Variance Reduction in Stochastic Particle-Optimization Sampling

Jul 12, 2020

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Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently, SPOS avoids the particle-collapsing pitfall of SVGD. Nevertheless, variance reduction in SPOS has never been studied. In this paper, we bridge the gap by presenting several variance-reduction techniques for SPOS. Specifically, we propose three variants of variance-reduced SPOS, called SAGA particle-optimization sampling (SAGA-POS), SVRG particle optimization sampling (SVRG-POS) and a variant of SVRG-POS which avoids full gradient computations, denoted as SVRG-POS+. Importantly, we provide non-asymptotic convergence guarantees for these algorithms in terms of 2- Wasserstein metric and analyze their complexities. Remarkably, the results show our algorithms yield better convergence rates than existing variance reduced variants of stochastic Langevin dynamics, even though more space is required to store the particles in training. Our theory well aligns with experimental results on both synthetic and real datasets.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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