# LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch

arXiv: https://arxiv.org/abs/2409.02969 · HTML: https://mlsanity.com/paper/2409.02969/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 70 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 28 of 28)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [Panacea: Pareto Alignment via Preference Adaptation for LLMs](https://mlsanity.com/paper/2402.02030/) (2024)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Controllable Pareto Multi-Task Learning](https://mlsanity.com/paper/2010.06313/) (2020)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (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)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [Robust Multi-Task Learning with Excess Risks](https://mlsanity.com/paper/2402.02009/) (2024)
- [Addressing Fairness in Classification with a Model-Agnostic Multi-Objective Algorithm](https://mlsanity.com/paper/2009.04441/) (2020)
- [EvoX: A Distributed GPU-accelerated Framework for Scalable Evolutionary Computation](https://mlsanity.com/paper/2301.12457/) (2023)
- [Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization](https://mlsanity.com/paper/2102.04523/) (2021)
- [Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferences](https://mlsanity.com/paper/2407.08056/) (2024)
- [Gradient-Based Multiobjective Optimization with Uncertainties](https://mlsanity.com/paper/1612.03815/) (2016)
- [PMGDA: A Preference-based Multiple Gradient Descent Algorithm](https://mlsanity.com/paper/2402.09492/) (2024)
- [EvoTorch: Scalable Evolutionary Computation in Python](https://mlsanity.com/paper/2302.12600/) (2023)
- [Efficient Pareto Manifold Learning with Low-Rank Structure](https://mlsanity.com/paper/2407.20734/) (2024)
- [UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition](https://mlsanity.com/paper/2402.09486/) (2024)

## Built on by (most cited first, 10 of 10)

- [PARM: Multi-Objective Test-Time Alignment via Preference-Aware Autoregressive Reward Model](https://mlsanity.com/paper/2505.06274/) (2025)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraints](https://mlsanity.com/paper/2508.00830/) (2025)
- [Adaptive Online Mirror Descent for Tchebycheff Scalarization in Multi-Objective Learning](https://mlsanity.com/paper/2410.21764/) (2024)
- [UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment](https://mlsanity.com/paper/2602.09538/) (2026)
- [SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion](https://mlsanity.com/paper/2509.21058/) (2025)
- [Robust Causal Discovery under Imperfect Structural Constraints](https://mlsanity.com/paper/2511.06790/) (2025)
- [Controllable Pareto Trade-off between Fairness and Accuracy](https://mlsanity.com/paper/2509.13651/) (2025)
- [GLUE: Coordinating Pre-Trained Generative Models for System-Level Design](https://mlsanity.com/paper/2512.19469/) (2025)
- [A Unified Framework for Gradient Aggregation in Multi-Objective Optimization](https://mlsanity.com/paper/2605.30452/) (2026)

## Abstract (arXiv)

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with thousands / millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order / meta-heuristic methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with thousands / millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.