Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Cooling

תקציר מקורי באנגליתarXiv:2609.06196v2 Announce Type: replace-cross Abstract: This paper addresses a fundamental question in non-convex optimization: \textit{How should a stochastic optimizer allocate computation between global exploration and local exploitation?} We study this question in continuous time, using Langevin dynamics for global exploration and deterministic gradient flow for local exploitation. The simplest algorithm in this class is the best-state Langevin--gradient method: several Langevin trajectories explore the objective landscape, the best state encountered is retained, and a single gradient trajectory then refines this state to high terminal accuracy. Our main objective is to characterize the computational work required to achieve a prescribed accuracy with prescribed confidence. We develo