Online Linear Optimization with the Log-Determinant Regularizer
نویسندگان
چکیده
منابع مشابه
Online linear optimization with the log-determinant regularizer
We consider online linear optimization over symmetric positive semidefinite matrices, which has various applications including the online collaborative filtering. The problem is formulated as a repeated game between the algorithm and the adversary, where in each round t the algorithm and the adversary choose matrices Xt and Lt, respectively, and then the algorithm suffers a loss given by the Fr...
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Now, let us consider the case ofK = Kb with b ∈ (1,∞). For v ∈ R andQ ⊆ [d], let vQ denote the 6 projection of v to those dimensions inQ. Then for any v ∈ R, and any w ∈ Kb withQ = {i : wi 6= 7 0}, we know by Hölder’s inequality that 〈w,v〉 = 〈wQ,vQ〉 ≥ −‖w‖b · ‖vQ‖a , for a = b/(b− 1). 8 Moreover, one can have 〈wQ,vQ〉 = −‖w‖b · ‖vQ‖a , when |wi| /‖w‖b = |vi|/‖v‖a and 9 wivi ≤ 0 for every i ∈ Q. ...
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ژورنال
عنوان ژورنال: IEICE Transactions on Information and Systems
سال: 2018
ISSN: 0916-8532,1745-1361
DOI: 10.1587/transinf.2017edp7317