Federated Representation Learning in the Under-Parameterized Regime

• URL: http://arxiv.org/abs/2406.04596v4
• Date: Wed, 17 Jul 2024 22:11:08 GMT
• Title: Federated Representation Learning in the Under-Parameterized Regime
• Authors: Renpu Liu, Cong Shen, Jing Yang,
• Abstract summary: 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. We propose a novel FRL algorithm FLUTE, and theoretically characterize its sample complexity and convergence rate for linear models. Experimental results demonstrate that FLUTE outperforms state-of-the-art FRL solutions in both synthetic and real-world tasks.
• Score: 10.551397415936309
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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