Achieving Linear Speedup in Non-IID Federated Bilevel Learning

TL;DR

This paper introduces FedMBO, a novel federated bilevel optimization algorithm that achieves linear speedup in convergence rate for non-i.i.d. datasets, addressing key open problems in federated learning.

Contribution

We propose FedMBO with a new client sampling scheme, providing the first theoretical linear speedup results for non-i.i.d. federated bilevel optimization.

Findings

FedMBO achieves a convergence rate of O(1/√(nK) + 1/K + √n/K^{3/2}) on non-i.i.d. datasets.

FedMBO demonstrates linear speedup with respect to the number of clients in theory.

Experimental results validate the theoretical convergence rate and effectiveness of FedMBO.

Abstract

Federated bilevel optimization has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d.~datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$ on non-i.i.d.~datasets, where $n$ is the number of participating clients in each round, and $K$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d.~federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.