  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.
