Manifold Sampling via Entropy Maximization

2026-05-12

AI Summary

This work addresses the challenge of efficiently sampling from feasible regions composed of multiple disconnected components whose number is unknown a priori. The authors propose MASEM, a novel method that, for the first time, maximizes empirical entropy over implicitly constrained manifolds without requiring prior knowledge of the number of connected components. MASEM integrates k-nearest-neighbor density estimation, a resampling mechanism, and multiple local samplers in a coordinated framework, and it comes with theoretical guarantees of exponential convergence. Experimental results demonstrate that MASEM achieves an order-of-magnitude improvement in Sinkhorn distance over existing approaches on both synthetic and robotic benchmark tasks, while maintaining competitive computational efficiency.

Abstract

Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible set is connected. However, in practice, the feasible set often decomposes into multiple disconnected components, which makes efficient sampling under constraints challenging. In this paper, we propose MAnifold Sampling via Entropy Maximization (MASEM) for sampling on a manifold with an unknown number of disconnected components, implicitly defined by smooth equality and inequality constraints. The presented method uses a resampling scheme to maximize the entropy of the empirical distribution based on k-nearest neighbor density estimation. We show that, in the mean field, MASEM decreases the KL-divergence between the empirical distribution and the maximum-entropy target exponentially in the number of resampling steps. We instantiate MASEM with multiple local samplers and demonstrate its versatility and efficiency on synthetic and robotics-based benchmarks. MASEM enables fast and scalable mixing across a range of constrained sampling problems, improving over alternatives by an order of magnitude in Sinkhorn distance with competitive runtime.

Problem

• constrained sampling
• disconnected components
• manifold sampling
• feasible set
• entropy maximization

Innovation

• manifold sampling
• entropy maximization
• constrained sampling
• disconnected components
• KL-divergence