Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional Gradient Method for Stochastic Submodular Maximization:
  Closing the Gap   In this paper, we study the problem of \textit{constrained} and
\textit{stochastic} continuous submodular maximization. Even though the
objective function is not concave (nor convex) and is defined in terms of an
expectation, we develop a variant of the conditional gradient method, called
\alg, which achieves a \textit{tight} approximation guarantee. More precisely,
for a monotone and continuous DR-submodular function and subject to a
\textit{general} convex body constraint, we prove that \alg achieves a
$[(1-1/e)\text{OPT} -\eps]$ guarantee (in expectation) with
$\mathcal{O}{(1/\eps^3)}$ stochastic gradient computations. This guarantee
matches the known hardness results and closes the gap between deterministic and
stochastic continuous submodular maximization. By using stochastic continuous
optimization as an interface, we also provide the first $(1-1/e)$ tight
approximation guarantee for maximizing a \textit{monotone but stochastic}
submodular \textit{set} function subject to a general matroid constraint.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: q-bio