# Scalable Pareto Front Approximation for Deep Multi-Objective Learning

arXiv: https://arxiv.org/abs/2103.13392 · HTML: https://mlsanity.com/paper/2103.13392/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 24 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [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)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution](https://mlsanity.com/paper/1804.09081/) (2018)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Efficient Continuous Pareto Exploration in Multi-Task Learning](https://mlsanity.com/paper/2006.16434/) (2020)
- [Controllable Pareto Multi-Task Learning](https://mlsanity.com/paper/2010.06313/) (2020)
- [Addressing Fairness in Classification with a Model-Agnostic Multi-Objective Algorithm](https://mlsanity.com/paper/2009.04441/) (2020)

## Built on by (most cited first, 30 of 45)

- [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)
- [Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task models](https://mlsanity.com/paper/2210.09759/) (2022)
- [Debiasing Methods for Fairer Neural Models in Vision and Language Research: A Survey](https://mlsanity.com/paper/2211.05617/) (2022)
- [MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation](https://mlsanity.com/paper/2406.07529/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Improving Pareto Front Learning via Multi-Sample Hypernetworks](https://mlsanity.com/paper/2212.01130/) (2022)
- [Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferences](https://mlsanity.com/paper/2407.08056/) (2024)
- [A Survey of Controllable Learning: Methods and Applications in Information Retrieval](https://mlsanity.com/paper/2407.06083/) (2024)
- [PMGDA: A Preference-based Multiple Gradient Descent Algorithm](https://mlsanity.com/paper/2402.09492/) (2024)
- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)
- [Efficient Pareto Manifold Learning with Low-Rank Structure](https://mlsanity.com/paper/2407.20734/) (2024)
- [Reasoning BO: Enhancing Bayesian Optimization with Long-Context Reasoning Power of LLMs](https://mlsanity.com/paper/2505.12833/) (2025)
- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)
- [Multi-Objective Optimization for Sparse Deep Multi-Task Learning](https://mlsanity.com/paper/2308.12243/) (2023)
- [Risk-Controlling Model Selection via Guided Bayesian Optimization](https://mlsanity.com/paper/2312.01692/) (2023)
- [COS-DPO: Conditioned One-Shot Multi-Objective Fine-Tuning Framework](https://mlsanity.com/paper/2410.08316/) (2024)
- [Towards Fairness-Aware Multi-Objective Optimization](https://mlsanity.com/paper/2207.12138/) (2022)
- [Generalization In Multi-Objective Machine Learning](https://mlsanity.com/paper/2208.13499/) (2022)
- [Evolutionary Preference Sampling for Pareto Set Learning](https://mlsanity.com/paper/2404.08414/) (2024)
- [Multi-task problems are not multi-objective](https://mlsanity.com/paper/2110.07301/) (2021)
- [Bi-level Multi-objective Evolutionary Learning: A Case Study on Multi-task Graph Neural Topology Search](https://mlsanity.com/paper/2302.02565/) (2023)
- [A multiobjective continuation method to compute the regularization path of deep neural networks](https://mlsanity.com/paper/2308.12044/) (2023)
- [Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow](https://mlsanity.com/paper/2311.13159/) (2023)
- [Multi-Task Learning with Multi-Task Optimization](https://mlsanity.com/paper/2403.16162/) (2024)
- [Pareto Front Approximation for Multi-Objective Session-Based Recommender Systems](https://mlsanity.com/paper/2407.16828/) (2024)
- [Federated Communication-Efficient Multi-Objective Optimization](https://mlsanity.com/paper/2410.16398/) (2024)
- [Common pitfalls to avoid while using multiobjective optimization in machine learning](https://mlsanity.com/paper/2405.01480/) (2024)
- [Preference-Optimized Pareto Set Learning for Blackbox Optimization](https://mlsanity.com/paper/2408.09976/) (2024)

## Abstract (arXiv)

Multi-objective optimization (MOO) is a prevalent challenge for Deep Learning, however, there exists no scalable MOO solution for truly deep neural networks. Prior work either demand optimizing a new network for every point on the Pareto front, or induce a large overhead to the number of trainable parameters by using hyper-networks conditioned on modifiable preferences. In this paper, we propose to condition the network directly on these preferences by augmenting them to the feature space. Furthermore, we ensure a well-spread Pareto front by penalizing the solutions to maintain a small angle to the preference vector. In a series of experiments, we demonstrate that our Pareto fronts achieve state-of-the-art quality despite being computed significantly faster. Furthermore, we showcase the scalability as our method approximates the full Pareto front on the CelebA dataset with an EfficientNet network at a tiny training time overhead of 7% compared to a simple single-objective optimization. We make our code publicly available at https://github.com/ruchtem/cosmos.