  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.
