source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Problems.Bandits/GaussianMixtureBandit.cs @ 12830

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

namespace HeuristicLab.Algorithms.Bandits {
  // uses a gaussian mixture reward distribution for each arm
  public class GaussianMixtureBandit : IBandit {
    public int NumArms { get; private set; }
    public double OptimalExpectedReward { get; private set; } // reward of the best arm, for calculating regret
    public int OptimalExpectedRewardArm { get; private set; }
    public int OptimalMaximalRewardArm { get; private set; }

    private readonly Random random;
    private readonly double[] expReward; // for each component components
    private readonly double[][] componentProb; // arms x components
    public GaussianMixtureBandit(Random random, int nArms) {
      this.random = random;
      this.NumArms = nArms;
      var numComponents = 0;
      expReward = new double[] { 0.1, 0.3, 0.5, 0.7, 0.9 };
      componentProb = new double[nArms][];
      OptimalExpectedReward = double.NegativeInfinity;
      // decide on optimal arm
      OptimalMaximalRewardArm = random.Next(NumArms);
      OptimalExpectedRewardArm = OptimalMaximalRewardArm;
      for (int i = 0; i < nArms; i++) {
        componentProb[i] = new double[numComponents];
        if (i == OptimalMaximalRewardArm) {
          componentProb[i] = new double[] { 0.24, 0.24, 0.24, 0.24, 0.04 };
        } else {
          componentProb[i] = new double[] { 0.25, 0.25, 0.25, 0.25, 0 };
        }
      }

      OptimalExpectedReward = Enumerable.Range(0, 100000).Select(_ => Pull(OptimalExpectedRewardArm)).Average();
    }

    // std.dev = 0.1 
    // and truncation to the interval [0..1]
    public double Pull(int arm) {
      double x = 0;
      do {
        var k = Enumerable.Range(0, componentProb[arm].Length).SampleProportional(random, componentProb[arm]);

        var z = Rand.RandNormal(random);
        x = z * 0.1 + expReward[k];
      }
      while (x < 0 || x > 1);
      return x;
    }
  }
}