2020/12/10 by Yaxiong Liu, Liu, Yaxiong, Ken-ichiro Moridomi +5
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC) #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2012.05632
openalex publication_date 2020/12/10 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28
We consider a variant of online semi-definite programming problem (OSDP): The decision space consists of semi-definite matrices with bounded Γ-trace norm, which is a generalization of trace norm defined by a positive definite matrix Γ. To solve this problem, we utilise the follow-the-regularized-leader algorithm with a Γ-dependent log-determinant regularizer. Then we apply our generalised setting and our proposed algorithm to online matrix completion(OMC) and online similarity prediction with side information. In particular, we reduce the online matrix completion problem to the generalised OSDP problem, and the side information is represented as the Γ matrix. Hence, due to our regret bound for the generalised OSDP, we obtain an optimal mistake bound for the OMC by removing the logarithmic factor.