Magnitude theory applied to quality-diversity algorithms in abstract metric spaces

A new research direction combines magnitude theory—a mathematical tool for measuring and promoting diversity—with quality-diversity optimization, enabling algorithms to work in any abstract dissimilarity space rather than being tied to specific problem domains.

The magnitude framework#

Magnitude theory offers a formal mathematical foundation for understanding what "diversity" means and how to maximize it. By applying this theory to algorithm design, researchers can create optimization procedures that don't depend on domain-specific features or distance metrics. Instead, the approach works generically across any space where dissimilarity between solutions can be measured.

Generalizing quality-diversity algorithms#

The work demonstrates how to instantiate a generalized version of Go-Explore—a quality-diversity algorithm that balances finding high-performing solutions with maintaining diverse candidates—within this broader theoretical framework. This generalization allows the algorithm to operate in arbitrary dissimilarity spaces, making it more universally applicable.

Performance implications#

Early results suggest this generalized approach delivers competitive performance across different problem settings, indicating that grounding quality-diversity algorithms in magnitude theory may offer both theoretical rigor and practical benefits.

The research was first submitted in November 2022 and underwent several revisions through 2026. Full paper available on arXiv.