This paper presents the private-outsourced-Gaussian process-upper confidence
bound (PO-GP-UCB) algorithm, which is the first algorithm for
privacy-preserving Bayesian optimization (BO) in the outsourced setting with a
provable performance guarantee. We consider the outsourced setting where the
entity holding the dataset and the entity performing BO are represented by
different parties, and the dataset cannot be released non-privately. For
example, a hospital holds a dataset of sensitive medical records and outsources
the BO task on this dataset to an industrial AI company. The key idea of our
approach is to make the BO performance of our algorithm similar to that of
non-private GP-UCB run using the original dataset, which is achieved by using a
random projection-based transformation that preserves both privacy and the
pairwise distances between inputs. Our main theoretical contribution is to show
that a regret bound similar to that of the standard GP-UCB algorithm can be
established for our PO-GP-UCB algorithm. We empirically evaluate the
performance of our PO-GP-UCB algorithm with synthetic and real-world datasets.

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