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Dynamic programming and heuristic search are at the core of state-of-the-artsolvers for sequential decision-making problems. In partially observable orcollaborative settings (\eg, POMDPs and Dec-POMDPs), this requires introducingan appropriate statistic that induces a fully observable problem as well asbounding (convex) approximators of the optimal value function. This approachhas succeeded in some subclasses of 2-player zero-sum partially observablestochastic games (zs-POSGs) as well, but failed in the general case despiteknown concavity and convexity properties, which only led to heuristicalgorithms with poor convergence guarantees. We overcome this issue, leveragingon these properties to derive bounding approximators and efficient update andselection operators, before deriving a prototypical solver inspired by HSVIthat provably converges to an $\epsilon$-optimal solution in finite time, andwhich we empirically evaluate. This opens the door to a novel family ofpromising approaches complementing those relying on linear programming oriterative methods.

HSVI for zs-POSGs using Concavity, Convexity and Lipschitz Properties