Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Perceptron: Efficient and Label-Optimal Learning of
  Halfspaces   It has been a long-standing problem to efficiently learn a halfspace using as
few labels as possible in the presence of noise. In this work, we propose an
efficient Perceptron-based algorithm for actively learning homogeneous
halfspaces under the uniform distribution over the unit sphere. Under the
bounded noise condition~\cite{MN06}, where each label is flipped with
probability at most $\eta < \frac 1 2$, our algorithm achieves a near-optimal
label complexity of
$\tilde{O}\left(\frac{d}{(1-2\eta)^2}\ln\frac{1}{\epsilon}\right)$ in time
$\tilde{O}\left(\frac{d^2}{\epsilon(1-2\eta)^3}\right)$. Under the adversarial
noise condition~\cite{ABL14, KLS09, KKMS08}, where at most a $\tilde
\Omega(\epsilon)$ fraction of labels can be flipped, our algorithm achieves a
near-optimal label complexity of $\tilde{O}\left(d\ln\frac{1}{\epsilon}\right)$
in time $\tilde{O}\left(\frac{d^2}{\epsilon}\right)$. Furthermore, we show that
our active learning algorithm can be converted to an efficient passive learning
algorithm that has near-optimal sample complexities with respect to $\epsilon$
and $d$.

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom