While recent reductions of zero-sum partially observable stochastic games (zs-POSGs) to transition-independent stochastic games (TI-SGs) theoretically admit dynamic programming, practical solutions remain stifled by the inherent non-linearity and exponential complexity of the simultaneous minimax backup. In this work, we surmount this computational barrier by rigorously recasting the simultaneous interaction as a sequential decision process via the principle of separation. We introduce distinct sufficient statistics for valuation and execution, the sequential occupancy state and the private occupancy family, which reveal a latent geometry in the optimal value function. This structural insight allows us to linearise the backup operator, reducing the update complexity from exponential to polynomial while enabling the direct extraction of safe policies without heuristic bookkeeping. Experimental results demonstrate that algorithms leveraging this sequential framework significantly outperform state-of-the-art methods, effectively rendering previously intractable domains solvable.

翻译：尽管近期将零和部分可观测随机博弈（zs-POSGs）约简为转移独立随机博弈（TI-SGs）的理论研究已为动态规划方法提供了可能，但同步极小极大备份算子固有的非线性和指数级复杂度仍阻碍着实际求解。本研究通过严格运用分离原理将同步交互重构为序贯决策过程，从而突破了这一计算瓶颈。我们引入了用于估值与执行的两种独立充分统计量——序贯占用状态与私有占用族，它们揭示了最优值函数中潜在的几何结构。这一结构洞见使我们能够线性化备份算子，将更新复杂度从指数级降至多项式级，同时无需启发式记录即可直接提取安全策略。实验结果表明，基于此序贯框架的算法显著超越了现有最优方法，使得先前难以处理的博弈领域变得可解。