Benefits of Monotonicity in Safe Exploration with Gaussian Processes

TL;DR

This paper introduces M-SafeUCB, a Gaussian process-based algorithm for safe sequential optimization that leverages monotonicity assumptions to improve safety guarantees, efficiency, and simplicity, with applications in clinical trials and robotics.

Contribution

The paper proposes a novel monotonicity-aware safe optimization algorithm, M-SafeUCB, with theoretical safety and regret guarantees, demonstrating advantages over previous methods.

Findings

M-SafeUCB guarantees safety and near-optimality under monotonicity.

Monotonicity assumption simplifies algorithm design and improves efficiency.

Empirical results validate theoretical advantages in simulated clinical trials.

Abstract

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 \emph{safety variable}. This assumption is motivated by various practical applications such as adaptive clinical trial design and robotics. Taking inspiration from the \textsc{\sffamily GP-UCB} and \textsc{\sffamily SafeOpt} algorithms, we propose an algorithm, monotone safe {\sffamily UCB} (\textsc{\sffamily M-SafeUCB}) for this task. We show that \textsc{\sffamily 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.