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

TL;DR

This paper introduces a recursive two-step lookahead Bayesian optimization method for finite-horizon, time-dependent problems, with applications demonstrated in quantum control.

Contribution

It presents a generalized two-step lookahead framework for Bayesian optimization that incorporates customizable utility functions and extends classic acquisition functions.

Findings

Effective in synthetic test cases

Successfully applied to quantum optimal control

Improves decision-making over myopic methods

Abstract

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 \emph{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.