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AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.
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package aima.core.probability.mdp.impl;
import java.util.HashMap;
import java.util.Map;
import aima.core.agent.Action;
import aima.core.probability.mdp.MarkovDecisionProcess;
import aima.core.probability.mdp.PolicyEvaluation;
/**
* Artificial Intelligence A Modern Approach (3rd Edition): page 657.
*
* For small state spaces, policy evaluation using exact solution methods is
* often the most efficient approach. For large state spaces, O(n3)
* time might be prohibitive. Fortunately, it is not necessary to do exact
* policy evaluation. Instead, we can perform some number of simplified value
* iteration steps (simplified because the policy is fixed) to give a reasonably
* good approximation of utilities. The simplified Bellman update for this
* process is:
*
*
*
* Ui+1(s) <- R(s) + γΣs'P(s'|s,πi(s))Ui(s')
*
*
* and this is repeated k times to produce the next utility estimate. The
* resulting algorithm is called modified policy iteration. It is often
* much more efficient than standard policy iteration or value iteration.
*
*
* @param
* the state type.
* @param
* the action type.
*
* @author Ciaran O'Reilly
* @author Ravi Mohan
*
*/
public class ModifiedPolicyEvaluation implements PolicyEvaluation {
// # iterations to use to produce the next utility estimate
private int k;
// discount γ to be used.
private double gamma;
/**
* Constructor.
*
* @param k
* number iterations to use to produce the next utility estimate
* @param gamma
* discount γ to be used
*/
public ModifiedPolicyEvaluation(int k, double gamma) {
if (gamma > 1.0 || gamma <= 0.0) {
throw new IllegalArgumentException("Gamma must be > 0 and <= 1.0");
}
this.k = k;
this.gamma = gamma;
}
//
// START-PolicyEvaluation
@Override
public Map evaluate(Map pi_i, Map U,
MarkovDecisionProcess mdp) {
Map U_i = new HashMap(U);
Map U_ip1 = new HashMap(U);
// repeat k times to produce the next utility estimate
for (int i = 0; i < k; i++) {
// Ui+1(s) <- R(s) +
// γΣs'P(s'|s,πi(s))Ui(s')
for (S s : U.keySet()) {
A ap_i = pi_i.get(s);
double aSum = 0;
// Handle terminal states (i.e. no actions)
if (null != ap_i) {
for (S sDelta : U.keySet()) {
aSum += mdp.transitionProbability(sDelta, s, ap_i)
* U_i.get(sDelta);
}
}
U_ip1.put(s, mdp.reward(s) + gamma * aSum);
}
U_i.putAll(U_ip1);
}
return U_ip1;
}
// END-PolicyEvaluation
//
}