Quality-Diversity optimisation (QD) has proven to yield promising results across a broad set of applications. However, QD approaches struggle in the presence of uncertainty in the environment, as it impacts their ability to quantify the true performance and novelty of solutions. This problem has been highlighted multiple times independently in previous literature. In this work, we propose to uniformise the view on this problem through four main contributions. First, we formalise a common framework for uncertain domains: the Uncertain QD setting, a special case of QD in which fitness and descriptors for each solution are no longer fixed values but distribution over possible values. Second, we propose a new methodology to evaluate Uncertain QD approaches, relying on a new per-generation sampling budget and a set of existing and new metrics specifically designed for Uncertain QD. Third, we propose three new Uncertain QD algorithms: Archive-sampling, Parallel-Adaptive-sampling and Deep-Grid-sampling. We propose these approaches taking into account recent advances in the QD community toward the use of hardware acceleration that enable large numbers of parallel evaluations and make sampling an affordable approach to uncertainty. Our final and fourth contribution is to use this new framework and the associated comparison methods to benchmark existing and novel approaches. We demonstrate once again the limitation of MAP-Elites in uncertain domains and highlight the performance of the existing Deep-Grid approach, and of our new algorithms. The goal of this framework and methods is to become an instrumental benchmark for future works considering Uncertain QD.

翻译：质量-多样性优化（QD）已在广泛应用中展现出显著潜力。然而，在面对环境不确定性时，QD方法难以准确量化解决方案的真实性能与新颖性，这一问题在既往文献中已被多次独立强调。本文通过四项主要贡献统一对该问题的认知：首先，我们形式化了不确定性领域的通用框架——不确定QD设定，该框架是QD的特例，其中每个解决方案的适应度与描述符不再是固定值，而是可能取值的分布。其次，我们提出一种基于新定义的逐代采样预算及专为不确定QD设计的现有与新指标的不确定QD方法评估新体系。第三，我们提出三种新型不确定QD算法：存档采样、并行自适应采样与深度网格采样。这些算法充分考虑了QD社区近期在硬件加速方面的进展，使其能支持大规模并行评估，从而将采样转化为应对不确定性的可行方案。第四项且最终贡献是，利用该新框架及其配套比较方法对现有及新型方法进行基准测试。我们再次证实MAP-Elites在不确定领域中的局限性，并凸显现有深度网格方法及我们新算法的性能优势。该框架与方法的核心理念在于成为未来不确定QD研究的标准化基准。