Compressing gradients by exploiting temporal correlation in momentum-SGD

TL;DR

This paper introduces compression methods that leverage the temporal correlation in momentum-SGD updates to significantly reduce communication in decentralized optimization, with proven convergence guarantees under expected error bounds.

Contribution

It proposes novel compression techniques exploiting temporal correlation in momentum-SGD and provides convergence analysis under expected error bounds, extending theoretical guarantees.

Findings

Significant reduction in communication rate with negligible computational overhead.

Effective compression methods for systems with and without error-feedback.

Convergence guarantees for SGD with compression under expected error bounds.

Abstract

An increasing bottleneck in decentralized optimization is communication. Bigger models and growing datasets mean that decentralization of computation is important and that the amount of information exchanged is quickly growing. While compression techniques have been introduced to cope with the latter, none has considered leveraging the temporal correlations that exist in consecutive vector updates. An important example is distributed momentum-SGD where temporal correlation is enhanced by the low-pass-filtering effect of applying momentum. In this paper we design and analyze compression methods that exploit temporal correlation in systems both with and without error-feedback. Experiments with the ImageNet dataset demonstrate that our proposed methods offer significant reduction in the rate of communication at only a negligible increase in computation complexity. We further analyze the convergence of SGD when compression is applied with error-feedback. In the literature, convergence guarantees are developed only for compressors that provide error-bounds point-wise, i.e., for each input to the compressor. In contrast, many important codes (e.g. rate-distortion codes) provide error-bounds only in expectation and thus provide a more general guarantee. In this paper we prove the convergence of SGD under an expected error assumption by establishing a bound for the minimum gradient norm.