Learning Rate Free Sampling in Constrained Domains

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Abstract

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.

Citation

Sharrock, L., Mackey, L. and Nemeth, C. (2023). Learning Rate Free Sampling in Constrained Domains. Advances in Neural Information Processing Systems (NeurIPS). Vol. 36, p. 65380-65415.

@article{sharrock2023learning,
  title={Learning rate free sampling in constrained domains},
  author={Sharrock, Louis and Mackey, Lester and Nemeth, Christopher},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  pages={65380--65415},
  year={2023}
}