Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top
This work addresses robustness issues in distributed learning systems, offering improved rates and weaker assumptions, but it is incremental as it builds on existing Byzantine-tolerant methods.
The paper tackles the problem of Byzantine-robustness in collaborative and federated learning by proposing Byz-VR-MARINA, a method that uses variance reduction to improve robustness and communication compression for efficiency, achieving better theoretical convergence rates for non-convex and Polyak-Lojasiewicz loss functions.
Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work addresses this gap and proposes Byz-VR-MARINA - a new Byzantine-tolerant method with variance reduction and compression. A key message of our paper is that variance reduction is key to fighting Byzantine workers more effectively. At the same time, communication compression is a bonus that makes the process more communication efficient. We derive theoretical convergence guarantees for Byz-VR-MARINA outperforming previous state-of-the-art for general non-convex and Polyak-Lojasiewicz loss functions. Unlike the concurrent Byzantine-robust methods with variance reduction and/or compression, our complexity results are tight and do not rely on restrictive assumptions such as boundedness of the gradients or limited compression. Moreover, we provide the first analysis of a Byzantine-tolerant method supporting non-uniform sampling of stochastic gradients. Numerical experiments corroborate our theoretical findings.