# Multi-Objective Quality-Diversity in Unstructured and Unbounded Spaces

arXiv: https://arxiv.org/abs/2504.03715 · HTML: https://mlsanity.com/paper/2504.03715/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Rainbow Teaming: Open-Ended Generation of Diverse Adversarial Prompts](https://mlsanity.com/paper/2402.16822/) (2024)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Quality and Diversity Optimization: A Unifying Modular Framework](https://mlsanity.com/paper/1708.09251/) (2017)
- [Differentiable Quality Diversity](https://mlsanity.com/paper/2106.03894/) (2021)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Discovering the Elite Hypervolume by Leveraging Interspecies Correlation](https://mlsanity.com/paper/1804.03906/) (2018)
- [Mapping Hearthstone Deck Spaces through MAP-Elites with Sliding Boundaries](https://mlsanity.com/paper/1904.10656/) (2019)
- [QDax: A Library for Quality-Diversity and Population-based Algorithms with Hardware Acceleration](https://mlsanity.com/paper/2308.03665/) (2023)
- [Uncertain Quality-Diversity: Evaluation methodology and new methods for Quality-Diversity in Uncertain Domains](https://mlsanity.com/paper/2302.00463/) (2023)
- [Relevance-guided Unsupervised Discovery of Abilities with Quality-Diversity Algorithms](https://mlsanity.com/paper/2204.09828/) (2022)
- [Online Damage Recovery for Physical Robots with Hierarchical Quality-Diversity](https://mlsanity.com/paper/2210.09918/) (2022)
- [Exploring the Performance-Reproducibility Trade-off in Quality-Diversity](https://mlsanity.com/paper/2409.13315/) (2024)
- [Preference-Conditioned Gradient Variations for Multi-Objective Quality-Diversity](https://mlsanity.com/paper/2411.12433/) (2024)

## Built on by (most cited first, 2 of 2)

- [Quality-Diversity Optimization as Multi-Objective Optimization](https://mlsanity.com/paper/2602.00478/) (2026)
- [Distributional Value Estimation Without Target Networks for Robust Quality-Diversity](https://mlsanity.com/paper/2604.20381/) (2026)

## Abstract (arXiv)

Quality-Diversity algorithms are powerful tools for discovering diverse, high-performing solutions. Recently, Multi-Objective Quality-Diversity (MOQD) extends QD to problems with several objectives while preserving solution diversity. MOQD has shown promise in fields such as robotics and materials science, where finding trade-offs between competing objectives like energy efficiency and speed, or material properties is essential. However, existing methods in MOQD rely on tessellating the feature space into a grid structure, which prevents their application in domains where feature spaces are unknown or must be learned, such as complex biological systems or latent exploration tasks. In this work, we introduce Multi-Objective Unstructured Repertoire for Quality-Diversity (MOUR-QD), a MOQD algorithm designed for unstructured and unbounded feature spaces. We evaluate MOUR-QD on five robotic tasks. Importantly, we show that our method excels in tasks where features must be learned, paving the way for applying MOQD to unsupervised domains. We also demonstrate that MOUR-QD is advantageous in domains with unbounded feature spaces, outperforming existing grid-based methods. Finally, we demonstrate that MOUR-QD is competitive with established MOQD methods on existing MOQD tasks and achieves double the MOQD-score in some environments. MOUR-QD opens up new opportunities for MOQD in domains like protein design and image generation.