Collaborative Compressors in Distributed Mean Estimation with Limited Communication Budget
This work addresses communication bottlenecks in distributed optimization for applications like federated learning, offering incremental improvements over existing correlation-aware methods by removing the need for known correlations and extending error analysis.
The paper tackles the problem of distributed high-dimensional mean estimation under communication constraints by proposing four collaborative compression schemes that exploit similarities among vectors without prior knowledge of correlations, achieving significant communication savings with theoretical analysis of error metrics.
Distributed high dimensional mean estimation is a common aggregation routine used often in distributed optimization methods. 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 close to each other. To exploit these similarities, recently Suresh et al., 2022, Jhunjhunwala et al., 2021, Jiang et al, 2023, proposed multiple 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 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. The analysis of our proposed schemes show how the $\ell_2$, $\ell_\infty$ and cosine estimation error varies with the degree of similarity among vectors.