Learning Rate Free Sampling in Constrained Domains
Louis Sharrock, Lester Mackey, Christopher Nemeth
Abstract
We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling as a mirrored optimisation problem on the space of probability measures. Based on this viewpoint, we also introduce a unifying framework for several existing constrained sampling algorithms, including mirrored Langevin dynamics and mirrored Stein variational gradient descent. We demonstrate the performance of our algorithms on a range of numerical examples, including sampling from targets on the simplex, sampling with fairness constraints, and constrained sampling problems in post-selection inference. Our results indicate that our algorithms achieve competitive performance with existing constrained sampling methods, without the need to tune any hyperparameters.
BibTeX
@inproceedings{
sharrock2023learning,
title={Learning Rate Free Bayesian Inference in Constrained Domains},
author={Louis Sharrock and Lester Mackey and Christopher Nemeth},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=TNAGFUcSP7}
}