Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909215280332800 |
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| author | Zheng, Haoyang Du, Hengrong Feng, Qi Deng, Wei Lin, Guang |
| author_facet | Zheng, Haoyang Du, Hengrong Feng, Qi Deng, Wei Lin, Guang |
| contents | Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a $\textit{quadratic}$ behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics Zheng, Haoyang Du, Hengrong Feng, Qi Deng, Wei Lin, Guang Machine Learning Artificial Intelligence Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a $\textit{quadratic}$ behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency. |
| title | Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2405.07839 |