Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of nonsmooth stochastic approximation: the differential
  inclusion approach   In this paper we address the convergence of stochastic approximation when the
functions to be minimized are not convex and nonsmooth. We show that the
"mean-limit" approach to the convergence which leads, for smooth problems, to
the ODE approach can be adapted to the non-smooth case. The limiting dynamical
system may be shown to be, under appropriate assumption, a differential
inclusion. Our results expand earlier works in this direction by Benaim et al.
(2005) and provide a general framework for proving convergence for
unconstrained and constrained stochastic approximation problems, with either
explicit or implicit updates. In particular, our results allow us to establish
the convergence of stochastic subgradient and proximal stochastic gradient
descent algorithms arising in a large class of deep learning and
high-dimensional statistical inference with sparsity inducing penalties.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph