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This paper presents a multi-staged approach to nonmyopic adaptive Gaussianprocess optimization (GPO) for Bayesian optimization (BO) of unknown, highlycomplex objective functions that, in contrast to existing nonmyopic adaptive BOalgorithms, exploits the notion of macro-actions for scaling up to a furtherlookahead to match up to a larger available budget. To achieve this, wegeneralize GP upper confidence bound to a new acquisition function definedw.r.t. a nonmyopic adaptive macro-action policy, which is intractable to beoptimized exactly due to an uncountable set of candidate outputs. Thecontribution of our work here is thus to derive a nonmyopic adaptiveepsilon-Bayes-optimal macro-action GPO (epsilon-Macro-GPO) policy. To performnonmyopic adaptive BO in real time, we then propose an asymptotically optimalanytime variant of our epsilon-Macro-GPO policy with a performance guarantee.We empirically evaluate the performance of our epsilon-Macro-GPO policy and itsanytime variant in BO with synthetic and real-world datasets.

Nonmyopic Gaussian Process Optimization with Macro-Actions