论文标题
用于在线半准编程及其应用程序的广义日志确定规则
A generalised log-determinant regularizer for online semi-definite programming and its applications
论文作者
论文摘要
我们考虑了在线半准编程问题（OSDP）的变体：决策空间由具有限制的$γ$ - 跟踪规范的半定量矩阵组成，这是由积极确定的矩阵$γ定义的痕量规范的概括。然后，我们将广义设置和提议的算法应用于在线矩阵完成（OMC）以及与附带信息的在线相似性预测。特别是，我们将在线矩阵完成问题减少到广义OSDP问题，侧面信息表示为$γ$矩阵。因此，由于我们对广义OSDP的遗憾，我们通过删除对数因素获得了一个最佳的OMC绑定的错误。
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.
