Dynamic Stochastic Variational Inequalities and Their Applications in AI

Speaker：

Xiaojun Chen (The Hong Kong Polytechnic University)

Time：

Fri., 16:00-17:00, May 30, 2025

Venue：C548, Shuangqing Complex Building A

Abstract：

The dynamic stochastic variational inequality (DSVI) is an ordinary differential equation whose right-hand side is defined by the two-stage stochastic variational inequality (SVI). The DSVI provides a unified modelling framework for various applications in which dynamics, uncertainties and equilibrium are present. We show the existence and uniqueness of a solution for two classes of the DSVI in the space of continuously differentiable functions with the space of measurable functions. The first class is defined by a strongly monotone SVI in the second stage, and the second class pertains to a box-constrained P-matrix linear SVI in the second stage. We develop sample average approximation and time-stepping schemes to compute a solution of the DSVI. The uniform convergence and exponential convergence are established for the discrete approximation. We show applications of the DSVI for optimizing multimodal lager model-based embodied intelligence system for the elderly, where the two-stage SVI arises from stochastic bilevel optimization.