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arXiv · 2303.02957

Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems

Atsushi Nitanda·Kazusato Oko·Denny Wu·Nobuhito Takenouchi·Taiji Suzuki
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Abstract

The entropic fictitious play (EFP) is a recently proposed algorithm that minimizes the sum of a convex functional and entropy in the space of measures -- such an objective naturally arises in the optimization of a two-layer neural network in the mean-field regime. In this work, we provide a concise primal-dual analysis of EFP in the setting where the learning problem exhibits a finite-sum structure. We establish quantitative global convergence guarantees for both the continuous-time and discrete-time dynamics based on properties of a proximal Gibbs measure introduced in Nitanda et al. (2022). Furthermore, our primal-dual framework entails a memory-efficient particle-based implementation of the EFP update, and also suggests a connection to gradient boosting methods. We illustrate the efficiency of our novel implementation in experiments including neural network optimization and image synthesis.

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Atsushi Nitanda, Kazusato Oko, Denny Wu, Nobuhito Takenouchi, Taiji Suzuki. 2023-03-06. Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems. https://arxiv.org/abs/2303.02957

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