Monte Carlo with Soft Constraints: the Surface Augmented Sampler

TL;DR

This paper introduces a novel MCMC sampling method for distributions with soft constraints, combining soft and hard distribution sampling to improve performance near constraint boundaries.

Contribution

It proposes a new surface augmented sampler that effectively handles soft constraints, maintaining performance as constraints become nearly hard.

Findings

Performance remains uniform as constraints approach hard limits

The method successfully samples target soft distributions

Computational experiments confirm robustness of the approach

Abstract

We describe an MCMC method for sampling distributions with soft constraints, which are constraints that are almost but not exactly satisfied. We sample a total distribution that is a convex combination of the target soft distribution with the nearby hard distribution supported on the constraint surface. Hard distribution moves lead to performance that is uniform in the softness parameter. On and Off moves related to the Holmes-Cerfon Stratification Sampler enable sampling the target soft distribution. Computational experiments verify that performance is uniform in the soft constraints limit.