Recursive Two-Step Lookahead Expected Payoff for Time-Dependent Bayesian Optimization

TL;DR

This paper introduces a recursive two-step lookahead Bayesian optimization method, $ exttt{r2LEY}$, designed for efficient decision-making in time-dependent, expensive-to-evaluate scenarios with a finite horizon.

Contribution

It presents a novel recursive two-step lookahead acquisition function that efficiently approximates multistep planning in time-dependent Bayesian optimization.

Findings

$ exttt{r2LEY}$ outperforms myopic methods in time-dependent settings.

It effectively balances exploration and exploitation near the horizon.

Demonstrated superior performance on synthetic and real-world datasets.

Abstract

We propose a novel Bayesian method to solve the maximization of a time-dependent expensive-to-evaluate oracle. We are interested in the decision that maximizes the oracle at a finite time horizon, when relatively few noisy evaluations can be performed before the horizon. Our recursive, two-step lookahead expected payoff ($\texttt{r2LEY}$) acquisition function makes nonmyopic decisions at every stage by maximizing the estimated expected value of the oracle at the horizon. $\texttt{r2LEY}$ circumvents the evaluation of the expensive multistep (more than two steps) lookahead acquisition function by recursively optimizing a two-step lookahead acquisition function at every stage; unbiased estimators of this latter function and its gradient are utilized for efficient optimization. $\texttt{r2LEY}$ is shown to exhibit natural exploration properties far from the time horizon, enabling accurate emulation of the oracle, which is exploited in the final decision made at the horizon. To demonstrate the utility of $\texttt{r2LEY}$, we compare it with time-dependent extensions of popular myopic acquisition functions via both synthetic and real-world datasets.