Reflected replica exchange Langevin Monte Carlo

This is the code repository for Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics (to appear in ICML 2024).

@article{zheng2024constrained,
  title={Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics},
  author={Zheng, Haoyang and Du, Hengrong and Feng, Qi and Deng, Wei and Lin, Guang},
  journal={International Conference on Machine Learning},
  year={2024}
}

Introduction

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.

Prerequisites

For dynamic system identification and multi-modal simulation, please refer to "env_dynamic_multimodal.yml";

For image classification, please refer to "env_image_classification.yml".

Dynamic System Identification

See

./dynamic_system

Multi-modal Simulation

See

./multimodal_simulation

Image Classification

See

./image_classification

Contact

Haoyang Zheng, Ph.D. candidate at the School of Mechanical Engineering, Purdue University

Email: zheng+528 at purdue dot edu

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