NLP Sampling: Combining MCMC and NLP Methods for Diverse Constrained Sampling
This work addresses a core sampling problem for researchers in fields like robotics and optimization, but appears to be an incremental integration of existing methods rather than a breakthrough.
The paper tackles the challenge of generating diverse samples under hard constraints by proposing NLP Sampling as a general problem formulation and a family of restarting two-phase methods that integrate techniques from MCMC, constrained optimization, and robotics. It evaluates these methods on analytical and robotic manipulation planning problems, though no concrete numerical results are provided in the 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.