# Lookahead Acquisition Functions for Finite-Horizon Time-Dependent Bayesian Optimization and Application to Quantum Optimal Control

arXiv: https://arxiv.org/abs/2105.09824 · HTML: https://mlsanity.com/paper/2105.09824/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2021.

## Built on by (most cited first, 6 of 6)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Data-Driven Wind Turbine Wake Modeling via Probabilistic Machine Learning](https://mlsanity.com/paper/2109.02411/) (2021)
- [FigBO: A Generalized Acquisition Function Framework with Look-Ahead Capability for Bayesian Optimization](https://mlsanity.com/paper/2504.20307/) (2025)
- [REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis](https://mlsanity.com/paper/2606.13245/) (2026)
- [Multifidelity Cross-validation](https://mlsanity.com/paper/2407.01495/) (2024)
- [A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification](https://mlsanity.com/paper/2606.28871/) (2026)

## Abstract (arXiv)

We propose a novel Bayesian method to solve the maximization of a time-dependent expensive-to-evaluate stochastic oracle. We are interested in the decision that maximizes the oracle at a finite time horizon, given a limited budget of noisy evaluations of the oracle that can be performed before the horizon. Our recursive two-step lookahead acquisition function for Bayesian optimization makes nonmyopic decisions at every stage by maximizing the expected utility at the specified time horizon. Specifically, we propose a generalized two-step lookahead framework with a customizable value function that allows users to define the utility. We illustrate how lookahead versions of classic acquisition functions such as the expected improvement, probability of improvement, and upper confidence bound can be obtained with this framework. We demonstrate the utility of our proposed approach on several carefully constructed synthetic cases and a real-world quantum optimal control problem.