Collaborative Compressors in Distributed Mean Estimation with Limited Communication Budge

ICLR 2025 Conference Submission13383 Authors

Keywords: Distributed Mean Estimation, Compression

TL;DR: For communication-efficient distributed mean estimation of vectors, we provide compression/decompression schemes that exploit the similarity between the said vectors.

Abstract:

Distributed high dimensional mean estimation is a common aggregation routine used often in distributed optimization methods (e.g. federated learning). Most of these applications call for a communication-constrained setting where vectors, whose mean is to be estimated, have to be compressed before sharing. One could independently encode and decode these to achieve compression, but that overlooks the fact that these vectors are often similar with each other. To exploit these similarities, recently Suresh et al., 2022, Jhunjhunwala et al., 2021, Jiang et al, 2023, proposed multiple {\em correlation-aware compression schemes.} However, in most cases, the correlations have to be known for these schemes to work. Moreover, a theoretical analysis of graceful degradation of these correlation-aware compression schemes with increasing {\em dissimilarity} is limited to only the $\ell_2$-error in the literature.
In this paper, we propose four different collaborative compression schemes that agnostically exploit the similarities among vectors in a distributed setting. Our schemes are all simple to implement and computationally efficient, while resulting in big savings in communication. We do a rigorous theoretical analysis of our proposed schemes to show how the $\ell_2$, $\ell_\infty$ and cosine estimation error varies with the degree of similarity among vectors. In the process, we come up with appropriate dissimilarity-measures for these applications as well.

Primary Area: learning theory

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Submission Number: 13383