First-order methods for Stochastic Variational Inequality problems with Function Constraints
Published in arXiv, 2023
The monotone Variational Inequality (VI) framework has broad applications in engineering and science, often involving data-driven function constraints, making standard projections challenging. This paper introduces first-order methods for function-constrained VI (FCVI) problems in smooth, nonsmooth, and stochastic settings.
We propose AdOpEx, which applies operator extrapolation to the KKT operator in smooth deterministic settings, using an adaptive two-timescale approach to ensure bounded multipliers and optimal convergence. For nonsmooth and stochastic VIs, we introduce P-OpEx, a partial extrapolation method, and OpConEx, which improves dependence on noise and Lipschitz constants via constraint extrapolation.
Our algorithms extend naturally to generalized Nash equilibrium problem (GNEP) with function constraints, maintaining the same complexity guarantees.
Recommended citation: D Boob, Q Deng, M Khalafi - arXiv preprint arXiv:2304.04778, 2023
Download Paper | Download Slides