# Adapting Nonstationary Multi-output Gaussian Processes to Bayesian Optimization

arXiv: https://arxiv.org/abs/2609.32464 · HTML: https://mlsanity.com/paper/2609.32464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [No-regret Algorithms for Multi-task Bayesian Optimization](https://mlsanity.com/paper/2008.08885/) (2020)
- [Online Calibrated and Conformal Prediction Improves Bayesian Optimization](https://mlsanity.com/paper/2112.04620/) (2021)
- [Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures](https://mlsanity.com/paper/2202.09233/) (2022)

## Abstract (arXiv)

Multi-objective Bayesian optimization (MOBO) commonly relies on independent Gaussian processes (GPs) with stationary kernels, limiting its ability to represent nonstationary structure and share information between objectives. However, expressive nonstationary GPs do not necessarily make reliable BO decisions. We study this mismatch for the multi-output low-rank nonstationary (MO-LRN) GP: strong training fit can coexist with large off-design errors and optimistic acquisition predictions. We introduce MOLRN-BO, which combines a regularized shared-spectral surrogate with objective-specific residuals, prequential mean correction and tempered covariance scaling, and Pareto-local qLogEHVI optimization with periodic global search. Experiments on 12 deterministic bi-objective benchmarks show that MOLRN-BO substantially improves upon the original MO-LRN and achieves the best average problem ranks for final normalized hypervolume and normalized inverted generational distance among nine evaluated algorithms. It also achieves the strongest adverse-tail performance while remaining competitive with the leading baselines in anytime optimization. Ablation studies further show that the shared spectral construction improves off-design prediction, the local--global decision policy improves optimization performance, and hierarchical calibration reduces systematic candidate bias. These results demonstrate that nonstationary multi-output surrogates can deliver strong and robust MOBO performance when their structure and use are explicitly adapted to the demands of sequential optimization.