Robustness to Byzantine attacks is a necessity for various distributed
training scenarios. When the training reduces to the process of solving a
minimization problem, Byzantine robustness is relatively well-understood.
However, other problem formulations, such as min-max problems or, more
generally, variational inequalities, arise in many modern machine learning and,
in particular, distributed learning tasks. These problems significantly differ
from the standard minimization ones and, therefore, require separate
consideration. Nevertheless, only one work (Adibi et al., 2022) addresses this
important question in the context of Byzantine robustness. Our work makes a
further step in this direction by providing several (provably) Byzantine-robust
methods for distributed variational inequality, thoroughly studying their
theoretical convergence, removing the limitations of the previous work, and
providing numerical comparisons supporting the theoretical findings.

对于分布式训练场景来说，对拜占庭攻击的鲁棒性是必需的。本研究提供了几种（可证明的）适用于分布式变分不等式问题的拜占庭鲁棒方法，并全面研究了它们的理论收敛性，消除了先前工作的局限，并提供了支持理论发现的数值比较。