Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Cooling
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 a...
| Authors | Ioannis Kontoyiannis, Sean Meyn |
|---|---|
| Primary category | math.OC |
| Published | 5 September 2026 |
| Last updated at source | 28 September 2026 |
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