/// <summary>
/// Policy iteration for MDP
/// </summary>
/// <param name="basePolicy">Starting policy</param>
/// <param name="optimalPolicy">Resulting optimal policy</param>
/// <param name="tolerance">Convergence tolerance</param>
/// <returns>Optimal value</returns>
public double GetOptimalValueViaPolicyIteration(
IDeterministicPolicy <TState> basePolicy,
out IDeterministicPolicy <TState> optimalPolicy,
double tolerance = 0.0001)
{
var policy = (IDeterministicPolicy <TState>)basePolicy.Clone();
var node = Policies.AddFirst(basePolicy);
var value = GetOptimalValue(policy, tolerance);
optimalPolicy = policy = PolicyIteration(policy);
var outputStates = new List <TState> {
_initialState
};
outputStates.AddRange(policy.GetAllowedActions(_initialState).Where(a => a != null)
.SelectMany(a => a[_initialState]));
while (policy.IsModified)
{
node = Policies.AddAfter(node, policy);
var nextValue = GetOptimalValue(policy, tolerance, false, outputStates.Distinct().ToArray());
if (LogProgress)
{
Log?.Info($"{value.Mean}->{nextValue.Mean} at variance {Math.Sqrt(value.Variance - (value.Mean * value.Mean))}->{Math.Sqrt(nextValue.Variance - (nextValue.Mean * nextValue.Mean))} with {policy.Modifications.Length} modifications");
}
var ratio = value.Mean > 0 ? nextValue.Mean / value.Mean : value.Mean / nextValue.Mean;
if ((nextValue.Mean - (tolerance * 100) < value.Mean) || Math.Abs(ratio) < 1 + RelativeOptimalTolerance)
{
value = nextValue;
break;
}
value = nextValue;
policy = PolicyIteration(policy);
if (node.Previous == null)
{
continue;
}
ValueFunctions[node.Previous.Value].Clear();
ValueFunctions.Remove(node.Previous.Value);
Policies.Remove(node.Previous);
}
value = GetOptimalValue(policy, tolerance);
optimalPolicy = (IDeterministicPolicy <TState>)basePolicy.Clone();
foreach (var state in AllStateSpace)
{
optimalPolicy[state] = policy[state];
}
ValueFunctions.Clear();
Policies.Clear();
return(value.Mean);
}