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info.json
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{
"abstract": "We consider a contextual online learning (multi-armed bandit) problem with high-dimensional covariate $x$ and decision $y$. The reward function to learn, $f(x,y)$, does not have a particular parametric form. The literature has shown that the optimal regret is $\\tilde{O}(T^{(d_x\\!+\\!d_y\\!+\\!1)/(d_x\\!+\\!d_y\\!+\\!2)})$, where $d_x$ and $d_y$ are the dimensions of $x$ and $y$, and thus it suffers from the curse of dimensionality. In many applications, only a small subset of variables in the covariate affect the value of $f$, which is referred to as sparsity in statistics. To take advantage of the sparsity structure of the covariate, we propose a variable selection algorithm called BV-LASSO, which incorporates novel ideas such as binning and voting to apply LASSO to nonparametric settings. Using it as a subroutine, we can achieve the regret $\\tilde{O}(T^{(d_x^*\\!+\\!d_y\\!+\\!1)/(d_x^*\\!+\\!d_y\\!+\\!2)})$, where $d_x^*$ is the effective covariate dimension. The regret matches the optimal regret when the covariate is $d^*_x$-dimensional and thus cannot be improved. Our algorithm may serve as a general recipe to achieve dimension reduction via variable selection in nonparametric settings.",
"authors": [
"Wenhao Li",
"Ningyuan Chen",
"L. Jeff Hong"
],
"emails": [
"zjuliwenhao@gmail.com",
"ningyuan.chen@utoronto.ca",
"hong_liu@fudan.edu.cn"
],
"id": "21-0818",
"issue": 136,
"pages": [
1,
84
],
"title": "Dimension Reduction in Contextual Online Learning via Nonparametric Variable Selection",
"volume": 24,
"year": 2023
}