Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces

2026-01-03

arXiv.org

AI Summary

This work addresses the challenge of exploration stagnation in quality-diversity (QD) optimization within high-dimensional metric spaces, where metric distortion impedes the discrimination of similar solutions. To overcome this limitation, we propose Discount Model Search (DMS), which introduces—for the first time—a continuously smooth discount-value model into the QD framework, replacing the conventional discrete histogram. This innovation enables finer decomposition of high-dimensional spaces and provides sustained guidance for exploration. Notably, DMS supports defining the metric space directly from image data, thereby extending the applicability of QD to high-dimensional black-box optimization settings. Experimental results demonstrate that DMS significantly outperforms state-of-the-art methods such as CMA-MAE on both high-dimensional benchmarks and image-based behavioral characterization tasks, achieving efficient and effective image-driven QD optimization.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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.

Problem

• Quality Diversity Optimization
• High-Dimensional Measure Spaces
• Measure Distortion
• Exploration Stagnation

Innovation

• Discount Model Search
• Quality Diversity Optimization
• High-Dimensional Measure Spaces
• Continuous Discount Model
• Image-Based Measures