A Resampling-Free Stochastic Projection Contraction Algorithm for Solving Stochastic Variational Inequalities

Abstract

Sampling is a major computational bottleneck in stochastic algorithms. This paper proposes a stochastic projection contraction algorithm for stochastic variational inequality problems, significantly reducing runtime by eliminating resampling in the correction step. We introduce an adjustable offset weight to optimize search direction, along with different adaptive step size strategies in prediction and correction steps. We further present discrete differential equation interpretations for specific offset weight values. To address bias due to the absence of resampling in the correction step, we develop an error control scheme and provide convergence guarantees. Numerical experiments demonstrate the algorithm’s efficiency.