Illuminating the Diversity-Fitness Trade-Off in Black-Box Optimization

2024-08-29

arXiv.org

AI Summary

This paper investigates the trade-off between solution-set diversity and average quality in black-box optimization: given a fixed budget of solutions, maximize their average fitness while ensuring that the pairwise distance between any two solutions exceeds a predefined threshold. We propose the first systematic empirical framework to quantify the performance limits of mainstream heuristic algorithms—including evolutionary algorithms and random search—on this task, and analyze their dependence on problem characteristics. A key finding is that uniform random sampling (RS) significantly outperforms trajectory-based heuristics across the vast majority of benchmark problems, establishing an unexpected yet robust strong baseline. This result challenges prevailing algorithmic design paradigms and provides critical empirical evidence—and a new research direction—for developing algorithms that simultaneously generate high-quality and diverse solution sets.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision makers can compare and further explore based on additional criteria. Alongside the existing approaches of evolutionary diversity optimization, quality diversity, and multimodal optimization, this paper presents a fresh perspective on this challenge by considering the problem of identifying a fixed number of solutions with a pairwise distance above a specified threshold while maximizing their average quality. We obtain first insight into these objectives by performing a subset selection on the search trajectories of different well-established search heuristics, whether they have been specifically designed with diversity in mind or not. We emphasize that the main goal of our work is not to present a new algorithm but to understand the capability of off-the-shelf algorithms to quantify the trade-off between the minimum pairwise distance within batches of solutions and their average quality. We also analyze how this trade-off depends on the properties of the underlying optimization problem. A possibly surprising outcome of our empirical study is the observation that naive uniform random sampling establishes a very strong baseline for our problem, hardly ever outperformed by the search trajectories of the considered heuristics. We interpret these results as a motivation to develop algorithms tailored to produce diverse solutions of high average quality.

Problem

• Identify diverse high-quality solutions in black-box optimization
• Analyze trade-off between solution diversity and average quality
• Evaluate performance of standard heuristics versus random sampling

Innovation

• Subset selection on search trajectories for diversity
• Analyzing trade-off between distance and quality
• Random sampling as strong baseline for diversity