Federated Representation Learning in the Under-Parameterized Regime
<|reference_start|>Federated Representation Learning in the Under-Parameterized Regime: 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.<|reference_end|>
@article{liu2024federated,
    title={Federated Representation Learning in the Under-Parameterized Regime},
    author={Renpu Liu, Cong Shen and Jing Yang},
    journal={arXiv preprint arXiv:2406.04596},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.04596},
    primaryClass={cs.LG}
}