# Multi-Step Bayesian Optimization for One-Dimensional Feasibility Determination

arXiv: https://arxiv.org/abs/1607.03195 · HTML: https://mlsanity.com/paper/1607.03195/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2016.

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

- [Cost-aware Stopping for Bayesian Optimization](https://mlsanity.com/paper/2507.12453/) (2025)

## Abstract (arXiv)

Bayesian optimization methods allocate limited sampling budgets to maximize expensive-to-evaluate functions. One-step-lookahead policies are often used, but computing optimal multi-step-lookahead policies remains a challenge. We consider a specialized Bayesian optimization problem: finding the superlevel set of an expensive one-dimensional function, with a Markov process prior. We compute the Bayes-optimal sampling policy efficiently, and characterize the suboptimality of one-step lookahead. Our numerical experiments demonstrate that the one-step lookahead policy is close to optimal in this problem, performing within 98% of optimal in the experimental settings considered.