Learning Rate Free Sampling in Constrained Domains

Published in NeurIPS, 2023

Recommended citation: Sharrock, L., Mackey, L. and Nemeth, C. (2023). "Learning Rate Free Sampling in Constrained Domains" NeurIPS 2023.. https://openreview.net/forum?id=TNAGFUcSP7

We introduce a suite of new particle-based algorithms for sampling on 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.