# Benefits of Monotonicity in Safe Exploration with Gaussian Processes

arXiv: https://arxiv.org/abs/2211.01561 · HTML: https://mlsanity.com/paper/2211.01561/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 21 of 21)

- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Safe Reinforcement Learning via Curriculum Induction](https://mlsanity.com/paper/2006.12136/) (2020)
- [Gaussian Process Bandit Optimization with Few Batches](https://mlsanity.com/paper/2110.07788/) (2021)
- [High-Dimensional Experimental Design and Kernel Bandits](https://mlsanity.com/paper/2105.05806/) (2021)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [On Multi-Armed Bandit Designs for Dose-Finding Clinical Trials](https://mlsanity.com/paper/1903.07082/) (2019)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Best Arm Identification with Safety Constraints](https://mlsanity.com/paper/2111.12151/) (2021)
- [Learning for Dose Allocation in Adaptive Clinical Trials with Safety Constraints](https://mlsanity.com/paper/2006.05026/) (2020)
- [Contextual Constrained Learning for Dose-Finding Clinical Trials](https://mlsanity.com/paper/2001.02463/) (2020)
- [Regret Bounds for Safe Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2005.01936/) (2020)
- [Bayesian Optimization Using Monotonicity Information and Its Application in Machine Learning Hyperparameter](https://mlsanity.com/paper/1802.03532/) (2018)

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

- [No-Regret Algorithms for Safe Bayesian Optimization with Monotonicity Constraints](https://mlsanity.com/paper/2406.03264/) (2024)

## Abstract (arXiv)

We consider the problem of sequentially maximising an unknown function over a set of actions while ensuring that every sampled point has a function value below a given safety threshold. We model the function using kernel-based and Gaussian process methods, while differing from previous works in our assumption that the function is monotonically increasing with respect to a safety variable. This assumption is motivated by various practical applications such as adaptive clinical trial design and robotics. Taking inspiration from the textscsffamily GP-UCB and textscsffamily SafeOpt algorithms, we propose an algorithm, monotone safe sffamily UCB (textscsffamily M-SafeUCB) for this task. We show that textscsffamily M-SafeUCB enjoys theoretical guarantees in terms of safety, a suitably-defined regret notion, and approximately finding the entire safe boundary. In addition, we illustrate that the monotonicity assumption yields significant benefits in terms of the guarantees obtained, as well as algorithmic simplicity and efficiency. We support our theoretical findings by performing empirical evaluations on a variety of functions, including a simulated clinical trial experiment.