Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Sample Complexity of Data-Driven Inference of the
  $\mathcal{L}_2$-gain   Lately, data-driven control has become a widespread area of research. A few
recent big-data based approaches for data-driven control of nonlinear systems
try to use classical input-output techniques to design controllers for systems
for which only a finite number of (input-output) samples are known. These
methods focus on using the given data to compute bounds on the
$\mathcal{L}_2$-gain or on the shortage of passivity from finite input-output
data, allowing for the application of the small gain theorem or the feedback
theorem for passive systems. One question regarding these methods asks about
their sample complexity, namely how many input-output samples are needed to get
an approximation of the operator norm or of the shortage of passivity. We show
that the number of samples needed to estimate the operator norm of a system is
roughly the same as the number of samples required to approximate the system in
the operator norm.

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The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th