Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Submodular Optimization under Noise   We consider the problem of maximizing a monotone submodular function under
noise. There has been a great deal of work on optimization of submodular
functions under various constraints, resulting in algorithms that provide
desirable approximation guarantees. In many applications, however, we do not
have access to the submodular function we aim to optimize, but rather to some
erroneous or noisy version of it. This raises the question of whether provable
guarantees are obtainable in presence of error and noise. We provide initial
answers, by focusing on the question of maximizing a monotone submodular
function under a cardinality constraint when given access to a noisy oracle of
the function. We show that:
  - For a cardinality constraint $k \geq 2$, there is an approximation
algorithm whose approximation ratio is arbitrarily close to $1-1/e$;
  - For $k=1$ there is an algorithm whose approximation ratio is arbitrarily
close to $1/2$. No randomized algorithm can obtain an approximation ratio
better than $1/2+o(1)$;
  -If the noise is adversarial, no non-trivial approximation guarantee can be
obtained.

6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an