The Geometry of Efficient Nonconvex Sampling

Abstract

We present an efficient algorithm for uniformly sampling from an arbitrary compact body X R^n from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincaré constant of the uniform distribution on X and the volume growth constant of the set X.

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