Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Second-order Convergence Properties of Random Search Methods   We study the theoretical convergence properties of random-search methods when
optimizing non-convex objective functions without having access to derivatives.
We prove that standard random-search methods that do not rely on second-order
information converge to a second-order stationary point. However, they suffer
from an exponential complexity in terms of the input dimension of the problem.
In order to address this issue, we propose a novel variant of random search
that exploits negative curvature by only relying on function evaluations. We
prove that this approach converges to a second-order stationary point at a much
faster rate than vanilla methods: namely, the complexity in terms of the number
of function evaluations is only linear in the problem dimension. We test our
algorithm empirically and find good agreements with our theoretical results.

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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci