Stochastic Multiple Target Sampling Gradient Descent

TL;DR

This paper introduces MT-SGD, a novel stochastic gradient method that efficiently samples from multiple unnormalized distributions by flowing through intermediate distributions, extending the principles of SVGD to multi-objective scenarios.

Contribution

It proposes a new stochastic gradient algorithm for multi-target sampling, connecting multi-objective optimization with probabilistic sampling methods.

Findings

MT-SGD effectively samples from multiple distributions.

The method converges to a joint high-likelihood region.

Experimental results show improvements in multi-task learning.

Abstract

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of particles to approximate the distribution of interest. Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem. A natural question then arises: "Can we derive a probabilistic version of the multi-objective optimization?". To answer this question, we propose Stochastic Multiple Target Sampling Gradient Descent (MT-SGD), enabling us to sample from multiple unnormalized target distributions. Specifically, our MT-SGD conducts a flow of intermediate distributions gradually orienting to multiple target distributions, which allows the sampled particles to move to the joint high-likelihood region of the target distributions. Interestingly, the asymptotic analysis shows that our approach reduces exactly to the multiple-gradient descent algorithm for multi-objective optimization, as expected. Finally, we conduct comprehensive experiments to demonstrate the merit of our approach to multi-task learning.