# Learning the Pareto Front with Hypernetworks

arXiv: https://arxiv.org/abs/2010.04104 · HTML: https://mlsanity.com/paper/2010.04104/

## Key facts

- Cited by 125 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2020.

## Built on by (most cited first, 30 of 125)

- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Personalized Federated Learning using Hypernetworks](https://mlsanity.com/paper/2103.04628/) (2021)
- [Neural Architecture Search: Insights from 1000 Papers](https://mlsanity.com/paper/2301.08727/) (2023)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [C-TPT: Calibrated Test-Time Prompt Tuning for Vision-Language Models via Text Feature Dispersion](https://mlsanity.com/paper/2403.14119/) (2024)
- [Panacea: Pareto Alignment via Preference Adaptation for LLMs](https://mlsanity.com/paper/2402.02030/) (2024)
- [PD-MORL: Preference-Driven Multi-Objective Reinforcement Learning Algorithm](https://mlsanity.com/paper/2208.07914/) (2022)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [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)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [DUET: A Tuning-Free Device-Cloud Collaborative Parameters Generation Framework for Efficient Device Model Generalization](https://mlsanity.com/paper/2209.05227/) (2022)
- [Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task models](https://mlsanity.com/paper/2210.09759/) (2022)
- [Controllable Dynamic Multi-Task Architectures](https://mlsanity.com/paper/2203.14949/) (2022)
- [Label Shift Adapter for Test-Time Adaptation under Covariate and Label Shifts](https://mlsanity.com/paper/2308.08810/) (2023)
- [Pareto Domain Adaptation](https://mlsanity.com/paper/2112.04137/) (2021)
- [MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation](https://mlsanity.com/paper/2406.07529/) (2024)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve](https://mlsanity.com/paper/2212.03905/) (2022)
- [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)
- [Collaboration Equilibrium in Federated Learning](https://mlsanity.com/paper/2108.07926/) (2021)
- [Improving Pareto Front Learning via Multi-Sample Hypernetworks](https://mlsanity.com/paper/2212.01130/) (2022)
- [Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspective](https://mlsanity.com/paper/2211.13723/) (2022)
- [Stochastic Multiple Target Sampling Gradient Descent](https://mlsanity.com/paper/2206.01934/) (2022)
- [Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approach](https://mlsanity.com/paper/2210.12624/) (2022)
- [Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement](https://mlsanity.com/paper/2310.15195/) (2023)

## Abstract (arXiv)

Multi-objective optimization (MOO) problems are prevalent in machine learning. These problems have a set of optimal solutions, called the Pareto front, where each point on the front represents a different trade-off between possibly conflicting objectives. Recent MOO methods can target a specific desired ray in loss space however, most approaches still face two grave limitations: (i) A separate model has to be trained for each point on the front; and (ii) The exact trade-off must be known before the optimization process. Here, we tackle the problem of learning the entire Pareto front, with the capability of selecting a desired operating point on the front after training. We call this new setup Pareto-Front Learning (PFL). We describe an approach to PFL implemented using HyperNetworks, which we term Pareto HyperNetworks (PHNs). PHN learns the entire Pareto front simultaneously using a single hypernetwork, which receives as input a desired preference vector and returns a Pareto-optimal model whose loss vector is in the desired ray. The unified model is runtime efficient compared to training multiple models and generalizes to new operating points not used during training. We evaluate our method on a wide set of problems, from multi-task regression and classification to fairness. PHNs learn the entire Pareto front at roughly the same time as learning a single point on the front and at the same time reach a better solution set. Furthermore, we show that PHNs can scale to generate large models like ResNet18. PFL opens the door to new applications where models are selected based on preferences that are only available at run time.