Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbed Iterate SGD for Lipschitz Continuous Loss Functions   This paper presents an extension of stochastic gradient descent for the
minimization of Lipschitz continuous loss functions. Our motivation is for use
in non-smooth non-convex stochastic optimization problems, which are frequently
encountered in applications such as machine learning. Using the Clarke
$\epsilon$-subdifferential, we prove the non-asymptotic convergence to an
approximate stationary point in expectation for the proposed method. From this
result, a method with non-asymptotic convergence with high probability, as well
as a method with asymptotic convergence to a Clarke stationary point almost
surely are developed. Our results hold under the assumption that the stochastic
loss function is a Carath\'eodory function which is almost everywhere Lipschitz
continuous in the decision variables. To the best of our knowledge this is the
first non-asymptotic convergence analysis under these minimal assumptions.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an