# Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning

arXiv: https://arxiv.org/abs/2402.18260 · HTML: https://mlsanity.com/paper/2402.18260/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes](https://mlsanity.com/paper/2011.12916/) (2020)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Robustness Guarantees for Bayesian Inference with Gaussian Processes](https://mlsanity.com/paper/1809.06452/) (2018)
- [Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients](https://mlsanity.com/paper/2212.14319/) (2022)
- [Integrals over Gaussians under Linear Domain Constraints](https://mlsanity.com/paper/1910.09328/) (2019)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Safe Active Learning for Time-Series Modeling with Gaussian Processes](https://mlsanity.com/paper/2402.06276/) (2024)
- [Information-Theoretic Safe Exploration with Gaussian Processes](https://mlsanity.com/paper/2212.04914/) (2022)
- [Structural Kernel Search via Bayesian Optimization and Symbolical Optimal Transport](https://mlsanity.com/paper/2210.11836/) (2022)
- [Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/2101.05328/) (2021)

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

- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [Physics-informed Gaussian Processes as Linear Model Predictive Controller](https://mlsanity.com/paper/2412.04502/) (2024)

## Abstract (arXiv)

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte-Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.