  Dynamic programming and heuristic search are at the core of state-of-the-art
solvers for sequential decision-making problems. In partially observable or
collaborative settings (\eg, POMDPs and Dec-POMDPs), this requires 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 failed in the general case despite
known concavity and convexity properties, which only led to heuristic
algorithms with poor convergence guarantees. We overcome this issue, leveraging
on these properties to derive bounding approximators and efficient update and
selection operators, before deriving a prototypical solver inspired by HSVI
that provably converges to an $\epsilon$-optimal solution in finite time, and
which we empirically evaluate. This opens the door to a novel family of
promising approaches complementing those relying on linear programming or
iterative methods.

Computer Science and Game Theory;Artificial Intelligence;Machine Learning