Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. We present a new optimization-based method for sampling called mollified interaction energy descent (MIED), that minimizes an energy on probability measures called mollified interaction energie (MIE). The latter converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence, as the mollifiers approach Dirac deltas. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show the performance of our algorithm on both unconstrained and constrained sampling in comparison to state-of-the-art alternatives.
Paul Pegon
