Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints
arXiv:2504.15243v2 Announce Type: replace-cross Abstract: Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly convex. Existing methods often face limitations, including slow convergence rates or reliance on double-loop algorithmic designs. To overcome these challenges, we introduce a novel single-loop penalty-based stochastic algorithm. Following the classical exact penalty method, our approach employs a {bf hinge-based penalty}, which […]