HPO X ELA: Investigating Hyperparameter Optimization Landscapes by Means of Exploratory Landscape Analysis

TL;DR

This paper applies exploratory landscape analysis to hyperparameter optimization problems, comparing their structure to benchmark problems and evaluating optimizer performance to better understand the landscape of HPO tasks.

Contribution

It introduces a methodology to analyze HPO landscapes using ELA features and compares them with benchmark problems, revealing structural similarities and differences.

Findings

HPO problems share structural features with certain BBOB benchmark problems.

Optimizer performance correlates with landscape similarity in ELA feature space.

Identifies open challenges and future directions for ELA in HPO.

Abstract

Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications.