Mastering the game of Stratego with model-free multiagent reinforcement learning

TLDR

Stratego remains an AI grand challenge due to its enormous game tree (~10^535 nodes), imperfect information, long episodes, and lack of sub‑problem decomposition, leaving existing methods at an amateur level. The authors present DeepNash, an autonomous agent that learns to play Stratego from scratch and reaches human expert performance. DeepNash employs a model‑free, game‑theoretic deep reinforcement learning approach that self‑plays without search, using the Regularised Nash Dynamics algorithm to converge to an approximate Nash equilibrium by directly adjusting multi‑agent learning dynamics. DeepNash surpasses current state‑of‑the‑art AI in Stratego, achieving a top‑3 yearly and all‑time ranking on the Gravon games platform and competing with human experts.

Abstract

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.