CMA-ES for Post Hoc Ensembling in AutoML: A Great Success and Salvageable Failure

TL;DR

This paper compares CMA-ES and greedy ensemble selection in AutoML, revealing that CMA-ES's overfitting depends on the metric and proposing normalization techniques to improve its performance.

Contribution

It demonstrates the metric-dependent overfitting of CMA-ES in AutoML ensembling and introduces a normalization method to mitigate overfitting for ROC AUC.

Findings

CMA-ES overfits for ROC AUC and underperforms GES

CMA-ES outperforms GES for balanced accuracy

Normalization of CMA-ES weights improves ROC AUC performance

Abstract

Many state-of-the-art automated machine learning (AutoML) systems use greedy ensemble selection (GES) by Caruana et al. (2004) to ensemble models found during model selection post hoc. Thereby, boosting predictive performance and likely following Auto-Sklearn 1's insight that alternatives, like stacking or gradient-free numerical optimization, overfit. Overfitting in Auto-Sklearn 1 is much more likely than in other AutoML systems because it uses only low-quality validation data for post hoc ensembling. Therefore, we were motivated to analyze whether Auto-Sklearn 1's insight holds true for systems with higher-quality validation data. Consequently, we compared the performance of covariance matrix adaptation evolution strategy (CMA-ES), state-of-the-art gradient-free numerical optimization, to GES on the 71 classification datasets from the AutoML benchmark for AutoGluon. We found that Auto-Sklearn's insight depends on the chosen metric. For the metric ROC AUC, CMA-ES overfits drastically and is outperformed by GES -- statistically significantly for multi-class classification. For the metric balanced accuracy, CMA-ES does not overfit and outperforms GES significantly. Motivated by the successful application of CMA-ES for balanced accuracy, we explored methods to stop CMA-ES from overfitting for ROC AUC. We propose a method to normalize the weights produced by CMA-ES, inspired by GES, that avoids overfitting for CMA-ES and makes CMA-ES perform better than or similar to GES for ROC AUC.