Quality diversity (QD) optimization searches for a collection of solutions that optimize an objective while attaining diverse outputs of a user-specified, vector-valued measure function. Contemporary QD algorithms are typically limited to low-dimensional measures because high-dimensional measures are prone to distortion, where many solutions found by the QD algorithm map to similar measures. For example, the state-of-the-art CMA-MAE algorithm guides measure space exploration with a histogram in measure space that records so-called discount values. However, CMA-MAE stagnates in domains with high-dimensional measure spaces because solutions with similar measures fall into the same histogram cell and hence receive the same discount value. To address these limitations, we propose Discount Model Search (DMS), which guides exploration with a model that provides a smooth, continuous representation of discount values. In high-dimensional measure spaces, this model enables DMS to distinguish between solutions with similar measures and thus continue exploration. We show that DMS facilitates new capabilities for QD algorithms by introducing two new domains where the measure space is the high-dimensional space of images, which enables users to specify their desired measures by providing a dataset of images rather than hand-designing the measure function. Results in these domains and on high-dimensional benchmarks show that DMS outperforms CMA-MAE and other existing black-box QD algorithms.

翻译：质量多样性（Quality Diversity，QD）优化旨在寻找一组解，这些解在优化目标函数的同时，还能实现用户指定的向量值度量函数输出的多样性。现有的QD算法通常局限于低维度度量，因为高维度度量容易产生畸变，即QD算法找到的许多解会映射到相似的度量值。例如，当前最先进的CMA-MAE算法通过度量空间中的直方图来指导度量空间的探索，该直方图记录了所谓的折扣值。然而，在具有高维度度量空间的领域中，CMA-MAE会陷入停滞，因为具有相似度量的解会落入直方图的同一单元，从而获得相同的折扣值。为了应对这些限制，我们提出了折扣模型搜索（Discount Model Search，DMS），它通过一个模型来指导探索，该模型提供了折扣值的平滑、连续表示。在高维度度量空间中，该模型使DMS能够区分具有相似度量的解，从而持续进行探索。我们通过引入两个新领域来展示DMS为QD算法带来的新能力，在这两个领域中，度量空间是高维度的图像空间，这使得用户可以通过提供图像数据集而非手动设计度量函数来指定其期望的度量。在这些领域以及高维度基准测试上的结果表明，DMS优于CMA-MAE及其他现有的黑盒QD算法。