# PMBO: Enhancing Black-Box Optimization through Multivariate Polynomial Surrogates

arXiv: https://arxiv.org/abs/2403.07485 · HTML: https://mlsanity.com/paper/2403.07485/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness](https://mlsanity.com/paper/2001.10818/) (2020)
- [Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search](https://mlsanity.com/paper/1705.04405/) (2017)
- [PyBADS: Fast and robust black-box optimization in Python](https://mlsanity.com/paper/2306.15576/) (2023)
- [Gradient-free Multi-domain Optimization for Autonomous Systems](https://mlsanity.com/paper/2202.13525/) (2022)

## Abstract (arXiv)

We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error between the objective and its polynomial fit. We describe the algorithmic design of PMBO and compare the results of the performance of PMBO with several optimization methods for a set of analytic test functions. The results show that PMBO outperforms the classic Bayesian optimization and is robust with respect to the choice of its correlation function family and its hyper-parameter setting, which, on the contrary, need to be carefully tuned in classic Bayesian optimization. Remarkably, PMBO performs comparably with state-of-the-art evolutionary algorithms such as the Covariance Matrix Adaptation -- Evolution Strategy (CMA-ES). This finding suggests that PMBO emerges as the pivotal choice among surrogate-based optimization methods when addressing low-dimensional optimization problems. Hereby, the simple nature of polynomials opens the opportunity for interpretation and analysis of the inferred surrogate model, providing a macroscopic perspective on the landscape of the objective function.