Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding

Author:

Ryo Hagiwara, Satoshi Takabe

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Machine Learning (cs.LG), Machine Learning (stat.ML)

journal:

date:

2024-02-21 00:00:00

Abstract

This study proposes a trainable sampling-based solver for combinatorial optimization problems (COPs) using a deep-learning technique called deep unfolding. The proposed solver is based on the Ohzeki method that combines Markov-chain Monte-Carlo (MCMC) and gradient descent, and its step sizes are trained by minimizing a loss function. In the training process, we propose a sampling-based gradient estimation that substitutes auto-differentiation with a variance estimation, thereby circumventing the failure of back propagation due to the non-differentiability of MCMC. The numerical results for a few COPs demonstrated that the proposed solver significantly accelerated the convergence speed compared with the original Ohzeki method.

PDF: Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding.pdf