Federated Representation Learning in the Under-Parameterized Regime

TL;DR

This paper introduces FLUTE, a novel federated representation learning algorithm designed for the under-parameterized regime, providing the first provable guarantees and demonstrating superior performance over existing methods.

Contribution

The paper develops FLUTE, the first federated representation learning algorithm with theoretical guarantees for under-parameterized models, and extends it beyond linear representations.

Findings

FLUTE outperforms existing FRL methods in experiments.

Theoretical analysis shows sample complexity and convergence guarantees.

Bridges low-rank matrix approximation with federated learning analysis.

Abstract

Federated representation learning (FRL) is a popular personalized federated learning (FL) framework where clients work together to train a common representation while retaining their personalized heads. Existing studies, however, largely focus on the over-parameterized regime. In this paper, we make the initial efforts to investigate FRL in the under-parameterized regime, where the FL model is insufficient to express the variations in all ground-truth models. We propose a novel FRL algorithm FLUTE, and theoretically characterize its sample complexity and convergence rate for linear models in the under-parameterized regime. To the best of our knowledge, this is the first FRL algorithm with provable performance guarantees in this regime. FLUTE features a data-independent random initialization and a carefully designed objective function that aids the distillation of subspace spanned by the global optimal representation from the misaligned local representations. On the technical side, we bridge low-rank matrix approximation techniques with the FL analysis, which may be of broad interest. We also extend FLUTE beyond linear representations. Experimental results demonstrate that FLUTE outperforms state-of-the-art FRL solutions in both synthetic and real-world tasks.