A Strong Duality Result for Cooperative Decentralized Constrained POMDPs

Nouman Khan, Vijay G. Subramanian

Abstract: The work studies cooperative decentralized constrained POMDPs with asymmetric information. Using an extension of Sion's Minimax theorem for functions with positive infinity and results on weak-convergence of measures, strong duality and existence of a saddle point are established for the setting of infinite-horizon expected total discounted costs when the observations lie in a countable space, the actions are chosen from a finite space, the immediate constraint costs are bounded, and the immediate objective cost is bounded from below.