  Distributed learning has emerged as a leading paradigm for training large
machine learning models. However, in real-world scenarios, participants may be
unreliable or malicious, posing a significant challenge to the integrity and
accuracy of the trained models. Byzantine fault tolerance mechanisms have been
proposed to address these issues, but they often assume full participation from
all clients, which is not always practical due to the unavailability of some
clients or communication constraints. In our work, we propose the first
distributed method with client sampling and provable tolerance to Byzantine
workers. The key idea behind the developed method is the use of gradient
clipping to control stochastic gradient differences in recursive variance
reduction. This allows us to bound the potential harm caused by Byzantine
workers, even during iterations when all sampled clients are Byzantine.
Furthermore, we incorporate communication compression into the method to
enhance communication efficiency. Under general assumptions, we prove
convergence rates for the proposed method that match the existing
state-of-the-art (SOTA) theoretical results. We also propose a heuristic on
adjusting any Byzantine-robust method to a partial participation scenario via
clipping.
