source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Problems.Bandits/GaussianBandit.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 {
  public class GaussianBandit : 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[] exp;
    private readonly double[] stdDev;
    public GaussianBandit(Random random, int nArms) {
      this.random = random;
      this.NumArms = nArms;
      // expected reward of arms is iid and uniformly distributed 
      exp = new double[nArms];
      stdDev = new double[nArms];
      OptimalExpectedReward = double.NegativeInfinity;
      var bestQ = double.NegativeInfinity;
      for (int i = 0; i < nArms; i++) {
        exp[i] = Rand.RandNormal(random);  // exp values for arms is N(0,1) distributed
        stdDev[i] = 1.0 / Rand.GammaRand(random, 1); // variance is inv-gamma distributed 
        if (exp[i] > OptimalExpectedReward) {
          OptimalExpectedReward = exp[i];
          OptimalExpectedRewardArm = i;
        }
        var q = alglib.invnormaldistribution(0.99) * stdDev[i] + exp[i];
        if (q > bestQ) {
          bestQ = q;
          OptimalMaximalRewardArm = i;
        }
      }
    }

    // pulling an arm results in a truncated normally distributed reward 
    // with mean expReward[i] and std.dev 0.1
    public double Pull(int arm) {
      var z = Rand.RandNormal(random);
      var x = z * stdDev[arm] + exp[arm];
      return x;
    }
  }
}