In two-player zero-sum extensive-form games, Nash equilibrium prescribes optimal strategies against perfectly rational opponents. However, it does not guarantee rational play in parts of the game tree that can only be reached by the players making mistakes. This can be problematic when operationalizing equilibria in the real world among imperfect players. Trembling-hand refinements are a sound remedy to this issue, and are subsets of Nash equilibria that are designed to handle the possibility that any of the players may make mistakes. In this paper, we initiate the study of equilibrium refinements for settings where one of the players is perfectly rational (the "machine") and the other may make mistakes.

In two-player zero-sum extensive-form games, Nash equilibrium prescribes optimal strategies against perfectly rational opponents. However, it does not guarantee rational play in parts of the game tree that can only be reached by the players making mistakes. This can be problematic when operationalizing equilibria in the real world among imperfect players. Trembling-hand refinements are a sound remedy to this issue, and are subsets of Nash equilibria that are designed to handle the possibility that any of the players may make mistakes. In this paper, we initiate the study of equilibrium refinements for settings where one of the players is perfectly rational (the "machine") and the other may make mistakes.

We study Online Lazy Gradient Descent for optimisation on a strongly convex domain. The algorithm is known to achieve O( N) regret against adversarial opponents; here we show it is universal in the sense that it also achieves O(log N) expected regret against i.i.d opponents. This improves upon the more complex metaalgorithm of Huang et al [20] that only gets O( Nlog N) and O(log N) bounds. In addition we show that, unlike for the simplex, order bounds for pseudo-regret and expected regret are equivalent for strongly convex domains.

Measuring and promoting policy diversity is critical for solving games with strong non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). With that in mind, maintaining a pool of diverse policies via open-ended learning is an attractive solution, which can generate auto-curricula to avoid being exploited. However, in conventional open-ended learning algorithms, there are no widely accepted definitions for diversity, making it hard to construct and evaluate the diverse policies. In this work, we summarize previous concepts of diversity and work towards offering a unified measure of diversity in multi-agent open-ended learning to include all elements in Markov games, based on both Behavioral Diversity (BD) and Response Diversity (RD).

Training agents in multi-agent games presents significant challenges due to their intricate nature. These challenges are exacerbated by dynamics influenced not only by the environment but also by strategies of opponents. Existing methods often struggle with slow convergence and instability.To address these challenges, we harness the potential of imitation learning (IL) to comprehend and anticipate actions of the opponents, aiming to mitigate uncertainties with respect to the game dynamics.Our key contributions include:(i) a new multi-agent IL model for predicting next moves of the opponents - our model works with hidden actions of opponents and local observations;(ii) a new multi-agent reinforcement learning (MARL) algorithm that combines our IL model and policy training into one single training process;and (iii) extensive experiments in three challenging game environments, including an advanced version of the Star-Craft multi-agent challenge (i.e., SMACv2).Experimental results show that our approach achieves superior performance compared to state-of-the-art MARL algorithms.

When an agent is in a multi-agent environment, it may face previously unseen opponents, and it is a challenge to cooperate with other agents to accomplish the task together or to maximize its own rewards. Most opponent modeling methods deal with the non-stationarity caused by unknown opponent policies via predicting the opponent's actions. However, focusing on the opponent's action is shortsighted, which also constrains the adaptability to unknown opponents in complex tasks. In this paper, we propose opponent modeling based on subgoal inference, which infers the opponent's subgoals through historical trajectories. As subgoals are likely to be shared by different opponent policies, predicting subgoals can yield better generalization to unknown opponents.

Cooperation between self-interested individuals is a widespread phenomenon in the natural world, but remains elusive in interactions between artificially intelligent agents.

We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an adversary. We propose the \textsc{UCSG} algorithm that achieves a sublinear regret compared to the game value when competing with an arbitrary opponent. This result improves previous ones under the same setting. The regret bound has a dependency on the \textit{diameter}, which is an intrinsic value related to the mixing property of SGs.