Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems

• URL: http://arxiv.org/abs/2203.10215v3
• Date: Tue, 13 Aug 2024 20:33:53 GMT
• Title: Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems
• Authors: Kanji Sato, Akiko Takeda, Reiichiro Kawai, Taiji Suzuki,
• Abstract summary: Gradient Langevin dynamics and its variants have attracted increasing attention to their convergence towards the global optimal solution, initially in the global equation. In this paper we present a new type of convex constrained non-constrained boundary problem.
• Score: 38.544941658428534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex constrained non-convex problems. In the present work, we extend those frameworks to non-convex problems on a non-convex feasible region with a global optimization algorithm built upon reflected gradient Langevin dynamics and derive its convergence rates. By effectively making use of its reflection at the boundary in combination with the probabilistic representation for the Poisson equation with the Neumann boundary condition, we present promising convergence rates, particularly faster than the existing one for convex constrained non-convex problems.

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