Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusion

• URL: http://arxiv.org/abs/2305.11493v1
• Date: Fri, 19 May 2023 07:49:40 GMT
• Title: Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusion
• Authors: Ryo Fujino
• Abstract summary: Langevin Dynamics has been extensively in global non- optimization experiments. Our proposed method is used to investigate the trade-off between speed and discretization error.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to utilize a more comprehensive class of stochastic processes, known as reversible diffusion, and apply the Euler-Maruyama discretization for global non-convex optimization. We design the diffusion coefficient to be larger when distant from the optimum and smaller when near, thus enabling accelerated convergence while regulating discretization error, a strategy inspired by landscape modifications. Our proposed method can also be seen as a time change of Langevin Dynamics, and we prove convergence with respect to KL divergence, investigating the trade-off between convergence speed and discretization error. The efficacy of our proposed method is demonstrated through numerical experiments.

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