Martin Schmid

David Sychrovský, Michal Šustr, Elnaz Davoodi et al.

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical games, such as playing poker with different public cards or trading correlated assets on the stock market. As these similar games feature similar equilibra, we investigate a way to accelerate equilibrium finding on such a distribution. We present a novel "learning not to regret" framework, enabling us to meta-learn a regret minimizer tailored to a specific distribution. Our key contribution, Neural Predictive Regret Matching, is uniquely meta-learned to converge rapidly for the chosen distribution of games, while having regret minimization guarantees on any game. We validated our algorithms' faster convergence on a distribution of river poker games. Our experiments show that the meta-learned algorithms outpace their non-meta-learned counterparts, achieving more than tenfold improvements.

Matej Straka, Martin Schmid

We introduce a real-time strategy game environment based on Generals.io, a game with thousands of weekly active players. Our environment is fully compatible with Gymnasium and PettingZoo and is capable of running thousands of frames per second on commodity hardware. We also present a reference agent, trained with supervised pre-training and self-play, which reached the top 0.003% of the 1v1 human leaderboard after only 36 hours on a single H100 GPU. To accelerate learning, we incorporate potential-based reward shaping and memory features. Our contributions of a modular RTS benchmark and a competitive baseline agent provide an accessible yet challenging platform for advancing multi-agent reinforcement learning research. The documented code, together with examples and tutorials, is available at https://github.com/strakam/generals-bots.

Samuel Sokota, Edward Lockhart, Finbarr Timbers et al.

For artificially intelligent learning systems to have widespread applicability in real-world settings, it is important that they be able to operate decentrally. Unfortunately, decentralized control is difficult -- computing even an epsilon-optimal joint policy is a NEXP complete problem. Nevertheless, a recently rediscovered insight -- that a team of agents can coordinate via common knowledge -- has given rise to algorithms capable of finding optimal joint policies in small common-payoff games. The Bayesian action decoder (BAD) leverages this insight and deep reinforcement learning to scale to games as large as two-player Hanabi. However, the approximations it uses to do so prevent it from discovering optimal joint policies even in games small enough to brute force optimal solutions. This work proposes CAPI, a novel algorithm which, like BAD, combines common knowledge with deep reinforcement learning. However, unlike BAD, CAPI prioritizes the propensity to discover optimal joint policies over scalability. While this choice precludes CAPI from scaling to games as large as Hanabi, empirical results demonstrate that, on the games to which CAPI does scale, it is capable of discovering optimal joint policies even when other modern multi-agent reinforcement learning algorithms are unable to do so. Code is available at https://github.com/ssokota/capi .

Christopher Solinas, Radovan Haluska, David Sychrovsky et al.

We present Neural Bayesian Filtering (NBF), an algorithm for maintaining distributions over hidden states, called beliefs, in partially observable systems. NBF is trained to find a good latent representation of the beliefs induced by a task. It maps beliefs to fixed-length embedding vectors, which condition generative models for sampling. During filtering, particle-style updates compute posteriors in this embedding space using incoming observations and the environment's dynamics. NBF combines the computational efficiency of classical filters with the expressiveness of deep generative models - tracking rapidly shifting, multimodal beliefs while mitigating the risk of particle impoverishment. We validate NBF in state estimation tasks in three partially observable environments.

David Sychrovský, Martin Schmid, Michal Šustr et al.

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in isolation. However, in practice, players often encounter a distribution of similar but distinct games. For example, when trading correlated assets on the stock market, or when refining the strategy in subgames of a much larger game. Recently, offline meta-learning was used to accelerate one-sided equilibrium finding on such distributions. We build upon this, extending the framework to the more challenging self-play setting, which is the basis for most state-of-the-art equilibrium approximation algorithms for domains at scale. When selecting the strategy, our method uniquely integrates information across all decision states, promoting global communication as opposed to the traditional local regret decomposition. Empirical evaluation on normal-form games and river poker subgames shows our meta-learned algorithms considerably outperform other state-of-the-art regret minimization algorithms.

Martin Schmid, Matej Moravcik, Neil Burch et al.

Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and learning demonstrated strong performance for specific imperfect information poker variants. We introduce Student of Games, a general-purpose algorithm that unifies previous approaches, combining guided search, self-play learning, and game-theoretic reasoning. Student of Games achieves strong empirical performance in large perfect and imperfect information games -- an important step towards truly general algorithms for arbitrary environments. We prove that Student of Games is sound, converging to perfect play as available computation and approximation capacity increases. Student of Games reaches strong performance in chess and Go, beats the strongest openly available agent in heads-up no-limit Texas hold'em poker, and defeats the state-of-the-art agent in Scotland Yard, an imperfect information game that illustrates the value of guided search, learning, and game-theoretic reasoning.

Vojtěch Kovařík, Martin Schmid, Neil Burch et al.

Multiagent decision-making in partially observable environments is usually modelled as either an extensive-form game (EFG) in game theory or a partially observable stochastic game (POSG) in multiagent reinforcement learning (MARL). One issue with the current situation is that while most practical problems can be modelled in both formalisms, the relationship of the two models is unclear, which hinders the transfer of ideas between the two communities. A second issue is that while EFGs have recently seen significant algorithmic progress, their classical formalization is unsuitable for efficient presentation of the underlying ideas, such as those around decomposition. To solve the first issue, we introduce factored-observation stochastic games (FOSGs), a minor modification of the POSG formalism which distinguishes between private and public observation and thereby greatly simplifies decomposition. To remedy the second issue, we show that FOSGs and POSGs are naturally connected to EFGs: by "unrolling" a FOSG into its tree form, we obtain an EFG. Conversely, any perfect-recall timeable EFG corresponds to some underlying FOSG in this manner. Moreover, this relationship justifies several minor modifications to the classical EFG formalization that recently appeared as an implicit response to the model's issues with decomposition. Finally, we illustrate the transfer of ideas between EFGs and MARL by presenting three key EFG techniques -- counterfactual regret minimization, sequence form, and decomposition -- in the FOSG framework.