# Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization

arXiv: https://arxiv.org/abs/2405.19650 · HTML: https://mlsanity.com/paper/2405.19650/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 75 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 31)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Efficiently Identifying Task Groupings for Multi-Task Learning](https://mlsanity.com/paper/2109.04617/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [GCN-RL Circuit Designer: Transferable Transistor Sizing with Graph Neural Networks and Reinforcement Learning](https://mlsanity.com/paper/2005.00406/) (2020)
- [FAMO: Fast Adaptive Multitask Optimization](https://mlsanity.com/paper/2306.03792/) (2023)
- [Auto-Lambda: Disentangling Dynamic Task Relationships](https://mlsanity.com/paper/2202.03091/) (2022)
- [Independent Component Alignment for Multi-Task Learning](https://mlsanity.com/paper/2305.19000/) (2023)
- [In Defense of the Unitary Scalarization for Deep Multi-Task Learning](https://mlsanity.com/paper/2201.04122/) (2022)
- [Do Current Multi-Task Optimization Methods in Deep Learning Even Help?](https://mlsanity.com/paper/2209.11379/) (2022)
- [Efficient Continuous Pareto Exploration in Multi-Task Learning](https://mlsanity.com/paper/2006.16434/) (2020)
- [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)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning](https://mlsanity.com/paper/1907.04472/) (2019)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [On Graduated Optimization for Stochastic Non-Convex Problems](https://mlsanity.com/paper/1503.03712/) (2015)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [Robust Multi-Task Learning with Excess Risks](https://mlsanity.com/paper/2402.02009/) (2024)
- [Scalarization for Multi-Task and Multi-Domain Learning at Scale](https://mlsanity.com/paper/2310.08910/) (2023)
- [Many-Objective Multi-Solution Transport](https://mlsanity.com/paper/2403.04099/) (2024)

## Built on by (most cited first, 16 of 16)

- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Balanced Rate-Distortion Optimization in Learned Image Compression](https://mlsanity.com/paper/2502.20161/) (2025)
- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [Federated Communication-Efficient Multi-Objective Optimization](https://mlsanity.com/paper/2410.16398/) (2024)
- [UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment](https://mlsanity.com/paper/2602.09538/) (2026)
- [FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimization](https://mlsanity.com/paper/2509.03244/) (2025)
- [Few-for-Many Personalized Federated Learning](https://mlsanity.com/paper/2603.11992/) (2026)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [MOS-Attack: A Scalable Multi-objective Adversarial Attack Framework](https://mlsanity.com/paper/2501.07251/) (2025)
- [Covering Multiple Objectives with a Small Set of Solutions Using Bayesian Optimization](https://mlsanity.com/paper/2501.19342/) (2025)
- [A study of EHVI vs fixed scalarization for molecule design](https://mlsanity.com/paper/2507.13704/) (2025)
- [Enabling Pareto-Stationarity Exploration in Multi-Objective Reinforcement Learning: A Multi-Objective Weighted-Chebyshev Actor-Critic Approach](https://mlsanity.com/paper/2507.21397/) (2025)
- [Quality-Diversity Optimization as Multi-Objective Optimization](https://mlsanity.com/paper/2602.00478/) (2026)
- [Adaptive Smooth Tchebycheff Attention for Multi-Objective Policy Optimization](https://mlsanity.com/paper/2605.12771/) (2026)
- [Multi-Objective Exploration and Preference Optimization via Mutual Information](https://mlsanity.com/paper/2607.01392/) (2026)
- [Few-for-Many Best-Arm Identification in Multi-Objective Bandits](https://mlsanity.com/paper/2610.16840/) (2026)

## Abstract (arXiv)

Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., >100) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.