Infinite-Horizon Average Reward Markov Decision Processes
Infinite-Horizon Average Reward Markov Decision Processes
Infinite-Horizon Average Reward Markov Decision Processes
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Existence of Optimal Policies – Unichain ModelsTheoremSuppose S and A s are finite, r(s, a) is bounded, and the model isunichain. Then(i) there exists a stationary average optimal policy;(ii) there exists a scalar g ∗ and an h ∗ ∈ V for whichB(g ∗ , h ∗ ) = 0;(iii) any stationary policy derived from an h ∗ -improving decisionrule is average optimal;(iv) g ∗ e = g ∗ + = g ∗ −.Dan Zhang, Spring 2012 <strong>Infinite</strong> <strong>Horizon</strong> <strong>Average</strong> <strong>Reward</strong> MDP 11
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