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On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games
We propose a two-timescale algorithm for finding local Nash equilibria i...
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Minimax Theorem for Latent Games or: How I Learned to Stop Worrying about Mixed-Nash and Love Neural Nets
Adversarial training, a special case of multi-objective optimization, is...
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Stability of Gradient Learning Dynamics in Continuous Games: Vector Action Spaces
Towards characterizing the optimization landscape of games, this paper a...
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Smoothed Complexity of 2-player Nash Equilibria
We prove that computing a Nash equilibrium of a two-player (n × n) game ...
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Game on Random Environment, Mean-field Langevin System and Neural Networks
In this paper we study a type of games regularized by the relative entro...
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Extra-gradient with player sampling for provable fast convergence in n-player games
Data-driven model training is increasingly relying on finding Nash equil...
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On the Existence and Structure of Mixed Nash Equilibria for In-Band Full-Duplex Wireless Networks
This article offers the first characterisation of mixed Nash equilibria ...
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A mean-field analysis of two-player zero-sum games
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.
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