# No-Regret Algorithms for Safe Bayesian Optimization with Monotonicity Constraints

arXiv: https://arxiv.org/abs/2406.03264 · HTML: https://mlsanity.com/paper/2406.03264/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 15 of 15)

- [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)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [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 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)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [On the Sublinear Regret of GP-UCB](https://mlsanity.com/paper/2307.07539/) (2023)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Multi-Scale Zero-Order Optimization of Smooth Functions in an RKHS](https://mlsanity.com/paper/2005.04832/) (2020)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Regret Bounds for Safe Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2005.01936/) (2020)
- [Benefits of Monotonicity in Safe Exploration with Gaussian Processes](https://mlsanity.com/paper/2211.01561/) (2022)

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

- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)

## Abstract (arXiv)

We consider the problem of sequentially maximizing an unknown function f over a set of actions of the form (s,x), where the selected actions must satisfy a safety constraint with respect to an unknown safety function g. We model f and g as lying in a reproducing kernel Hilbert space (RKHS), which facilitates the use of Gaussian process methods. While existing works for this setting have provided algorithms that are guaranteed to identify a near-optimal safe action, the problem of attaining low cumulative regret has remained largely unexplored, with a key challenge being that expanding the safe region can incur high regret. To address this challenge, we show that if g is monotone with respect to just the single variable s (with no such constraint on f), sublinear regret becomes achievable with our proposed algorithm. In addition, we show that a modified version of our algorithm is able to attain sublinear regret (for suitably defined notions of regret) for the task of finding a near-optimal s corresponding to every x, as opposed to only finding the global safe optimum. Our findings are supported with empirical evaluations on various objective and safety functions.