## Online Density Estimation of Bradley-Terry Models

author: Eiji Takimoto, Department of Informatics, Kyushu University
published: Aug. 20, 2015,   recorded: July 2015,   views: 30
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# Description

We consider an online density estimation problem for Bradley-Terry models which determine the probability of a match result between any pair in the set of $n$ teams. An annoying issue is that the loss function is not convex. A standard solution to avoid the non-convexity is to change variables so that the new loss function w.r.t.new variables is convex. But, then the radius $K$ of the new domain might be huge or infinite in general. When $K$ is regarded as a constant, standard algorithms OGD and ONS have regret bounds $O(n^{\frac{1}{2}}(\ln K)\sqrt{T})$ and $O(n^{\frac{3}{2}}K\ln T)$, respectively.