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（QD）优化旨在寻找一组解，这些解在优化目标的同时，能实现用户指定的向量值测量函数中多样化的输出。当前的QD算法通常局限于低维测量，因为高维测量容易产生扭曲，即QD算法找到的许多解映射到相似的测量值。例如，最先进的CMA-MAE算法通过记录所谓折扣值的直方图来指导测量空间探索。然而，在高维测量空间中，CMA-MAE会陷入停滞，因为具有相似测量值的解落入同一直方图单元，从而获得相同的折扣值。为解决这些局限性，我们提出折扣模型搜索（DMS），该方法利用一个提供平滑连续折扣值表示的模型来指导探索。在高维测量空间中，该模型使DMS能够区分具有相似测量值的解，从而继续探索。通过引入两个以高维图像空间为测量空间的新领域（用户可通过提供图像数据集而非手工设计测量函数来指定所需测量值），我们证明DMS为QD算法带来了新能力。在这些领域及高维基准测试中的结果表明，DMS优于CMA-MAE及其他现有的黑箱QD算法。