Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization

arXiv:2012.11554v2 Announce Type: replace
Abstract: We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises widely in machine learning and statistics, with Monte-Carlo sampling, variational inference, policy optimization, and generative adversarial network as examples. For this problem, we propose a novel particle-based algorithm, dubbed as variational transport, which approximately performs Wasserstein gradient descent over the manifold of …

abstract arxiv cs.lg family form functional inference machine machine learning math.oc math.st monte-carlo optimization particle policy probability sampling statistics stat.ml stat.th transport type