Abstract
In this paper, we study discrete infinite-time horizon undiscounted finite-state and finite-action \(\textit{MDP}\)s with average cost criteria. Based on a combinatorial approach, we show that completely ergodic \(\textit{MDP}\)s can be reduced to a generalized minimum cost circulation problem with equality constraints. We show that although the reduced problem has the same complexity as the original one, it enables a linear programming problem with an underlying network structure for which strongly polynomial algorithms can be developed.
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