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arXiv · 2310.09804

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

Ahmad Rammal·Kaja Gruntkowska·Nikita Fedin·Eduard Gorbunov·Peter Richtárik
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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.

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Ahmad Rammal, Kaja Gruntkowska, Nikita Fedin, Eduard Gorbunov, Peter Richtárik. 2023-10-15. Communication Compression for Byzantine Robust Learning: New Efficient Algorithms and Improved Rates. https://arxiv.org/abs/2310.09804

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