# Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance

arXiv: https://arxiv.org/abs/2305.20057 · HTML: https://mlsanity.com/paper/2305.20057/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 54 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 30)

- [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)
- [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)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)
- [In Defense of the Unitary Scalarization for Deep Multi-Task Learning](https://mlsanity.com/paper/2201.04122/) (2022)
- [A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Tasks](https://mlsanity.com/paper/1611.01587/) (2016)
- [Do Current Multi-Task Optimization Methods in Deep Learning Even Help?](https://mlsanity.com/paper/2209.11379/) (2022)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning](https://mlsanity.com/paper/1907.04472/) (2019)
- [Multi-Objective Meta Learning](https://mlsanity.com/paper/2102.07121/) (2021)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [Stability & Generalisation of Gradient Descent for Shallow Neural Networks without the Neural Tangent Kernel](https://mlsanity.com/paper/2107.12723/) (2021)
- [LibMTL: A Python Library for Multi-Task Learning](https://mlsanity.com/paper/2203.14338/) (2022)
- [Stability and Generalization of Stochastic Optimization with Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/2206.07082/) (2022)
- [Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks](https://mlsanity.com/paper/2209.09298/) (2022)
- [Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approach](https://mlsanity.com/paper/2210.12624/) (2022)
- [Multi-objective Optimization by Learning Space Partitions](https://mlsanity.com/paper/2110.03173/) (2021)
- [Generalization In Multi-Objective Machine Learning](https://mlsanity.com/paper/2208.13499/) (2022)

## Built on by (most cited first, 30 of 36)

- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Jacobian Descent for Multi-Objective Optimization](https://mlsanity.com/paper/2406.16232/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization](https://mlsanity.com/paper/2405.19650/) (2024)
- [Traversing Pareto Optimal Policies: Provably Efficient Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2407.17466/) (2024)
- [FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning](https://mlsanity.com/paper/2412.01773/) (2024)
- [MGDA Converges under Generalized Smoothness, Provably](https://mlsanity.com/paper/2405.19440/) (2024)
- [Towards Exact Gradient-based Training on Analog In-memory Computing](https://mlsanity.com/paper/2406.12774/) (2024)
- [LDC-MTL: Balancing Multi-Task Learning through Scalable Loss Discrepancy Control](https://mlsanity.com/paper/2502.08585/) (2025)
- [Controllable Unlearning for Image-to-Image Generative Models via varepsilon-Constrained Optimization](https://mlsanity.com/paper/2408.01689/) (2024)
- [How to Find the Exact Pareto Front for Multi-Objective MDPs?](https://mlsanity.com/paper/2410.15557/) (2024)
- [Balanced Rate-Distortion Optimization in Learned Image Compression](https://mlsanity.com/paper/2502.20161/) (2025)
- [SANet: A Semantic-aware Agentic AI Networking Framework for Cross-layer Optimization in 6G](https://mlsanity.com/paper/2512.22579/) (2025)
- [Adaptive Online Mirror Descent for Tchebycheff Scalarization in Multi-Objective Learning](https://mlsanity.com/paper/2410.21764/) (2024)
- [Federated Communication-Efficient Multi-Objective Optimization](https://mlsanity.com/paper/2410.16398/) (2024)
- [SANNet: A Semantic-Aware Agentic AI Networking Framework for Multi-Agent Cross-Layer Coordination](https://mlsanity.com/paper/2505.18946/) (2025)
- [MultiBalance: Multi-Objective Gradient Balancing in Industrial-Scale Multi-Task Recommendation System](https://mlsanity.com/paper/2411.11871/) (2024)
- [AutoScale: Linear Scalarization Guided by Multi-Task Optimization Metrics](https://mlsanity.com/paper/2508.13979/) (2025)
- [Uncovering Cross-Objective Interference in Multi-Objective Alignment](https://mlsanity.com/paper/2602.06869/) (2026)
- [Exploring Accuracy-Fairness Trade-off in Large Language Models](https://mlsanity.com/paper/2411.14500/) (2024)
- [Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity](https://mlsanity.com/paper/2506.09438/) (2025)
- [Unified Optimization of Source Weights and Transfer Quantities in Multi-Source Transfer Learning: An Asymptotic Framework](https://mlsanity.com/paper/2601.10779/) (2026)
- [Stochastic Gradient Descent with Momentum is Algorithmically Stable](https://mlsanity.com/paper/2605.28517/) (2026)
- [End-to-End Fairness Optimization with Fair Decision-Focused Learning](https://mlsanity.com/paper/2607.29441/) (2026)
- [Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization](https://mlsanity.com/paper/2504.02833/) (2025)
- [Objective Soups: Multilingual Multi-Task Modeling for Speech Processing](https://mlsanity.com/paper/2508.09228/) (2025)
- [Stability and Generalization of Stochastic Nonconvex Optimization under Heavy-Tailed Noise: From Gradient Norm to Goldstein Stationarity](https://mlsanity.com/paper/2601.19730/) (2026)
- [Feed m Birds with One Scone: Accelerating Multi-task Gradient Balancing via Bi-level Optimization](https://mlsanity.com/paper/2603.07389/) (2026)

## Abstract (arXiv)

Multi-objective learning (MOL) problems often arise in emerging machine learning problems when there are multiple learning criteria, data modalities, or learning tasks. Different from single-objective learning, one of the critical challenges in MOL is the potential conflict among different objectives during the iterative optimization process. Recent works have developed various dynamic weighting algorithms for MOL such as MGDA and its variants, where the central idea is to find an update direction that avoids conflicts among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not always outperform static ones. To understand this theory-practical gap, we focus on a new stochastic variant of MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm, and study the generalization performance of the dynamic weighting-based MoDo and its interplay with optimization through the lens of algorithm stability. Perhaps surprisingly, we find that the key rationale behind MGDA -- updating along conflict-avoidant direction - may hinder dynamic weighting algorithms from achieving the optimal cal O(1/√n) population risk, where n is the number of training samples. We further demonstrate the impact of the variability of dynamic weights on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL. We showcase the generality of our theoretical framework by analyzing other existing stochastic MOL algorithms under the framework. Experiments on various multi-task learning benchmarks are performed to demonstrate the practical applicability. Code is available at https://github.com/heshandevaka/Trade-Off-MOL.