# Information-Theoretic Safe Exploration with Gaussian Processes

arXiv: https://arxiv.org/abs/2212.04914 · HTML: https://mlsanity.com/paper/2212.04914/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Challenges of Real-World Reinforcement Learning](https://mlsanity.com/paper/1904.12901/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [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 in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [Gaussian Process Optimization with Mutual Information](https://mlsanity.com/paper/1311.4825/) (2013)

## Built on by (most cited first, 9 of 9)

- [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)
- [Safety and optimality in learning-based control at low computational cost](https://mlsanity.com/paper/2505.08026/) (2025)
- [Beyond Noisy-TVs: Noise-Robust Exploration Via Learning Progress Monitoring](https://mlsanity.com/paper/2509.25438/) (2025)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)
- [Information-Theoretic Safe Bayesian Optimization](https://mlsanity.com/paper/2402.15347/) (2024)
- [Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes](https://mlsanity.com/paper/2408.16307/) (2024)
- [Constrained Linear Thompson Sampling](https://mlsanity.com/paper/2503.02043/) (2025)
- [Safely Learning Controlled Stochastic Dynamics](https://mlsanity.com/paper/2506.02754/) (2025)

## Abstract (arXiv)

We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow evaluations only in regions that are safe with high probability. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. Moreover, the way in which they exploit regularity assumptions about the constraint introduces an additional critical hyperparameter. In this paper, we propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate. Our approach is naturally applicable to continuous domains and does not require additional hyperparameters. We theoretically analyze the method and show that we do not violate the safety constraint with high probability and that we explore by learning about the constraint up to arbitrary precision. Empirical evaluations demonstrate improved data-efficiency and scalability.