Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

• URL: http://arxiv.org/abs/2405.07839v2
• Date: Mon, 3 Jun 2024 13:48:52 GMT
• Title: Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics
• Authors: Haoyang Zheng, Hengrong Du, Qi Feng, Wei Deng, Guang Lin,
• Abstract summary: ReSGLD is an effective tool for non-vinquadatic learning tasks in large-scale datasets. We explore the role of the simulation efficiency in constrained multi-modal distributions and image classification.
• Score: 10.290462113848054
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\textit{quadratic}$ 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.

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