First-Order Federated Bilevel Learning

Abstract

Federated bilevel optimization (FBO) has garnered significant attention lately, driven by its promising applications in meta-learning and hyperparameter optimization. Existing algorithms generally aim to approximate the gradient of the upper-level objective function (hypergradient) in the federated setting. However, because of the nonlinearity of the hypergradient and client drift, they often involve complicated computations. These computations, like multiple optimization sub-loops and second-order derivative evaluations, end up with significant memory consumption and high computational costs. In this paper, we propose a computationally and memory-efficient FBO algorithm named MemFBO. MemFBO features a fully single-loop structure with all involved variables updated simultaneously, and uses only first-order gradient information for all local updates. We show that MemFBO exhibits a linear convergence speedup with milder assumptions in both partial and full client participation scenarios. We further implement MemFBO in a novel FBO application for federated data cleaning. Our experiments, conducted on this application and federated hyper-representation, demonstrate the effectiveness of the proposed algorithm.