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

arXiv: https://arxiv.org/abs/2307.00286 · HTML: https://mlsanity.com/paper/2307.00286/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 1 Jul 2023.

## Builds on (most cited first, 8 of 8)

- [AutoGluon-Tabular: Robust and Accurate AutoML for Structured Data](https://mlsanity.com/paper/2003.06505/) (2020)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Auto-PyTorch Tabular: Multi-Fidelity MetaLearning for Efficient and Robust AutoDL](https://mlsanity.com/paper/2006.13799/) (2020)
- [AMLB: an AutoML Benchmark](https://mlsanity.com/paper/2207.12560/) (2022)
- [CMA-ES for Hyperparameter Optimization of Deep Neural Networks](https://mlsanity.com/paper/1604.07269/) (2016)
- [Time Efficiency in Optimization with a Bayesian-Evolutionary Algorithm](https://mlsanity.com/paper/2005.04166/) (2020)
- [Warm Starting CMA-ES for Hyperparameter Optimization](https://mlsanity.com/paper/2012.06932/) (2020)
- [The Algorithm Selection Competitions 2015 and 2017](https://mlsanity.com/paper/1805.01214/) (2018)

## Built on by (most cited first, 8 of 8)

- [TabRepo: A Large Scale Repository of Tabular Model Evaluations and its AutoML Applications](https://mlsanity.com/paper/2311.02971/) (2023)
- [Reshuffling Resampling Splits Can Improve Generalization of Hyperparameter Optimization](https://mlsanity.com/paper/2405.15393/) (2024)
- [PSEO: Optimizing Post-hoc Stacking Ensemble Through Hyperparameter Tuning](https://mlsanity.com/paper/2508.05144/) (2025)
- [Ensembling Finetuned Language Models for Text Classification](https://mlsanity.com/paper/2410.19889/) (2024)
- [Regularized Neural Ensemblers](https://mlsanity.com/paper/2410.04520/) (2024)
- [Hardware Aware Ensemble Selection for Balancing Predictive Accuracy and Cost](https://mlsanity.com/paper/2408.02280/) (2024)
- [Multi-layer Stack Ensembles for Time Series Forecasting](https://mlsanity.com/paper/2511.15350/) (2025)
- [Ensembles at Any Cost? Accuracy-Energy Trade-offs in Recommender Systems](https://mlsanity.com/paper/2604.07869/) (2026)

## Abstract (arXiv)

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.