# No More Tuning: Prioritized Multi-Task Learning with Lagrangian Differential Multiplier Methods

arXiv: https://arxiv.org/abs/2412.12092 · HTML: https://mlsanity.com/paper/2412.12092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 16 Dec 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks](https://mlsanity.com/paper/1312.6229/) (2013)
- [UberNet: Training a `Universal' Convolutional Neural Network for Low-, Mid-, and High-Level Vision using Diverse Datasets and Limited Memory](https://mlsanity.com/paper/1609.02132/) (2016)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [DSelect-k: Differentiable Selection in the Mixture of Experts with Applications to Multi-Task Learning](https://mlsanity.com/paper/2106.03760/) (2021)
- [RotoGrad: Gradient Homogenization in Multitask Learning](https://mlsanity.com/paper/2103.02631/) (2021)
- [Tenrec: A Large-scale Multipurpose Benchmark Dataset for Recommender Systems](https://mlsanity.com/paper/2210.10629/) (2022)
- [Multi-Task Deep Recommender Systems: A Survey](https://mlsanity.com/paper/2302.03525/) (2023)
- [STEM: Unleashing the Power of Embeddings for Multi-task Recommendation](https://mlsanity.com/paper/2308.13537/) (2023)
- [Multi-Label Learning to Rank through Multi-Objective Optimization](https://mlsanity.com/paper/2207.03060/) (2022)
- [Multi-objective Learning to Rank by Model Distillation](https://mlsanity.com/paper/2407.07181/) (2024)
- [An Efficient Combinatorial Optimization Model Using Learning-to-Rank Distillation](https://mlsanity.com/paper/2201.00695/) (2021)

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

- [The Double Dilemma in Multi-Task Radiology Report Generation: A Gradient Dynamics Analysis and Solution](https://mlsanity.com/paper/2605.22635/) (2026)

## Abstract (arXiv)

Given the ubiquity of multi-task in practical systems, Multi-Task Learning (MTL) has found widespread application across diverse domains. In real-world scenarios, these tasks often have different priorities. For instance, In web search, relevance is often prioritized over other metrics, such as click-through rates or user engagement. Existing frameworks pay insufficient attention to the prioritization among different tasks, which typically adjust task-specific loss function weights to differentiate task priorities. However, this approach encounters challenges as the number of tasks grows, leading to exponential increases in hyper-parameter tuning complexity. Furthermore, the simultaneous optimization of multiple objectives can negatively impact the performance of high-priority tasks due to interference from lower-priority tasks. In this paper, we introduce a novel multi-task learning framework employing Lagrangian Differential Multiplier Methods for step-wise multi-task optimization. It is designed to boost the performance of high-priority tasks without interference from other tasks. Its primary advantage lies in its ability to automatically optimize multiple objectives without requiring balancing hyper-parameters for different tasks, thereby eliminating the need for manual tuning. Additionally, we provide theoretical analysis demonstrating that our method ensures optimization guarantees, enhancing the reliability of the process. We demonstrate its effectiveness through experiments on multiple public datasets and its application in Taobao search, a large-scale industrial search ranking system, resulting in significant improvements across various business metrics.