# Safe Active Learning for Multi-Output Gaussian Processes

arXiv: https://arxiv.org/abs/2203.14849 · HTML: https://mlsanity.com/paper/2203.14849/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 28 Mar 2022.

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

- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [A Framework for Interdomain and Multioutput Gaussian Processes](https://mlsanity.com/paper/2003.01115/) (2020)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Near-Optimal Active Learning of Multi-Output Gaussian Processes](https://mlsanity.com/paper/1511.06891/) (2015)

## Built on by (most cited first, 13 of 13)

- [Amortized Inference for Gaussian Process Hyperparameters of Structured Kernels](https://mlsanity.com/paper/2306.09819/) (2023)
- [Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systems](https://mlsanity.com/paper/2303.10022/) (2023)
- [Amortized Safe Active Learning for Real-Time Data Acquisition: Pretrained Neural Policies From Simulated Nonparametric Functions](https://mlsanity.com/paper/2501.15458/) (2025)
- [Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning](https://mlsanity.com/paper/2402.18260/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Constrained Bayesian Experimental Design via Online Planning](https://mlsanity.com/paper/2605.26990/) (2026)
- [Global Safe Sequential Learning via Efficient Knowledge Transfer](https://mlsanity.com/paper/2402.14402/) (2024)
- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [Information-Theoretic Safe Bayesian Optimization](https://mlsanity.com/paper/2402.15347/) (2024)
- [Amortized Active Learning for Nonparametric Functions](https://mlsanity.com/paper/2407.17992/) (2024)
- [Batch Active Learning in Gaussian Process Regression using Derivatives](https://mlsanity.com/paper/2408.01861/) (2024)
- [Reciprocal Learning](https://mlsanity.com/paper/2408.06257/) (2024)
- [Vector Optimization with Gaussian Process Bandits](https://mlsanity.com/paper/2412.02484/) (2024)

## Abstract (arXiv)

Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the inherent correlations and provide reliable uncertainty estimates. In many applications, however, acquiring the data is expensive and safety concerns might arise (e.g. robotics, engineering). We propose a safe active learning approach for multi-output Gaussian process regression. This approach queries the most informative data or output taking the relatedness between the regressors and safety constraints into account. We prove the effectiveness of our approach by providing theoretical analysis and by demonstrating empirical results on simulated datasets and on a real-world engineering dataset. On all datasets, our approach shows improved convergence compared to its competitors.