Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equivalence of different adaptive batch size selection strategies
  for stochastic gradient descent methods   In this study, we demonstrate that the norm test and inner
product/orthogonality test presented in \cite{Bol18} are equivalent in terms of
the convergence rates associated with Stochastic Gradient Descent (SGD) methods
if $\epsilon^2=\theta^2+\nu^2$ with specific choices of $\theta$ and $\nu$.
Here, $\epsilon$ controls the relative statistical error of the norm of the
gradient while $\theta$ and $\nu$ control the relative statistical error of the
gradient in the direction of the gradient and in the direction orthogonal to
the gradient, respectively. Furthermore, we demonstrate that the inner
product/orthogonality test can be as inexpensive as the norm test in the best
case scenario if $\theta$ and $\nu$ are optimally selected, but the inner
product/orthogonality test will never be more computationally affordable than
the norm test if $\epsilon^2=\theta^2+\nu^2$. Finally, we present two
stochastic optimization problems to illustrate our results.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph