A0441
Title: Sampling with constraints
Authors: Xin Tong - National University of Singapore (Singapore) [presenting]
Abstract: Sampling-based inference and learning techniques, especially Bayesian inference, provide an essential approach to handling uncertainty in machine learning (ML). As these techniques are increasingly used in daily life, it becomes essential to safeguard ML systems with various trustworthy-related constraints, such as fairness, safety, and interpretability. A family of constrained sampling algorithms which generalize Langevin Dynamics (LD) and Stein Variational Gradient Descent (SVGD) is proposed to incorporate a moment constraint or a level set specified by a general nonlinear function. By exploiting the gradient flow structure of LD and SVGD, algorithms are derived for handling constraints, including a primal-dual gradient approach and the constraint-controlled gradient descent approach. The continuous-time mean-field limit of these algorithms is investigated, and it is shown that they have O(1/t) convergence under mild conditions.
