Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Halfspaces with Tsybakov Noise   We study the efficient PAC learnability of halfspaces in the presence of
Tsybakov noise. In the Tsybakov noise model, each label is independently
flipped with some probability which is controlled by an adversary. This noise
model significantly generalizes the Massart noise model, by allowing the
flipping probabilities to be arbitrarily close to $1/2$ for a fraction of the
samples. Our main result is the first non-trivial PAC learning algorithm for
this problem under a broad family of structured distributions -- satisfying
certain concentration and (anti-)anti-concentration properties -- including
log-concave distributions. Specifically, we given an algorithm that achieves
misclassification error $\epsilon$ with respect to the true halfspace, with
quasi-polynomial runtime dependence in $1/\epsilin$. The only previous upper
bound for this problem -- even for the special case of log-concave
distributions -- was doubly exponential in $1/\epsilon$ (and follows via the
naive reduction to agnostic learning). Our approach relies on a novel
computationally efficient procedure to certify whether a candidate solution is
near-optimal, based on semi-definite programming. We use this certificate
procedure as a black-box and turn it into an efficient learning algorithm by
searching over the space of halfspaces via online convex optimization.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph