Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nested optimization problems within a multi-step scenario tree. Instead of solving these problems in a nested way, we equivalently optimize all decision variables in the full tree jointly, in a ``one-shot'' fashion. Combining this with an efficient method for implementing multi-step Gaussian process ``fantasization,'' we demonstrate that multi-step expected improvement is computationally tractable and exhibits performance superior to existing methods on a wide range of benchmarks.

提供用于优化昂贵黑匣子函数的一种多步先见性贝叶斯优化方法，采用多步方案树内嵌化简的方法，通过高效的多步高斯过程虚拟化实现，超过现有方法的表现。

通过一次多步树的方法高效非近视贝叶斯优化