myActionInfos = actionInfos.OfType<MeanAndVariancePolicyActionInfo>().ToArray(); // TODO: performance
      int bestAction = -1;
      double bestQ = double.NegativeInfinity;
      int totalTries = myActionInfos.Where(a => !a.Disabled).Sum(a => a.Tries);

      for (int a = 0; a < myActionInfos.Length; a++) {
        if (myActionInfos[a].Disabled) continue;
        if (totalTries <= 1 || myActionInfos[a].Tries <= 1 || myActionInfos[a].Tries <= Math.Ceiling(8 * Math.Log(totalTries))) return a;

        var tries = myActionInfos[a].Tries;
        var avgReward = myActionInfos[a].AvgReward;
        var rewardVariance = myActionInfos[a].RewardVariance;
        var estVariance = 16 * rewardVariance * (Math.Log(totalTries - 1) / tries);
        if (estVariance < 0) estVariance = 0; // numerical problems
        var q = avgReward
          + Math.Sqrt(estVariance);
        if (q > bestQ) {
          bestQ = q;
          bestAction = a;
        }
      }
      Debug.Assert(bestAction > -1);
      return bestAction;
    }

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

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