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Exploiting hidden structures in non-convex games for convergence to Nash equilibrium

Authors :
Sakos, Iosif
Vlatakis-Gkaragkounis, Emmanouil-Vasileios
Mertikopoulos, Panayotis
Piliouras, Georgios
Publication Year :
2023

Abstract

A wide array of modern machine learning applications - from adversarial models to multi-agent reinforcement learning - can be formulated as non-cooperative games whose Nash equilibria represent the system's desired operational states. Despite having a highly non-convex loss landscape, many cases of interest possess a latent convex structure that could potentially be leveraged to yield convergence to equilibrium. Driven by this observation, our paper proposes a flexible first-order method that successfully exploits such "hidden structures" and achieves convergence under minimal assumptions for the transformation connecting the players' control variables to the game's latent, convex-structured layer. The proposed method - which we call preconditioned hidden gradient descent (PHGD) - hinges on a judiciously chosen gradient preconditioning scheme related to natural gradient methods. Importantly, we make no separability assumptions for the game's hidden structure, and we provide explicit convergence rate guarantees for both deterministic and stochastic environments.<br />Comment: 32 pages, 18 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2312.16609
Document Type :
Working Paper