Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Games
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Mean-field games have been used as a theoretical tool to obtain an approximate Nash equilibrium for symmetric and anonymous N-player games in literature. However, limiting applicability, existing theoretical results assume variations of a "population generative model", which allows arbitrary modifications of the population distribution by the learning algorithm. Instead, we show that N agents running policy mirror ascent converge to the Nash equilibrium of the regularized game within 𝒪̃(ε^-2) samples from a single sample trajectory without a population generative model, up to a standard 𝒪(1/√(N)) error due to the mean field. Taking a divergent approach from literature, instead of working with the best-response map we first show that a policy mirror ascent map can be used to construct a contractive operator having the Nash equilibrium as its fixed point. Next, we prove that conditional TD-learning in N-agent games can learn value functions within 𝒪̃(ε^-2) time steps. These results allow proving sample complexity guarantees in the oracle-free setting by only relying on a sample path from the N agent simulator. Furthermore, we demonstrate that our methodology allows for independent learning by N agents with finite sample guarantees.
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