2022/10/26 by Aurélien Delage, Delage, Aurélien, Olivier Buffet +5 · 1 citation
Decision Sciences · #Artificial Intelligence (cs.AI) #Decision-Making and Behavioral Economics #FOS: Computer and information sciences #Game Theory and Applications #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2210.14640
openalex publication_date 2022/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of state-of-the-art solvers for other sequential decision-making problems. In partially observable or collaborative settings (e.g., POMDPs and Dec- POMDPs), DP and HS require introducing an appropriate statistic that induces a fully observable problem as well as bounding (convex) approximators of the optimal value function. This approach has succeeded in some subclasses of 2-player zero-sum partially observable stochastic games (zs- POSGs) as well, but how to apply it in the general case still remains an open question. We answer it by (i) rigorously defining an equivalent game to work with, (ii) proving mathematical properties of the optimal value function that allow deriving bounds that come with solution strategies, (iii) proposing for the first time an HSVI-like solver that provably converges to an ε-optimal solution in finite time, and (iv) empirically analyzing it. This opens the door to a novel family of promising approaches complementing those relying on linear programming or iterative methods.