Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual subgradient algorithms for large-scale nonsmooth learning problems   "Classical" First Order (FO) algorithms of convex optimization, such as
Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex
optimization, are well known to have optimal (theoretical) complexity estimates
which do not depend on the problem dimension. However, to attain the
optimality, the domain of the problem should admit a "good proximal setup". The
latter essentially means that 1) the problem domain should satisfy certain
geometric conditions of "favorable geometry", and 2) the practical use of these
methods is conditioned by our ability to compute at a moderate cost {\em
proximal transformation} at each iteration. More often than not these two
conditions are satisfied in optimization problems arising in computational
learning, what explains why proximal type FO methods recently became methods of
choice when solving various learning problems. Yet, they meet their limits in
several important problems such as multi-task learning with large number of
tasks, where the problem domain does not exhibit favorable geometry, and
learning and matrix completion problems with nuclear norm constraint, when the
numerical cost of computing proximal transformation becomes prohibitive in
large-scale problems. We propose a novel approach to solving nonsmooth
optimization problems arising in learning applications where Fenchel-type
representation of the objective function is available. The approach is based on
applying FO algorithms to the dual problem and using the {\em accuracy
certificates} supplied by the method to recover the primal solution. While
suboptimal in terms of accuracy guaranties, the proposed approach does not rely
upon "good proximal setup" for the primal problem but requires the problem
domain to admit a Linear Optimization oracle -- the ability to efficiently
maximize a linear form on the domain of the primal problem.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas