On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network

TL;DR

This paper introduces two new decentralized stochastic bilevel optimization algorithms for networked data, providing the first convergence rate analysis for nonconvex-strongly-convex problems and demonstrating their effectiveness in machine learning tasks.

Contribution

The paper develops the first decentralized stochastic bilevel algorithms with convergence guarantees for nonconvex-strongly-convex problems, expanding bilevel optimization to distributed settings.

Findings

Established convergence rates for the proposed algorithms.

Validated effectiveness through experiments on machine learning models.

Abstract

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the single-machine setting so that they are incapable of handling the distributed data. To address this issue, under the setting where all participants compose a network and perform peer-to-peer communication in this network, we developed two novel decentralized stochastic bilevel optimization algorithms based on the gradient tracking communication mechanism and two different gradient estimators. Additionally, we established their convergence rates for nonconvex-strongly-convex problems with novel theoretical analysis strategies. To our knowledge, this is the first work achieving these theoretical results. Finally, we applied our algorithms to practical machine learning models, and the experimental results confirmed the efficacy of our algorithms.