Multi-Objective Quality-Diversity in Unstructured and Unbounded Spaces

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.