Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding
<|reference_start|>Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding: 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.<|reference_end|>
@article{hagiwara2024convergence,
    title={Convergence Acceleration of Markov Chain Monte Carlo-based Gradient
  Descent by Deep Unfolding},
    author={Ryo Hagiwara and Satoshi Takabe},
    journal={arXiv preprint arXiv:2402.13608},
    year={2024},
    doi={10.7566/JPSJ.93.063801},
    archivePrefix={arXiv},
    eprint={2402.13608},
    primaryClass={cond-mat.dis-nn cs.LG stat.ML}
}