Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variance Reduction via Primal-Dual Accelerated Dual Averaging for
  Nonsmooth Convex Finite-Sums   We study structured nonsmooth convex finite-sum optimization that appears
widely in machine learning applications, including support vector machines and
least absolute deviation. For the primal-dual formulation of this problem, we
propose a novel algorithm called \emph{Variance Reduction via Primal-Dual
Accelerated Dual Averaging (\vrpda)}. In the nonsmooth and general convex
setting, \vrpda~has the overall complexity $O(nd\log\min \{1/\epsilon, n\} +
d/\epsilon )$ in terms of the primal-dual gap, where $n$ denotes the number of
samples, $d$ the dimension of the primal variables, and $\epsilon$ the desired
accuracy. In the nonsmooth and strongly convex setting, the overall complexity
of \vrpda~becomes $O(nd\log\min\{1/\epsilon, n\} + d/\sqrt{\epsilon})$ in terms
of both the primal-dual gap and the distance between iterate and optimal
solution. Both these results for \vrpda~improve significantly on
state-of-the-art complexity estimates, which are $O(nd\log \min\{1/\epsilon,
n\} + \sqrt{n}d/\epsilon)$ for the nonsmooth and general convex setting and
$O(nd\log \min\{1/\epsilon, n\} + \sqrt{n}d/\sqrt{\epsilon})$ for the nonsmooth
and strongly convex setting, in a much more simple and straightforward way.
Moreover, both complexities are better than \emph{lower} bounds for general
convex finite sums that lack the particular (common) structure that we
consider. Our theoretical results are supported by numerical experiments, which
confirm the competitive performance of \vrpda~compared to state-of-the-art.

0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph