Communication Compression for Byzantine Robust Learning: New Efficient Algorithms and Improved Rates

TL;DR

This paper introduces new Byzantine-robust algorithms with communication compression, achieving improved convergence rates and robustness in large-scale distributed and federated learning scenarios.

Contribution

It proposes two novel algorithms, Byz-DASHA-PAGE and Byz-EF21, with enhanced theoretical guarantees and practical performance for Byzantine-robust learning with compression.

Findings

Byz-DASHA-PAGE has better convergence rates than previous methods.

Byz-EF21 and Byz-EF21-BC demonstrate effective communication compression with error feedback.

Experimental results confirm the theoretical improvements.

Abstract

Byzantine robustness is an essential feature of algorithms for certain distributed optimization problems, typically encountered in collaborative/federated learning. These problems are usually huge-scale, implying that communication compression is also imperative for their resolution. These factors have spurred recent algorithmic and theoretical developments in the literature of Byzantine-robust learning with compression. In this paper, we contribute to this research area in two main directions. First, we propose a new Byzantine-robust method with compression - Byz-DASHA-PAGE - and prove that the new method has better convergence rate (for non-convex and Polyak-Lojasiewicz smooth optimization problems), smaller neighborhood size in the heterogeneous case, and tolerates more Byzantine workers under over-parametrization than the previous method with SOTA theoretical convergence guarantees (Byz-VR-MARINA). Secondly, we develop the first Byzantine-robust method with communication compression and error feedback - Byz-EF21 - along with its bidirectional compression version - Byz-EF21-BC - and derive the convergence rates for these methods for non-convex and Polyak-Lojasiewicz smooth case. We test the proposed methods and illustrate our theoretical findings in the numerical experiments.