Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Domain-Shrinking based Bayesian Optimization Algorithm with
  Order-Optimal Regret Performance   We consider sequential optimization of an unknown function in a reproducing
kernel Hilbert space. We propose a Gaussian process-based algorithm and
establish its order-optimal regret performance (up to a poly-logarithmic
factor). This is the first GP-based algorithm with an order-optimal regret
guarantee. The proposed algorithm is rooted in the methodology of domain
shrinking realized through a sequence of tree-based region pruning and refining
to concentrate queries in increasingly smaller high-performing regions of the
function domain. The search for high-performing regions is localized and guided
by an iterative estimation of the optimal function value to ensure both
learning efficiency and computational efficiency. Compared with the prevailing
GP-UCB family of algorithms, the proposed algorithm reduces computational
complexity by a factor of $O(T^{2d-1})$ (where $T$ is the time horizon and $d$
the dimension of the function domain).

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con