Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics
<|reference_start|>Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics: 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.<|reference_end|>
@article{zheng2024constrained,
    title={Constrained Exploration via Reflected Replica Exchange Stochastic
  Gradient Langevin Dynamics},
    author={Haoyang Zheng, Hengrong Du, Qi Feng, Wei Deng and Guang Lin},
    journal={arXiv preprint arXiv:2405.07839},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.07839},
    primaryClass={cs.LG cs.AI stat.ML}
}