Self-Play Reinforcement Learning under Imperfect Information in Big 2

Competitive multi-agent reinforcement learning in imperfect-information games requires agents to act under partial observability and against adversarial opponents, necessitating stochastic policies. While self-play reinforcement learning with Proximal Policy Optimization (PPO) has achieved strong empirical success, its standard advantage estimator, generalized advantage estimation, suffers from additional variance due to the sampling of stochastic future actions. This variance is amplified in equilibrium self-play because of the stochastic nature of the equilibrium policy and persists even when the critic is exact. We address this bottleneck by introducing $Q$-boosting, a variance-reduced advantage estimator based on a centralized action-value critic, and propose Variance-Reduced Policy Optimization (VRPO), incorporating this new estimator. The algorithm replaces sampled multi-step backups with a multi-step Expected SARSA$(λ)$ trace, computing policy expectations at each step to average out action-sampling noise, while retaining PPO's clipped objective and on-policy actor updates. Empirically, VRPO consistently achieves strong performance from mid-sized to large-scale games including Dou Dizhu and Heads-Up No-Limit Texas Hold'em.

Finding approximate equilibria for large-scale imperfect-information competitive games such as StarCraft, Dota, and CounterStrike remains computationally infeasible due to sparse rewards and challenging exploration over long horizons. In this paper, we propose a multi-agent starting-state sampling strategy designed to substantially accelerate online exploration in regularized policy-gradient game methods for two-player zero-sum (2p0s) games. Motivated by an assumption that offline demonstrations from skilled humans can provide good coverage of high-level strategies relevant to equilibrium play, we propose the initialization of reinforcement learning data collection at intermediate states sampled from offline data to facilitate exploration of strategically relevant subgames. Referring to this method as Data-Augmented Game Starts (DAGS), we perform experiments using synthetic datasets and analytically tractable, long-horizon control variants of two-player Kuhn Poker, Goofspiel, and a counterexample game designed to penalize biased beliefs over hidden information. Under fixed computational budgets, DAGS enables regularized policy gradient methods to achieve lower exploitability in games with significantly more challenging exploration. We show that augmenting starting state distributions when solving imperfect information games can lead to biased equilibria, and we provide a straightforward mitigation to this in the form of multi-task observation flags. Finally, we release a new set of benchmark environments that drastically increase exploration challenges and state counts in existing OpenSpiel games while keeping exploitability measurements analytically tractable.

We investigate the problem of learning useful policy representations (embeddings) in two-player zero-sum imperfect-information games. We make three contributions: First, we introduce methods of creating datasets of policies for a given game. Second, we propose methods to learn policy representations. Third, we introduce downstream tasks to evaluate the effectiveness of such representations. We evaluate each dataset method, embedding method, and downstream task on Kuhn and Leduc Poker. Although our methods are very basic, we demonstrate that useful behavioral representations are present in the learned embeddings. To our knowledge, this work is among the first to systematically compare self-supervised learning techniques for learning policy representations in games. Our code is available at https://github.com/VitamintK/ssl-project for others to extend.