  Variational Inequality (VI) problems have attracted great interest in the
machine learning (ML) community due to their application in adversarial and
multi-agent training. Despite its relevance in ML, the oft-used
strong-monotonicity and Lipschitz continuity assumptions on VI problems are
restrictive and do not hold in practice. To address this, we relax smoothness
and monotonicity assumptions and study structured non-monotone generalized
smoothness. The key idea of our results is in adaptive stepsizes. We prove the
first-known convergence results for solving generalized smooth VIs for the
three popular methods, namely, projection, Korpelevich, and Popov methods. Our
convergence rate results for generalized smooth VIs match or improve existing
results on smooth VIs. We present numerical experiments that support our
theoretical guarantees and highlight the efficiency of proposed adaptive
stepsizes.
