A Framework for Controllable Multi-objective Learning with Annealed Stein Variational Hypernetworks

Pareto Set Learning (PSL) is popular as an efficient approach to obtaining the complete optimal solution in Multi-objective Learning (MOL). A set of optimal solutions approximates the Pareto set, and its mapping is a set of dense points in the Pareto front in objective space. However, some current methods face a challenge: how to make the Pareto solution is diverse while maximizing the hypervolume value. In this paper, we propose a novel method to address this challenge, which employs Stein Variational Gradient Descent (SVGD) to approximate the entire Pareto set. SVGD pushes a set of particles towards the Pareto set by applying a form of functional gradient descent, which helps to converge and diversify optimal solutions. Additionally, we employ diverse gradient direction strategies to thoroughly investigate a unified framework for SVGD in multi-objective optimization and adapt this framework with an annealing schedule to promote stability. We introduce our method, SVH-MOL, and validate its effectiveness through extensive experiments on multi-objective problems and multi-task learning, demonstrating its superior performance.