Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PAC Ranking from Pairwise and Listwise Queries: Lower Bounds and Upper
  Bounds   This paper explores the adaptive (active) PAC (probably approximately
correct) top-$k$ ranking (i.e., top-$k$ item selection) and total ranking
problems from $l$-wise ($l\geq 2$) comparisons under the multinomial logit
(MNL) model. By adaptively choosing sets to query and observing the noisy
output of the most favored item of each query, we want to design ranking
algorithms that recover the top-$k$ or total ranking using as few queries as
possible. For the PAC top-$k$ ranking problem, we derive a lower bound on the
sample complexity (aka number of queries), and propose an algorithm that is
sample-complexity-optimal up to an $O(\log(k+l)/\log{k})$ factor. When $l=2$
(i.e., pairwise comparisons) or $l=O(poly(k))$, this algorithm matches the
lower bound. For the PAC total ranking problem, we derive a tight lower bound,
and propose an algorithm that matches the lower bound. When $l=2$, the MNL
model reduces to the popular Plackett-Luce (PL) model. In this setting, our
results still outperform the state-of-the-art both theoretically and
numerically. We also compare our algorithms with the state-of-the-art using
synthetic data as well as real-world data to verify the efficiency of our
algorithms.

2
The categories of this paper are: math
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th