We address scaling up equilibrium computation in Mean Field Games (MFGs)
using Online Mirror Descent (OMD). We show that continuous-time OMD provably
converges to a Nash equilibrium under a natural and well-motivated set of
monotonicity assumptions. This theoretical result nicely extends to
multi-population games and to settings involving common noise. A thorough
experimental investigation on various single and multi-population MFGs shows
that OMD outperforms traditional algorithms such as Fictitious Play (FP). We
empirically show that OMD scales up and converges significantly faster than FP
by solving, for the first time to our knowledge, examples of MFGs with hundreds
of billions states. This study establishes the state-of-the-art for learning in
large-scale multi-agent and multi-population games.

本研究使用在线镜像下降法（OMD）解决均值场游戏（MFG）中均衡计算的扩展性问题，在一系列合理的单调性假设下，证明连续时间 OMD 可收敛于纳什均衡，这一理论结果良好地扩展至多人口游戏和涉及共同噪声的设置。经过全面的实验研究，OMD 优于传统算法，如虚拟游戏（FP），以前所未有的速度解决了数十亿个状态的 MFG 实例。这项研究在大规模多代理和多人口游戏的学习方面确立了最新的状态。