NLP Sampling: Combining MCMC and NLP Methods for Diverse Constrained Sampling

TL;DR

This paper introduces NLP Sampling, a unified framework combining MCMC, constrained optimization, and robotics methods to improve diverse constrained sampling, with empirical evaluations on analytical and robotic planning problems.

Contribution

It proposes NLP Sampling as a general formulation and a family of restarting two-phase methods to integrate techniques across multiple fields.

Findings

Effective in generating diverse samples under constraints

Improves sampling efficiency in robotic manipulation planning

Provides conceptual insights into Lagrange parameters and global sampling

Abstract

Generating diverse samples under hard constraints is a core challenge in many areas. With this work we aim to provide an integrative view and framework to combine methods from the fields of MCMC, constrained optimization, as well as robotics, and gain insights in their strengths from empirical evaluations. We propose NLP Sampling as a general problem formulation, propose a family of restarting two-phase methods as a framework to integrated methods from across the fields, and evaluate them on analytical and robotic manipulation planning problems. Complementary to this, we provide several conceptual discussions, e.g. on the role of Lagrange parameters, global sampling, and the idea of a Diffused NLP and a corresponding model-based denoising sampler.