Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Doubly-Randomized Block-Coordinate Primal-Dual Method for Large-scale
  Saddle Point Problems   In this paper, we consider a large-scale convex-concave saddle point problem
in a finite-sum form that arises in machine learning problems involving
empirical risk minimization, e.g., robust classification, kernel matrix
learning, etc. To contend with the challenges in computing full gradients, we
employ a block-coordinate primal-dual scheme in which randomly selected primal
and dual blocks of variables are updated at every iteration. When the number of
component functions in the finite sum is massive, we can derive further
efficiency by utilizing an increasing batch-size of gradients, leading to
progressive variance reduction. An ergodic convergence rate of
$\mathcal{O}(\log(K)/K)$ is obtained using variance reduction which is the
first known rate result for a special purpose method to deal with finite-sum
non-bilinear saddle point problems, matching the best-known rate (up to a log
factor) associated with deterministic primal-dual schemes using full gradients.
Using an acceleration for the setting where a single component gradient is
utilized, a non-asymptotic rate of $\mathcal{O}(\log(K)/\sqrt{K})$ is obtained.
Finally, for both single and increasing sample size scenarios, almost sure
convergence of the iterate sequence to a saddle point is shown.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an