# Efficient Continuous Pareto Exploration in Multi-Task Learning

arXiv: https://arxiv.org/abs/2006.16434 · HTML: https://mlsanity.com/paper/2006.16434/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 30 of 57)

- [MMPareto: Boosting Multimodal Learning with Innocent Unimodal Assistance](https://mlsanity.com/paper/2405.17730/) (2024)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Pareto Self-Supervised Training for Few-Shot Learning](https://mlsanity.com/paper/2104.07841/) (2021)
- [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)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07766/) (2022)
- [AdaTask: A Task-aware Adaptive Learning Rate Approach to Multi-task Learning](https://mlsanity.com/paper/2211.15055/) (2022)
- [Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task models](https://mlsanity.com/paper/2210.09759/) (2022)
- [Neural Thickets: Diverse Task Experts Are Dense Around Pretrained Weights](https://mlsanity.com/paper/2603.12228/) (2026)
- [Continuously Discovering Novel Strategies via Reward-Switching Policy Optimization](https://mlsanity.com/paper/2204.02246/) (2022)
- [Delving into Multi-modal Multi-task Foundation Models for Road Scene Understanding: From Learning Paradigm Perspectives](https://mlsanity.com/paper/2402.02968/) (2024)
- [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)
- [Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization](https://mlsanity.com/paper/2405.19650/) (2024)
- [Relational Multi-Task Learning: Modeling Relations between Data and Tasks](https://mlsanity.com/paper/2303.07666/) (2023)
- [Domain Generalisation via Imprecise Learning](https://mlsanity.com/paper/2404.04669/) (2024)
- [All-in-One Image Coding for Joint Human-Machine Vision with Multi-Path Aggregation](https://mlsanity.com/paper/2409.19660/) (2024)
- [Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferences](https://mlsanity.com/paper/2407.08056/) (2024)
- [Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set](https://mlsanity.com/paper/2110.08713/) (2021)
- [A Survey of Controllable Learning: Methods and Applications in Information Retrieval](https://mlsanity.com/paper/2407.06083/) (2024)
- [A Systematic Performance Analysis of Deep Perceptual Loss Networks: Breaking Transfer Learning Conventions](https://mlsanity.com/paper/2302.04032/) (2023)
- [Efficient Pareto Manifold Learning with Low-Rank Structure](https://mlsanity.com/paper/2407.20734/) (2024)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [Enhancing Domain Adaptation through Prompt Gradient Alignment](https://mlsanity.com/paper/2406.09353/) (2024)
- [Task-Adaptive Meta-Learning Framework for Advancing Spatial Generalizability](https://mlsanity.com/paper/2212.06864/) (2022)
- [When Multi-Task Learning Meets Partial Supervision: A Computer Vision Review](https://mlsanity.com/paper/2307.14382/) (2023)
- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)

## Abstract (arXiv)

Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and directly cast multi-task learning as multi-objective optimization problems, but solutions returned by existing methods are typically finite, sparse, and discrete. We present a novel, efficient method that generates locally continuous Pareto sets and Pareto fronts, which opens up the possibility of continuous analysis of Pareto optimal solutions in machine learning problems. We scale up theoretical results in multi-objective optimization to modern machine learning problems by proposing a sample-based sparse linear system, for which standard Hessian-free solvers in machine learning can be applied. We compare our method to the state-of-the-art algorithms and demonstrate its usage of analyzing local Pareto sets on various multi-task classification and regression problems. The experimental results confirm that our algorithm reveals the primary directions in local Pareto sets for trade-off balancing, finds more solutions with different trade-offs efficiently, and scales well to tasks with millions of parameters.