# Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

Source: [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](<https://www.sota2.com/research/paper/68fa73671e209131cea5c3d1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T06:34:03.782Z

Authors: Haoyang Zheng, Hengrong Du, Qi Feng, Wei Deng, Guang Lin

Published: 2024-05-13T15:25:03.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2405.07839>)

[PDF](<https://arxiv.org/pdf/2405.07839.pdf>)