# Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes

arXiv: https://arxiv.org/abs/2405.10581 · HTML: https://mlsanity.com/paper/2405.10581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 97 references that are in the map.
- First posted on arXiv 17 May 2024.

## Builds on (most cited first, 30 of 39)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [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)
- [A Survey of Reinforcement Learning Algorithms for Dynamically Varying Environments](https://mlsanity.com/paper/2005.10619/) (2020)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [SAMBA: Safe Model-Based & Active Reinforcement Learning](https://mlsanity.com/paper/2006.09436/) (2020)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits](https://mlsanity.com/paper/1401.1123/) (2014)
- [Actively Learning Gaussian Process Dynamics](https://mlsanity.com/paper/1911.09946/) (2019)
- [Bayesian Active Learning with Fully Bayesian Gaussian Processes](https://mlsanity.com/paper/2205.10186/) (2022)
- [Safe Contextual Bayesian Optimization for Sustainable Room Temperature PID Control Tuning](https://mlsanity.com/paper/1906.12086/) (2019)
- [Batch Multi-Fidelity Active Learning with Budget Constraints](https://mlsanity.com/paper/2210.12704/) (2022)
- [Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients](https://mlsanity.com/paper/2212.14319/) (2022)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations](https://mlsanity.com/paper/2208.12515/) (2022)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [Safe Active Learning for Time-Series Modeling with Gaussian Processes](https://mlsanity.com/paper/2402.06276/) (2024)
- [Partitioned Active Learning for Heterogeneous Systems](https://mlsanity.com/paper/2105.08547/) (2021)
- [Amortized Inference for Gaussian Process Hyperparameters of Structured Kernels](https://mlsanity.com/paper/2306.09819/) (2023)

## Built on by (most cited first, 1 of 1)

- [Autonomous Reliability Qualification of Ga2O3-based diode sensors via Safe Active Learning](https://mlsanity.com/paper/2605.00868/) (2026)

## Abstract (arXiv)

Experimental exploration of high-cost systems with safety constraints, common in engineering applications, is a challenging endeavor. Data-driven models offer a promising solution, but acquiring the requisite data remains expensive and is potentially unsafe. Safe active learning techniques prove essential, enabling the learning of high-quality models with minimal expensive data points and high safety. This paper introduces a safe active learning framework tailored for time-varying systems, addressing drift, seasonal changes, and complexities due to dynamic behavior. The proposed Time-aware Integrated Mean Squared Prediction Error (T-IMSPE) method minimizes posterior variance over current and future states, optimizing information gathering also in the time domain. Empirical results highlight T-IMSPE's advantages in model quality through toy and real-world examples. State of the art Gaussian processes are compatible with T-IMSPE. Our theoretical contributions include a clear delineation which Gaussian process kernels, domains, and weighting measures are suitable for T-IMSPE and even beyond for its non-time aware predecessor IMSPE.