source: branches/HeuristicLab.Problems.GrammaticalOptimization-gkr/HeuristicLab.Algorithms.Bandits/Policies/ChernoffIntervalEstimationPolicy.cs @ 13401

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 {
  /* see: Streeter and Smith: A simple distribution-free approach to the max k-armed bandit problem, Proceedings  of the 12th
International Conference, CP 2006, Nantes, France, September 25-29, 2006. pp 560-574 */

  public class ChernoffIntervalEstimationPolicy : IBanditPolicy {
    private readonly double delta;

    public ChernoffIntervalEstimationPolicy(double delta = 0.01) {
      this.delta = delta;
    }
    public int SelectAction(Random random, IEnumerable<IBanditPolicyActionInfo> actionInfos) {
      Debug.Assert(actionInfos.Any());
      // select best
      var myActionInfos = actionInfos.OfType<DefaultPolicyActionInfo>();
      int k = myActionInfos.Count();
      int totalTries = myActionInfos.Sum(a => a.Tries);
      double bestQ = double.NegativeInfinity;
      var bestActions = new List<int>();
      var aIdx = -1;
      foreach (var aInfo in myActionInfos) {
        aIdx++;
        double q;
        if (aInfo.Tries == 0) {
          q = double.PositiveInfinity;
        } else {

          var avgReward = aInfo.SumReward / aInfo.Tries;          

          // page 5 of "A simple distribution-free approach to the max k-armed bandit problem"
          // var alpha = Math.Log(2 * totalTries * k / delta);
          double alpha = Math.Log(2.0) + Math.Log(totalTries) + Math.Log(k) - Math.Log(delta);
          // total tries is max tries in the original paper
          q = avgReward + (alpha + Math.Sqrt(2 * aInfo.Tries * avgReward * alpha + alpha * alpha)) / aInfo.Tries;
        }
        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 DefaultPolicyActionInfo();
    }

    public override string ToString() {
      return string.Format("ChernoffIntervalEstimationPolicy({0:F2})", delta);
    }
  }
}