  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.
