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

arXiv: https://arxiv.org/abs/2402.13608 · HTML: https://mlsanity.com/paper/2402.13608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 8 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Refined Gradient-Based Temperature Optimization for the Replica-Exchange Monte-Carlo Method](https://mlsanity.com/paper/2601.13542/) (2026)

## Abstract (arXiv)

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.