Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of Semi-Supervised Adversarially-Robust PAC
  Learnability   We study the problem of semi-supervised learning of an adversarially-robust
predictor in the PAC model, where the learner has access to both labeled and
unlabeled examples. The sample complexity in semi-supervised learning has two
parameters, the number of labeled examples and the number of unlabeled
examples. We consider the complexity measures, $VC_U \leq dim_U \leq VC$ and
$VC^*$, where $VC$ is the standard $VC$-dimension, $VC^*$ is its dual, and the
other two measures appeared in Montasser et al. (2019). The best sample bound
known for robust supervised PAC learning is $O(VC \cdot VC^*)$, and we will
compare our sample bounds to $\Lambda$ which is the minimal number of labeled
examples required by any robust supervised PAC learning algorithm. Our main
results are the following: (1) in the realizable setting it is sufficient to
have $O(VC_U)$ labeled examples and $O(\Lambda)$ unlabeled examples. (2) In the
agnostic setting, let $\eta$ be the minimal agnostic error. The sample
complexity depends on the resulting error rate. If we allow an error of
$2\eta+\epsilon$, it is still sufficient to have $O(VC_U)$ labeled examples and
$O(\Lambda)$ unlabeled examples. If we insist on having an error
$\eta+\epsilon$ then $\Omega(dim_U)$ labeled examples are necessary, as in the
supervised case. The above results show that there is a significant benefit in
semi-supervised robust learning, as there are hypothesis classes with $VC_U=0$
and $dim_U$ arbitrary large. In supervised learning, having access only to
labeled examples requires at least $\Lambda \geq dim_U$ labeled examples.
Semi-supervised require only $O(1)$ labeled examples and $O(\Lambda)$ unlabeled
examples. A byproduct of our result is that if we assume that the distribution
is robustly realizable by a hypothesis class, then with respect to the 0-1 loss
we can learn with only $O(VC_U)$ labeled examples, even if the $VC$ is
infinite.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org