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This chapter concerns discrete time Markov decision processes under a discounted optimality criterion with state-action-dependent discount factors, possibly unbounded costs, and noncompact admissible action sets. Under mild conditions, we show the existence of stationary optimal policies and we introduce the value iteration and the policy iteration algorithms to approximate the value function.

Iteration Algorithms in Markov Decision Processes with State- Action-Dependent Discount Factors and Unbounded Costs