# Geometric Learning in Black-Box Optimization: A GNN Framework for Algorithm Performance Prediction

arXiv: https://arxiv.org/abs/2506.16144 · HTML: https://mlsanity.com/paper/2506.16144/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Deep Graph Library: A Graph-Centric, Highly-Performant Package for Graph Neural Networks](https://mlsanity.com/paper/1909.01315/) (2019)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [A Survey of Methods for Automated Algorithm Configuration](https://mlsanity.com/paper/2202.01651/) (2022)
- [Neural Architecture Performance Prediction Using Graph Neural Networks](https://mlsanity.com/paper/2010.10024/) (2020)
- [Explainable Landscape-Aware Optimization Performance Prediction](https://mlsanity.com/paper/2110.11633/) (2021)
- [PerfSAGE: Generalized Inference Performance Predictor for Arbitrary Deep Learning Models on Edge Devices](https://mlsanity.com/paper/2301.10999/) (2023)
- [Using Graph Neural Networks to model the performance of Deep Neural Networks](https://mlsanity.com/paper/2108.12489/) (2021)

## Built on by (most cited first, 1 of 1)

- [Quantifying the Impact of Modules and Their Interactions in the PSO-X Framework](https://mlsanity.com/paper/2601.04100/) (2026)

## Abstract (arXiv)

Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph. This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions. Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.