Stochastic Multiple Target Sampling Gradient Descent

Hoang Viet Phan, Ngoc N. Tran, Trung Le, Toan Tran, Nhat Ho, Dinh Phung

Keywords: Multi objective optimization, Multi task learning, Stein Variational Gradient Descent

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.

TL;DR: We propose Stochastic Multiple Target Sampling Gradient Descent (MT-SGD), allowing us to sample the particles from the joint high-likelihood of multiple target distributions.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2206.01934/code)