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We propose a novel Bayesian method to solve the maximization of atime-dependent expensive-to-evaluate stochastic oracle. We are interested inthe decision that maximizes the oracle at a finite time horizon, given alimited budget of noisy evaluations of the oracle that can be performed beforethe horizon. Our recursive two-step lookahead acquisition function for Bayesianoptimization makes nonmyopic decisions at every stage by maximizing theexpected utility at the specified time horizon. Specifically, we propose ageneralized two-step lookahead framework with a customizable \emph{value}function that allows users to define the utility. We illustrate how lookaheadversions of classic acquisition functions such as the expected improvement,probability of improvement, and upper confidence bound can be obtained withthis framework. We demonstrate the utility of our proposed approach on severalcarefully constructed synthetic cases and a real-world quantum optimal controlproblem.

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