source: branches/HeuristicLab.Problems.GrammaticalOptimization-gkr/HeuristicLab.Algorithms.Bandits/Policies/ExtremeHunterPolicy.cs @ 13042

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 {
  // Extreme Bandits, NIPS2014
  public class ExtremeHunterPolicy : IBanditPolicy {


    public double E { get; set; }
    public double D { get; set; }
    public double delta { get; set; }
    public double b { get; set; }
    public double n { get; set; }
    public int minPulls { get; set; }

    public ExtremeHunterPolicy(double E = 1.0E-3, double D = 1.0E-2, double b = 1.0, double n = 1.0E4, int minPulls = 100) {
      this.E = E; // parameter TODO
      this.D = D; // parameter TODO
      this.b = b; // parameter: set to 1 in original paper "to consider a wide class of distributions"
      // private communication with Alexandra Carpentier: 
      // For instance, on our synthetic experiments, we calibrated the constants by 
      // cross validation, using exact Pareto distributions and b=1, and we found 
      // out that taking E =  1e-3 is acceptable. For all the datasets 
      // (exact Pareto, approximate Pareto, and network data), we kept this same constant

      // minPulls seems to be set to 100 in the experiments in extreme bandit paper
      this.minPulls = minPulls; // parameter: TODO (there are conditions for N given in the paper)
      this.n = n;
    }

    public int SelectAction(Random random, IEnumerable<IBanditPolicyActionInfo> actionInfos) {
      var myActionInfos = actionInfos.OfType<ExtremeHunterActionInfo>();
      double bestQ = double.NegativeInfinity;
      // int totalTries = myActionInfos.Sum(a => a.Tries);
      int K = myActionInfos.Count();

      this.delta = Math.Exp(-Math.Log(Math.Log(n))) / (2.0 * n * K); // TODO 

      var bestActions = new List<int>();
      int aIdx = -1;
      foreach (var aInfo in myActionInfos) {
        aIdx++;
        double q;
        if (aInfo.Tries <= minPulls) {
          q = double.PositiveInfinity;
        } else {
          double t = aInfo.Tries;
          double h = aInfo.Value;
          if (double.IsInfinity(h)) q = 0;
          else {
            var thres = Math.Pow(t, h / (2 * b + 1));
            double c = Math.Pow(t, 1.0 / (2 * b + 1)) * ((1.0 / t) * aInfo.Rewards.Count(r => r >= thres));
            q = Math.Pow((c + B2(t)) * n, h + B1(t)) * Gamma(h, B1(t)); // eqn (5)
            Debug.Assert(q > 0);
          }
        }
        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 double Gamma(double x, double y) {
      if (1.0 - x - y <= 0) return double.PositiveInfinity;
      else return alglib.gammafunction(1.0 - x - y); // comment on eqn 5
    }

    // eqn 2
    public double B1(double t) {
      return D * Math.Sqrt(Math.Log(1.0 / delta)) * Math.Pow(t, -b / (2 * b + 1));
    }

    // eqn 4
    public double B2(double t) {
      return E * Math.Sqrt(Math.Log(t / delta)) * Math.Log(t) * Math.Pow(t, -b / (2 * b + 1));
    }

    public IBanditPolicyActionInfo CreateActionInfo() {
      return new ExtremeHunterActionInfo();
    }
    public override string ToString() {
      return string.Format("ExtremeHunter(E={0:F2},D={1:F2},b={2:F2},n={3:F0},minPulls={4:F0}", E, D, b, n, minPulls);
    }
  }
}