Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stochastic Fej\'er-Monotone Hybrid Steepest Descent Method and the
  Hierarchical RLS   This paper introduces the stochastic Fej\'{e}r-monotone hybrid steepest
descent method (S-FM-HSDM) to solve affinely constrained and composite convex
minimization tasks. The minimization task is not known exactly; noise
contaminates the information about the composite loss function and the affine
constraints. S-FM-HSDM generates sequences of random variables that, under
certain conditions and with respect to a probability space, converge point-wise
to solutions of the noiseless minimization task. S-FM-HSDM enjoys desirable
attributes of optimization techniques such as splitting of variables and
constant step size (learning rate). Furthermore, it provides a novel way of
exploiting the information about the affine constraints via fixed-point sets of
appropriate nonexpansive mappings. Among the offsprings of S-FM-HSDM, the
hierarchical recursive least squares (HRLS) takes advantage of S-FM-HSDM's
versatility toward affine constraints and offers a novel twist to LS by
generating sequences of estimates that converge to solutions of a hierarchical
optimization task: Minimize a convex loss over the set of minimizers of the
ensemble LS loss. Numerical tests on a sparsity-aware LS task show that HRLS
compares favorably to several state-of-the-art convex, as well as non-convex,
stochastic-approximation and online-learning counterparts.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas