  Bayesian Optimization (BO) is a framework for black-box optimization that is
especially suitable for expensive cost functions. Among the main parts of a BO
algorithm, the acquisition function is of fundamental importance, since it
guides the optimization algorithm by translating the uncertainty of the
regression model in a utility measure for each point to be evaluated.
Considering such aspect, selection and design of acquisition functions are one
of the most popular research topics in BO. Since no single acquisition function
was proved to have better performance in all tasks, a well-established approach
consists of selecting different acquisition functions along the iterations of a
BO execution. In such an approach, the GP-Hedge algorithm is a widely used
option given its simplicity and good performance. Despite its success in
various applications, GP-Hedge shows an undesirable characteristic of
accounting on all past performance measures of each acquisition function to
select the next function to be used. In this case, good or bad values obtained
in an initial iteration may impact the choice of the acquisition function for
the rest of the algorithm. This fact may induce a dominant behavior of an
acquisition function and impact the final performance of the method. Aiming to
overcome such limitation, in this work we propose a variant of GP-Hedge, named
No-PASt-BO, that reduce the influence of far past evaluations. Moreover, our
method presents a built-in normalization that avoids the functions in the
portfolio to have similar probabilities, thus improving the exploration. The
obtained results on both synthetic and real-world optimization tasks indicate
that No-PASt-BO presents competitive performance and always outperforms
GP-Hedge.
