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.

翻译：从约束分布中采样具有广泛的应用，包括贝叶斯优化和机器人学。已有工作建立了约束采样的收敛性和可行性保证，但假设可行集是连通的。然而在实践中，可行集往往分解为多个不连通的分量，这使得约束下的高效采样极具挑战。本文提出基于熵最大化的流形采样（MASEM）方法，用于在由光滑等式和不等式约束隐式定义的、具有未知数量不连通分量的流形上进行采样。该方法采用重采样方案，基于k近邻密度估计最大化经验分布的熵。我们证明，在场平均意义上，MASEM能使经验分布与最大熵目标之间的KL散度随重采样步数呈指数级下降。我们通过多个局部采样器实例化MASEM，并在合成基准和机器人学基准上验证了其通用性和高效性。MASEM能在一系列约束采样问题中实现快速且可扩展的混合，在Sinkhorn距离上相比替代方法提升一个数量级，同时保持具有竞争力的运行时间。