Constrained Sampling

Constrained sampling focuses on efficiently generating random samples from a probability distribution while adhering to specified constraints. Current research emphasizes developing novel algorithms, including Langevin dynamics variants, diffusion models, and particle-based methods, often incorporating proximal frameworks or penalty functions to handle constraints effectively. These advancements improve the efficiency and accuracy of sampling in various applications, such as optimization problems with unknown constraints, Bayesian inference, and robotics motion planning, where traditional methods struggle with high-dimensional or complex constraint manifolds. The development of learning-rate-free algorithms and improved convergence guarantees are key areas of ongoing investigation.