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On Bellman's Optimality Principle for zs-POSGs

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Many non-trivial sequential decision-making problems are efficiently solved by relying on Bellman's optimality principle, i.e., exploiting the fact that sub-problems are nested recursively within the original problem. Here we show how it can apply to (infinite horizon) 2-player zero-sum partially observable stochastic games (zs-POSGs) by (i) taking a central planner's viewpoint, which can only reason on a sufficient statistic called occupancy state, and (ii) turning such problems into zero-sum occupancy Markov games (zs-OMGs). Then, exploiting the Lipschitz-continuity of the value function in occupancy space, one can derive a version of the HSVI algorithm (Heuristic Search Value Iteration) that provably finds an-Nash equilibrium in finite time.
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hal-03080287 , version 1 (18-12-2020)



Olivier Buffet, Jilles Dibangoye, Aurélien Delage, Abdallah Saffidine, Vincent Thomas. On Bellman's Optimality Principle for zs-POSGs. 2020. ⟨hal-03080287⟩
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