HSVI can solve zero-sum Partially Observable Stochastic Games

TL;DR

This paper introduces HSVI, a novel dynamic programming-based solver for zero-sum partially observable stochastic games, providing convergence guarantees and empirical validation, thus expanding the toolkit beyond linear programming and regret minimization methods.

Contribution

It defines an equivalent game, proves properties of the value function, and develops an HSVI-like solver with proven finite-time convergence for general zs-POSGs.

Findings

The HSVI-like solver converges to an ε-optimal solution in finite time.

Mathematical properties of the value function enable deriving bounds and strategies.

Empirical analysis demonstrates the effectiveness of the proposed method.

Abstract

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 $\epsilon$-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.