Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tightly Robust Optimization via Empirical Domain Reduction   Data-driven decision-making is performed by solving a parameterized
optimization problem, and the optimal decision is given by an optimal solution
for unknown true parameters. We often need a solution that satisfies true
constraints even though these are unknown. Robust optimization is employed to
obtain such a solution, where the uncertainty of the parameter is represented
by an ellipsoid, and the scale of robustness is controlled by a coefficient. In
this study, we propose an algorithm to determine the scale such that the
solution has a good objective value and satisfies the true constraints with a
given confidence probability. Under some regularity conditions, the scale
obtained by our algorithm is asymptotically $O(1/\sqrt{n})$, whereas the scale
obtained by a standard approach is $O(\sqrt{d/n})$. This means that our
algorithm is less affected by the dimensionality of the parameters.

26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin