Sampling on Random Subspaces under Limited Data in the Context of Exploratory Landscape Analysis

2026-07-08

AI Summary

This work addresses the challenge of reliably extracting Exploratory Landscape Analysis (ELA) features under severe budget constraints in high-dimensional black-box optimization, where conventional space-filling sampling often yields unstable estimates. To enhance robustness, the study introduces random linear embeddings into the ELA sampling procedure, allocating the limited evaluation budget within randomly projected low-dimensional subspaces. Empirical evaluation on the COCO BBOB benchmark suite—specifically the 20-dimensional noiseless problems—demonstrates that this approach yields more stable estimates for most ELA feature classes. The effectiveness varies with problem structure and feature type, yet overall significantly improves the reliability of landscape descriptors when computational resources are scarce.

Abstract

Classical space-filling designs often fail to provide reliable statistical results for Exploratory Landscape Analysis (ELA) when only limited evaluation budgets are available, as commonly occurs in high-dimensional problems or other resource-constrained settings, resulting in noisy and unstable landscape descriptors. To address this challenge, we propose an alternative sampling strategy for ELA based on random linear embeddings. Rather than sampling uniformly in the full decision space, we allocate the budget to randomly oriented low-dimensional subspaces and investigate whether this improves the robustness of the resulting landscape descriptors. We compare full-space and embedding-based sampling strategies across several classical ELA feature sets on the noiseless Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) environment, in a 20-dimensional setting. Our results suggest that random linear embeddings constitute a promising alternative for budget-constrained ELA, although their effectiveness remains dependent on the feature class and the underlying problem.

Problem

• Exploratory Landscape Analysis
• limited evaluation budget
• space-filling designs
• landscape descriptors
• high-dimensional problems

Innovation

• random linear embeddings
• exploratory landscape analysis
• budget-constrained sampling
• low-dimensional subspaces
• landscape descriptors