Lookahead Acquisition Functions for Finite-Horizon Time-Dependent Bayesian Optimization and Application to Quantum Optimal Control
arXiv:2105.09824
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.
arXiv comment22 pages, 11 figures
References in corpus (13)
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
- Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
- Training of Quantum Circuits on a Hybrid Quantum Computer
- Max-value Entropy Search for Efficient Bayesian Optimization
- A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes
- Parallel Bayesian Global Optimization of Expensive Functions
- GLASSES: Relieving The Myopia Of Bayesian Optimisation
- The reparameterization trick for acquisition functions
- Digital quantum simulation of molecular dynamics and control
- Time-Varying Gaussian Process Bandit Optimization
- Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization
- Bayesian Optimization for Dynamic Problems