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In many real-world problems, we want to infer some property of an expensiveblack-box function $f$, given a budget of $T$ function evaluations. One exampleis budget constrained global optimization of $f$, for which Bayesianoptimization is a popular method. Other properties of interest include localoptima, level sets, integrals, or graph-structured information induced by $f$.Often, we can find an algorithm $\mathcal{A}$ to compute the desired property,but it may require far more than $T$ queries to execute. Given such an$\mathcal{A}$, and a prior distribution over $f$, we refer to the problem ofinferring the output of $\mathcal{A}$ using $T$ evaluations as BayesianAlgorithm Execution (BAX). To tackle this problem, we present a procedure,InfoBAX, that sequentially chooses queries that maximize mutual informationwith respect to the algorithm's output. Applying this to Dijkstra's algorithm,for instance, we infer shortest paths in synthetic and real-world graphs withblack-box edge costs. Using evolution strategies, we yield variants of Bayesianoptimization that target local, rather than global, optima. On these problems,InfoBAX uses up to 500 times fewer queries to $f$ than required by the originalalgorithm. Our method is closely connected to other Bayesian optimalexperimental design procedures such as entropy search methods and optimalsensor placement using Gaussian processes.

Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information