Talk
Maximum Selection and Ranking under Noisy Comparisons
Moein Falahatgar · Alon Orlitsky · Venkatadheeraj Pichapati · Ananda Theertha Suresh
C4.1
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Abstract
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Abstract:
We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking
using pairwise comparisons for \nobreak{general} probabilistic models whose
comparison probabilities satisfy strong stochastic
transitivity and stochastic triangle inequality.
Modifying the popular knockout tournament, we propose a simple
maximum-selection algorithm that uses $\mathcal{O}\left(\frac{n}{\epsilon^2}
\left(1+\log \frac1{\delta}\right)\right)$ comparisons, optimal up to a constant
factor. We then derive a general framework that uses noisy binary
search to speed up many ranking algorithms, and
combine it with merge sort to obtain a ranking algorithm that uses
$\mathcal{O}\left(\frac n{\epsilon^2}\log n(\log \log n)^3\right)$ comparisons
for $\delta=\frac1n$, optimal up to a $(\log \log n)^3$ factor.
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