Quality-Diversity Algorithms Can Provably Be Helpful for Optimization

Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have found many successful applications in reinforcement learning and robotics, helping improve the robustness in complex environments. Furthermore, they often empirically find a better overall solution than traditional search algorithms which explicitly search for a single highest-performing solution. However, their theoretical analysis is far behind, leaving many fundamental questions unexplored. In this paper, we try to shed some light on the optimization ability of QD algorithms via rigorous running time analysis. By comparing the popular QD algorithm MAP-Elites with $(\mu+1)$-EA (a typical EA focusing on finding better objective values only), we prove that on two NP-hard problem classes with wide applications, i.e., monotone approximately submodular maximization with a size constraint, and set cover, MAP-Elites can achieve the (asymptotically) optimal polynomial-time approximation ratio, while $(\mu+1)$-EA requires exponential expected time on some instances. This provides theoretical justification for that QD algorithms can be helpful for optimization, and discloses that the simultaneous search for high-performing solutions with diverse behaviors can provide stepping stones to good overall solutions and help avoid local optima.

Diversity from Human Feedback

Diversity plays a significant role in many problems, such as ensemble learning, reinforcement learning, and combinatorial optimization. How to define the diversity measure is a longstanding problem. Many methods rely on expert experience to define a proper behavior space and then obtain the diversity measure, which is, however, challenging in many scenarios. In this paper, we propose the problem of learning a behavior space from human feedback and present a general method called Diversity from Human Feedback (DivHF) to solve it. DivHF learns a behavior descriptor consistent with human preference by querying human feedback. The learned behavior descriptor can be combined with any distance measure to define a diversity measure. We demonstrate the effectiveness of DivHF by integrating it with the Quality-Diversity optimization algorithm MAP-Elites and conducting experiments on the QDax suite. The results show that DivHF learns a behavior space that aligns better with human requirements compared to direct data-driven approaches and leads to more diverse solutions under human preference. Our contributions include formulating the problem, proposing the DivHF method, and demonstrating its effectiveness through experiments.