Paper ID: 2310.09804

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

Ahmad Rammal, Kaja Gruntkowska, Nikita Fedin, Eduard Gorbunov, Peter Richtárik

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.

Submitted: Oct 15, 2023