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.

翻译：在硬约束下生成多样化样本是众多领域的核心挑战。本研究旨在提供一个整合性视角与框架，以融合马尔可夫链蒙特卡洛（MCMC）、约束优化及机器人学等领域的方法，并通过实证评估深入理解其优势。我们提出将NLP采样作为一种通用问题表述形式，构建了基于重启双阶段方法的框架体系以整合跨领域技术，并在解析问题与机器人操作规划问题上进行了系统评估。作为补充，我们提供了若干概念性探讨，例如拉格朗日参数的作用机制、全局采样策略，以及扩散式非线性规划（Diffused NLP）的构想及其对应的基于模型的去噪采样器。