In many real-world problems, we want to infer some property of an expensive black-box function $f$, given a budget of $T$ function evaluations. One example is budget constrained global optimization of $f$, for which Bayesian optimization is a popular method. Other properties of interest include local optima, 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 of inferring the output of $\mathcal{A}$ using $T$ evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. Applying this to Dijkstra's algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to $f$ than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes.
翻译:在许多现实世界问题中, 我们想要推断一个昂贵的黑盒函数的某些属性, 美元美元, 预算为$T美元。 一个例子是预算限制的全球优化为$f美元, 贝叶西亚优化是一种流行的方法。 其他感兴趣的属性包括本地的opima、 级别集、 集成或图形结构化信息 $f美元 。 通常, 我们能找到一个算法 $\ mathcal{A} 美元来计算想要的属性, 但可能需要执行的查询远大于$T$, 但它可能需要远大于$T$的查询 。 以这样的$mathcal{A} 和之前的美元分配为例, 我们用美元来推断$mathcalfal优化全球的输出, 使用美元评价, 使用美元来计算Bayesian Algorithm 执行 (BAX) 。 为了解决这个问题, 我们提出了一个程序, InfBAX, 以顺序选择查询如何最大限度地分享关于算法产出的相互信息。 将这个方法应用Dijkstra的算算算法, 例如, 我们用最短的路径选择了最短的路径 和最精确的路径 格式的路径, 也就是的路径, 以我们最接近的路径 格式的路径的路径 的路径 的路径 的路径 的路径 的路径 的路径的路径是黑格 。