When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of who to compete with (i.e., the opponent mixture) and how to beat them (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the best-response module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that LMAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.
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