Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Impossibility of Statistically Improving Empirical Optimization:
  A Second-Order Stochastic Dominance Perspective   When the underlying probability distribution in a stochastic optimization is
observed only through data, various data-driven formulations have been studied
to obtain approximate optimal solutions. We show that no such formulations can,
in a sense, theoretically improve the statistical quality of the solution
obtained from empirical optimization. We argue this by proving that the
first-order behavior of the optimality gap against the oracle best solution,
which includes both the bias and variance, for any data-driven solution is
second-order stochastically dominated by empirical optimization, as long as
suitable smoothness holds with respect to the underlying distribution. We
demonstrate this impossibility of improvement in a range of examples including
regularized optimization, distributionally robust optimization, parametric
optimization and Bayesian generalizations. We also discuss the connections of
our results to semiparametric statistical inference and other perspectives in
the data-driven optimization literature.

28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int