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We consider a dynamic programming (DP) approach to approximately solving aninfinite-horizon constrained Markov decision process (CMDP) problem with afixed initial-state for the expected total discounted-reward criterion with auniform-feasibility constraint of the expected total discounted-cost in adeterministic, history-independent, and stationary policy set. We derive aDP-equation that recursively holds for a CMDP problem and its sub-CMDPproblems, where each problem, induced from the parameters of the original CMDPproblem, admits a uniformly-optimal feasible policy in its policy setassociated with the inputs to the problem. A policy constructed from theDP-equation is shown to achieve the optimal values, defined for the CMDPproblem the policy is a solution to, at all states. Based on the result, wediscuss off-line and on-line computational algorithms, motivated from policyiteration for MDPs, whose output sequences have local convergences for theoriginal CMDP problem.

Approximate Constrained Discounted Dynamic Programming with Uniform Feasibility and Optimality