  Computing a Gaussian process (GP) posterior has a computational cost cubical
in the number of historical points. A reformulation of the same GP posterior
highlights that this complexity mainly depends on how many \emph{unique}
historical points are considered. This can have important implication in active
learning settings, where the set of historical points is constructed
sequentially by the learner. We show that sequential black-box optimization
based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution
for multiple evaluation steps and switch only when necessary. Limiting the
number of switches also limits the number of unique points in the history of
the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply
compute the posteriors required to run the GP-Opt algorithms. This approach is
especially useful in real-world applications of GP-Opt with high switch costs
(e.g. switching chemicals in wet labs, data/model loading in hyperparameter
optimization). As examples of this meta-approach, we modify two
well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as
infrequently as possible adapting rules from batched GP-Opt. These versions
preserve all the theoretical no-regret guarantees while improving practical
aspects of the algorithms such as runtime, memory complexity, and the ability
of batching candidates and evaluating them in parallel.
