Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929333245837312 |
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| author | Hagiwara, Ryo Takabe, Satoshi |
| author_facet | Hagiwara, Ryo Takabe, Satoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding Hagiwara, Ryo Takabe, Satoshi Disordered Systems and Neural Networks Machine Learning 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. |
| title | Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding |
| topic | Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2402.13608 |