In multi-agent reinforcement learning, the behaviors that agents learn in a single Markov Game (MG) are typically confined to the given agent number (i.e., population size). Every single MG induced by varying population sizes may possess distinct optimal joint strategies and game-specific knowledge, which are modeled independently in modern multi-agent algorithms. In this work, we focus on creating agents that generalize across population-varying MGs. Instead of learning a unimodal policy, each agent learns a policy set that is formed by effective strategies across a variety of games. We propose Meta Representations for Agents (MRA) that explicitly models the game-common and game-specific strategic knowledge. By representing the policy sets with multi-modal latent policies, the common strategic knowledge and diverse strategic modes are discovered with an iterative optimization procedure. We prove that as an approximation to a constrained mutual information maximization objective, the learned policies can reach Nash Equilibrium in every evaluation MG under the assumption of Lipschitz game on a sufficiently large latent space. When deploying it at practical latent models with limited size, fast adaptation can be achieved by leveraging the first-order gradient information. Extensive experiments show the effectiveness of MRA on both training performance and generalization ability in hard and unseen games.
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