Differentiable Quality Diversity with Cross-Task Collaborative Discovery

Quality-Diversity (QD) optimization aims to discover collections of high-performing solutions with diverse behaviors. In many applications, however, multiple related QD tasks may need to be solved due to different execution environments. Existing methods typically optimize such multiple tasks independently, without explicitly coordinating their search processes, which can lead to repeated exploration of related regions and redundant rediscovery of useful solutions. In this paper, we propose Multitask Differentiable Quality-Diversity with Cross-Task Collaborative Discovery (MTQD-CoD), which jointly optimizes multiple related QD tasks through cross-task collaboration. Specifically, a subspace-projected repulsion mechanism encourages task-specific searchers to explore less-overlapping regions, while an inter-task transfer probability adaptation mechanism adjusts cross-task transfer probabilities according to the observed archive contributions of transferred candidates, thereby regulating how strongly discoveries are shared across tasks. By reducing redundant exploration while reusing transferable discoveries, MTQD-CoD creates more opportunities to explore undercovered behavioral regions and identify additional high-quality solutions. Experiments on arm repertoire, latent-space illumination, and policy optimization problems demonstrate the effectiveness of MTQD-CoD in discovering diverse and high-quality solutions across multiple related QD tasks.