Quality-Diversity Optimization as Multi-Objective Optimization

2026-01-31

AI Summary

This work rigorously formalizes the quality-diversity (QD) optimization problem as a high-dimensional multi-objective optimization (MOO) problem, establishing the first theoretical connection between QD and MOO. By integrating set-based scalarization techniques with a cooperative search mechanism, the proposed approach simultaneously optimizes solution performance and diversity within a user-defined behavior space. The framework inherits the theoretical guarantees of MOO, offering a general-purpose paradigm for QD optimization. Experimental results demonstrate that the method achieves performance comparable to state-of-the-art QD algorithms across multiple benchmark tasks, confirming its effectiveness and competitiveness.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Quality-Diversity
• Multi-Objective Optimization
• Behavior Space
• Diverse Solutions
• Optimization

Innovation

• Quality-Diversity Optimization
• Multi-Objective Optimization
• Set-based Scalarization
• Behavior Space
• Collaborative Search