Last Iterate Convergence in Monotone Mean Field Games
Keywords: mean field game, learning in games
TL;DR: We establish a novel algorithm with guaranteed last-iterate convergence in monotone MFG.
Abstract: Mean Field Game (MFG) is a framework utilized to model and approximate the behavior of a large number of agents, and the computation of equilibria in MFG has been a subject of interest. Despite the proposal of methods to approximate the equilibria, algorithms that can achieve equilibrium with the most recent policy of the algorithm, namely the last-iterate policy, have been limited.
We propose the use of a simple, proximal-point-type algorithm to compute strategies for MFGs. Subsequently, we provide the first last-iterate convergence guarantee under the Lasry--Lions-type monotonicity condition.
We further employ the Mirror Descent algorithm for the regularized MFG to efficiently approximate the update rules of the proximal point method for MFGs.
We demonstrate that the last-iterate strategy of Mirror Descent converges exponentially fast: we provide the guarantee of computing the $\varepsilon$ approximation in $\mathcal{O}(\log(1/\varepsilon))$ iterations. This research offers a tractable approach for large-scale and large-population games.
Primary Area: optimization
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Submission Number: 4391
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