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arXiv 2002.06277cs.LGmath.OCmath.PRstat.ML

A mean-field analysis of two-player zero-sum games

Courant Institute of Mathematical Sciences, New York University(纽约大学库朗数学科学研究所);Princeton University(普林斯顿大学);ENS Paris(巴黎高等师范学院);Center for Data Science, New York University(纽约大学数据科学中心);Institute for Advanced Study, Princeton(普林斯顿高等研究院)

Carles Domingo-Enrich, Samy Jelassi, Arthur Mensch, Grant Rotskoff, Joan Bruna

英文摘要:

Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be found using mirror descent. Yet this approach does not scale to high dimensions. To address this limitation, we parametrize mixed strategies as mixtures of particles, whose positions and weights are updated using gradient descent-ascent. We study this dynamics as an interacting gradient flow over measure spaces endowed with the Wasserstein-Fisher-Rao metric. We establish global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic. We prove a law of large numbers that relates particle dynamics to mean-field dynamics. Our method identifies mixed equilibria in high dimensions and is demonstrably effective for training mixtures of GANs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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