A new acquisition function for Bayesian optimization based on the moment-generating function

Bayesian Optimization or Efficient Global Optimization (EGO) is a global search strategy that is designed for expensive black-box functions. In this algorithm, a statistical model (usually the Gaussian process model) is constructed on some initial data samples. The global optimum is approached by iteratively maximizing a so-called acquisition function, that balances the exploration and exploitation effect of the search. The performance of such an algorithm is largely affected by the choice of the acquisition function. Inspired by the usage of higher moments from the Gaussian process model, it is proposed to construct a novel acquisition function based on the moment-generating function (MGF) of the improvement, which is the stochastic gain over the current best fitness value by sampling at an unknown point. This MGF-based acquisition function takes all the higher moments into account and introduces an additional real-valued parameter to control the trade-off between exploration and exploitation. The motivation, rationale and closed-form expression of the proposed function are discussed in detail. In addition, we also illustrate its advantage over other acquisition functions, especially the so-called generalized expected improvement.

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