# Safe Active Learning for Time-Series Modeling with Gaussian Processes

arXiv: https://arxiv.org/abs/2402.06276 · HTML: https://mlsanity.com/paper/2402.06276/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits](https://mlsanity.com/paper/1401.1123/) (2014)

## Built on by (most cited first, 12 of 12)

- [First, Learn What You Don't Know: Active Information Gathering for Driving at the Limits of Handling](https://mlsanity.com/paper/2411.00107/) (2024)
- [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)
- [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)
- [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)
- [Novel Pivoted Cholesky Decompositions for Efficient Gaussian Process Inference](https://mlsanity.com/paper/2507.20678/) (2025)
- [Generalized Information Gathering Under Dynamics Uncertainty](https://mlsanity.com/paper/2601.21988/) (2026)
- [Autonomous Reliability Qualification of Ga2O3-based diode sensors via Safe Active Learning](https://mlsanity.com/paper/2605.00868/) (2026)

## Abstract (arXiv)

Learning time-series models is useful for many applications, such as simulation and forecasting. In this study, we consider the problem of actively learning time-series models while taking given safety constraints into account. For time-series modeling we employ a Gaussian process with a nonlinear exogenous input structure. The proposed approach generates data appropriate for time series model learning, i.e. input and output trajectories, by dynamically exploring the input space. The approach parametrizes the input trajectory as consecutive trajectory sections, which are determined stepwise given safety requirements and past observations. We analyze the proposed algorithm and evaluate it empirically on a technical application. The results show the effectiveness of our approach in a realistic technical use case.