Learning Rate Free Sampling in Constrained Domains
This work addresses the practical challenge of hyperparameter tuning in constrained sampling problems for applications like fairness constraints and post-selection inference, though it appears incremental as it builds on existing methods.
The authors tackled the problem of sampling in constrained domains without requiring learning rate tuning by introducing particle-based algorithms based on coin betting ideas and a mirrored optimization framework. Their results show competitive performance with existing constrained sampling methods across various numerical examples while eliminating hyperparameter tuning.
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.