Quality-Diversity Optimization as Multi-Objective Optimization

TL;DR

This paper reformulates Quality-Diversity optimization as a multi-objective optimization problem, enabling the use of established MOO methods to improve solution diversity and quality across various applications.

Contribution

It introduces a novel perspective by casting QD as a large-scale MOO problem, allowing direct application of MOO techniques and providing theoretical guarantees.

Findings

Achieves performance comparable to state-of-the-art QD algorithms

Enables application of well-established MOO methods to QD problems

Provides theoretical analysis with inherited guarantees

Abstract

The Quality-Diversity (QD) optimization aims to discover a collection of high-performing solutions that simultaneously exhibit diverse behaviors within a user-defined behavior space. This paradigm has stimulated significant research interest and demonstrated practical utility in domains including robot control, creative design, and adversarial sample generation. A variety of QD algorithms with distinct design principles have been proposed in recent years. Instead of proposing a new QD algorithm, this work introduces a novel reformulation by casting the QD optimization as a multi-objective optimization (MOO) problem with a huge number of optimization objectives. By establishing this connection, we enable the direct adoption of well-established MOO methods, particularly set-based scalarization techniques, to solve QD problems through a collaborative search process. We further provide a theoretical analysis demonstrating that our approach inherits theoretical guarantees from MOO while providing desirable properties for the QD optimization. Experimental studies across several QD applications confirm that our method achieves performance competitive with state-of-the-art QD algorithms.