# Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernel

arXiv: https://arxiv.org/abs/2409.18000 · HTML: https://mlsanity.com/paper/2409.18000/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (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)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (2022)
- [Weighted Gaussian Process Bandits for Non-stationary Environments](https://mlsanity.com/paper/2107.02371/) (2021)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Safe Contextual Bayesian Optimization for Sustainable Room Temperature PID Control Tuning](https://mlsanity.com/paper/1906.12086/) (2019)
- [No-Regret Algorithms for Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2102.06296/) (2021)
- [An Optimization-based Algorithm for Non-stationary Kernel Bandits without Prior Knowledge](https://mlsanity.com/paper/2205.14775/) (2022)
- [Safe and Efficient Model-free Adaptive Control via Bayesian Optimization](https://mlsanity.com/paper/2101.07825/) (2021)
- [Tuning Legged Locomotion Controllers via Safe Bayesian Optimization](https://mlsanity.com/paper/2306.07092/) (2023)
- [Safe Bayesian Optimization using Interior-Point Methods -- Applied to Personalized Insulin Dose Guidance](https://mlsanity.com/paper/2205.02327/) (2022)
- [Event-Triggered Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2208.10790/) (2022)
- [Event-Triggered Safe Bayesian Optimization on Quadcopters](https://mlsanity.com/paper/2312.08058/) (2023)
- [Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints](https://mlsanity.com/paper/2304.06104/) (2023)
- [Safe Risk-averse Bayesian Optimization for Controller Tuning](https://mlsanity.com/paper/2306.13479/) (2023)
- [Detecting gradual changes in locally stationary processes](https://mlsanity.com/paper/1310.4678/) (2013)
- [Efficient sample selection for safe learning](https://mlsanity.com/paper/2211.14104/) (2022)

## Built on by (most cited first, 4 of 4)

- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Safely Learning Controlled Stochastic Dynamics](https://mlsanity.com/paper/2506.02754/) (2025)
- [Bayesian Modeling and Estimation of Linear Time-Varying Systems using Neural Networks and Gaussian Processes](https://mlsanity.com/paper/2507.12878/) (2025)
- [Autonomous Reliability Qualification of Ga2O3-based diode sensors via Safe Active Learning](https://mlsanity.com/paper/2605.00868/) (2026)

## Abstract (arXiv)

Ensuring safety is a key aspect in sequential decision making problems, such as robotics or process control. The complexity of the underlying systems often makes finding the optimal decision challenging, especially when the safety-critical system is time-varying. Overcoming the problem of optimizing an unknown time-varying reward subject to unknown time-varying safety constraints, we propose TVSafeOpt, a new algorithm built on Bayesian optimization with a spatio-temporal kernel. The algorithm is capable of safely tracking a time-varying safe region without the need for explicit change detection. Optimality guarantees are also provided for the algorithm when the optimization problem becomes stationary. We show that TVSafeOpt compares favorably against SafeOpt on synthetic data, both regarding safety and optimality. Evaluation on a realistic case study with gas compressors confirms that TVSafeOpt ensures safety when solving time-varying optimization problems with unknown reward and safety functions.