# Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization

arXiv: https://arxiv.org/abs/2206.03034 · HTML: https://mlsanity.com/paper/2206.03034/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 85 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Deep Gaussian Processes: A Survey](https://mlsanity.com/paper/2106.12135/) (2021)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Patchwork Kriging for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1701.06655/) (2017)
- [Ordinal Bayesian Optimisation](https://mlsanity.com/paper/1912.02493/) (2019)
- [Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression](https://mlsanity.com/paper/1812.07736/) (2018)
- [A new integral loss function for Bayesian optimization](https://mlsanity.com/paper/1408.4622/) (2014)

## Built on by (most cited first, 2 of 2)

- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)
- [Why not to use the Gaussian kernel](https://mlsanity.com/paper/2608.26974/) (2026)

## Abstract (arXiv)

This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive distributions no longer necessarily interpolates the observed values when they are outside ranges of interest, but are simply constrained to remain outside. This method called relaxed Gaussian process (reGP) interpolation provides better predictive distributions in ranges of interest, especially in cases where a stationarity assumption for the GP model is not appropriate. It can be viewed as a goal-oriented method and becomes particularly interesting in Bayesian optimization, for example, for the minimization of an objective function, where good predictive distributions for low function values are important. When the expected improvement criterion and reGP are used for sequentially choosing evaluation points, the convergence of the resulting optimization algorithm is theoretically guaranteed (provided that the function to be optimized lies in the reproducing kernel Hilbert space attached to the known covariance of the underlying Gaussian process). Experiments indicate that using reGP instead of stationary GP models in Bayesian optimization is beneficial.