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

arXiv: https://arxiv.org/abs/2506.06715 · HTML: https://mlsanity.com/paper/2506.06715/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Beyond One-Preference-Fits-All Alignment: Multi-Objective Direct Preference Optimization](https://mlsanity.com/paper/2310.03708/) (2023)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [MFTCoder: Boosting Code LLMs with Multitask Fine-Tuning](https://mlsanity.com/paper/2311.02303/) (2023)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Multi-Gradient Descent for Multi-Objective Recommender Systems](https://mlsanity.com/paper/2001.00846/) (2019)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization](https://mlsanity.com/paper/2102.04523/) (2021)
- [Improving Pareto Front Learning via Multi-Sample Hypernetworks](https://mlsanity.com/paper/2212.01130/) (2022)
- [A Framework for Controllable Pareto Front Learning with Completed Scalarization Functions and its Applications](https://mlsanity.com/paper/2302.12487/) (2023)
- [Stein Variational Gradient Descent with Multiple Kernel](https://mlsanity.com/paper/2107.09338/) (2021)
- [Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks](https://mlsanity.com/paper/2412.17312/) (2024)
- [Preference-Optimized Pareto Set Learning for Blackbox Optimization](https://mlsanity.com/paper/2408.09976/) (2024)
- [High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspaces](https://mlsanity.com/paper/2412.16554/) (2024)

## Built on by (most cited first, 1 of 1)

- [Universal Hypernetworks for Arbitrary Models](https://mlsanity.com/paper/2604.02215/) (2026)

## Abstract (arXiv)

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.