Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

Haoyang Zheng, Hengrong Du, Qi Feng, Wei Deng, Guang Lin
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:61321-61348, 2024.

Abstract

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zheng24d, title = {Constrained Exploration via Reflected Replica Exchange Stochastic Gradient {L}angevin Dynamics}, author = {Zheng, Haoyang and Du, Hengrong and Feng, Qi and Deng, Wei and Lin, Guang}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {61321--61348}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zheng24d/zheng24d.pdf}, url = {https://proceedings.mlr.press/v235/zheng24d.html}, abstract = {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 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.} }
Endnote
%0 Conference Paper %T Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics %A Haoyang Zheng %A Hengrong Du %A Qi Feng %A Wei Deng %A Guang Lin %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zheng24d %I PMLR %P 61321--61348 %U https://proceedings.mlr.press/v235/zheng24d.html %V 235 %X 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 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.
APA
Zheng, H., Du, H., Feng, Q., Deng, W. & Lin, G.. (2024). Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:61321-61348 Available from https://proceedings.mlr.press/v235/zheng24d.html.

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