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

2025-06-07

AI Summary

In multi-objective learning, simultaneously maximizing hypervolume and maintaining diversity within the Pareto set remains a fundamental challenge. Method: This paper proposes a controllable optimization framework based on annealed Stein Variational Gradient Descent (SVGD) for Pareto Set Learning (PSL)—the first application of SVGD to PSL. It introduces a diversity-aware gradient direction strategy coupled with a temperature-annealing schedule to jointly enhance convergence, distributional diversity, and training stability. The approach integrates multi-task learning with hypernetwork-based modeling to enable efficient, shared representation learning across objectives. Contribution/Results: Evaluated on multiple standard benchmarks, the method achieves significant improvements in Pareto front coverage and hypervolume, consistently outperforming state-of-the-art approaches while ensuring robust and stable optimization.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Diversify Pareto solutions while maximizing hypervolume value
• Approximate entire Pareto set using Stein Variational Gradient Descent
• Enhance stability with annealing schedule in multi-objective optimization

Innovation

• Uses SVGD for Pareto set approximation
• Employs diverse gradient direction strategies
• Incorporates annealing schedule for stability