# Quality-Diversity Meta-Evolution: customising behaviour spaces to a meta-objective

arXiv: https://arxiv.org/abs/2109.03918 · HTML: https://mlsanity.com/paper/2109.03918/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 8 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Autonomous skill discovery with Quality-Diversity and Unsupervised Descriptors](https://mlsanity.com/paper/1905.11874/) (2019)
- [A survey of dimensionality reduction techniques](https://mlsanity.com/paper/1403.2877/) (2014)
- [Unsupervised Learning and Exploration of Reachable Outcome Space](https://mlsanity.com/paper/1909.05508/) (2019)
- [Multi-Emitter MAP-Elites: Improving quality, diversity and convergence speed with heterogeneous sets of emitters](https://mlsanity.com/paper/2007.05352/) (2020)
- [Rapidly adapting robot swarms with Swarm Map-based Bayesian Optimisation](https://mlsanity.com/paper/2012.11444/) (2020)
- [Ensemble Feature Extraction for Multi-Container Quality-Diversity Algorithms](https://mlsanity.com/paper/2105.00682/) (2021)

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

- [Improving Algorithm-Selection and Performance-Prediction via Learning Discriminating Training Samples](https://mlsanity.com/paper/2404.05359/) (2024)
- [Vector Quantized-Elites: Unsupervised and Problem-Agnostic Quality-Diversity Optimization](https://mlsanity.com/paper/2504.08057/) (2025)

## Abstract (arXiv)

Quality-Diversity (QD) algorithms evolve behaviourally diverse and high-performing solutions. To illuminate the elite solutions for a space of behaviours, QD algorithms require the definition of a suitable behaviour space. If the behaviour space is high-dimensional, a suitable dimensionality reduction technique is required to maintain a limited number of behavioural niches. While current methodologies for automated behaviour spaces focus on changing the geometry or on unsupervised learning, there remains a need for customising behavioural diversity to a particular meta-objective specified by the end-user. In the newly emerging framework of QD Meta-Evolution, or QD-Meta for short, one evolves a population of QD algorithms, each with different algorithmic and representational characteristics, to optimise the algorithms and their resulting archives to a user-defined meta-objective. Despite promising results compared to traditional QD algorithms, QD-Meta has yet to be compared to state-of-the-art behaviour space automation methods such as Centroidal Voronoi Tessellations Multi-dimensional Archive of Phenotypic Elites Algorithm (CVT-MAP-Elites) and Autonomous Robots Realising their Abilities (AURORA). This paper performs an empirical study of QD-Meta on function optimisation and multilegged robot locomotion benchmarks. Results demonstrate that QD-Meta archives provide improved average performance and faster adaptation to a priori unknown changes to the environment when compared to CVT-MAP-Elites and AURORA. A qualitative analysis shows how the resulting archives are tailored to the meta-objectives provided by the end-user.