Conservative Policy Iteration For Zero-Sum POSGs

The Policy-Space Response Oracles (PSRO) framework scales equilibrium computation to large zero-sum games by iteratively expanding a restricted strategy set using deep reinforcement learning (DRL). A central challenge is to construct, under limited computational budgets, a small strategy population whose induced game well approximates the full game. Existing PSRO variants typically expand the population using best responses to meta-strategies computed from restricted-game payoffs, which can lead to inefficient expansions that provide limited global improvement. We propose to guide population expansion by directly evaluating the post-expansion population quality. Specifically, we adopt Population Exploitability (PE) to measure how well a restricted strategy set represents the full game, and introduce a two-phase exploration--selection framework that explicitly minimizes PE during expansion. We instantiate this framework as Global PSRO, a practical DRL-based algorithm that efficiently generates candidate responses and estimates PE via parameter-sharing conditional neural networks. Experiments across multiple two-player zero-sum games show that Global PSRO achieves lower exploitability and approximates Nash equilibria with significantly fewer policy iterations than prior PSRO methods.

Zero-sum Markov games arise in a wide variety of sequential decision-making problems such as adversarial learning and planning against modeled uncertainties. However, prior work on finite-sample guarantees on the learned state-action value function ($Q$-function) for zero-sum Markov games is largely restricted to finite-action settings, or to continuous-action games in which agents have linear dynamics and quadratic rewards (i.e. linear-quadratic, or LQ, games). A central challenge in extending such guarantees to more general continuous-action zero-sum Markov games is that the associated Bellman operator involves a minimax problem that need not admit a tractable saddle-point solution. To this end, we first introduce a class of neural network function approximators for the $Q$-function that is convex-concave in the players' actions, which guarantees that this minimax problem admits a pure-strategy saddle point. We then study an online variant of fitted $Q$-iteration employing this function class and establish, to the best of our knowledge, the first finite-sample guarantees for non-LQ zero-sum Markov games with continuous states and actions. Our code can be found at https://github.com/CLeARoboticsLab/QCanPlayThatGame.

Optimally solving decentralized decision-making problems modeled as Dec-POMDPs is known to be NEXP-complete. These optimal solutions are policies based on the entire history of observations and actions of an agent. However, some applications may require more compact policies because of limited compute capabilities, which can be modeled by considering a limited number of memory states (or agent states). While such an agent-state based policy class may not contain the optimal solution, it is still of practical interest to find the best agent-state policy within the class. We focus on an iterated best response style algorithm which guarantees monotonic improvements and convergence to a local optimum in polynomial runtime in the Dec-POMDP model size. In order to obtain a better local optimum, we use a modified objective which incentivizes risk-seeking alongside a conservative policy iteration update. Our empirical results show that our approach performs as well as state-of-the-art approaches on several benchmark Dec-POMDPs, achieving near-optimal performance while having polynomial runtime despite the limited memory. We also show that using more agent states (a larger memory) leads to greater performance. Our approach provides a novel way of incorporating memory constraints on the agents in the Dec-POMDP problem.