一个ε-最优序列方法用于求解zs-POSGs
An $ε$-Optimal Sequential Approach for Solving zs-POSGs
AI总结：
本文提出一种序列方法，通过分离原理将同时交互转换为序列决策过程，从而线性化备份算子，降低更新复杂度并提取安全策略，实验表明其在求解复杂领域方面优于现有方法。
摘要：
尽管最近将零和部分可观测随机游戏（zs-POSGs）减少为转移无关随机游戏（TI-SGs）的理论方法允许动态规划，但实际解决方案仍受同时极小极大备份的固有非线性和指数复杂性所限制。在本文中，我们通过分离原理严格地将同时交互转换为序列决策过程，引入了估值和执行的区分充分统计量，即序列占用状态和私人占用族，揭示了最优价值函数中的潜在几何结构。这一结构洞察使我们能够线性化备份算子，将更新复杂度从指数级降低到多项式级，同时允许在不使用启发式记账的情况下直接提取安全策略。实验结果表明，利用这种序列框架的算法在求解复杂领域方面显著优于现有方法。
英文摘要：
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.
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