论文标题
始终有效的在线矩阵完成的风险监控
Always Valid Risk Monitoring for Online Matrix Completion
论文作者
论文摘要
始终将注意力集中的不平等越来越多地用作在线统计学习的绩效指标，尤其是在学习生成模型和监督学习中。这种不平等通过允许在离线统计学习中随机，适应性选择的样本大小而不是固定的预指定尺寸来提高在线学习算法设计。但是，为矩阵完成任务建立这种始终存在类型的结果是具有挑战性的，并且在文献中远没有理解。由于这种类型的结果的重要性，这项工作为在线矩阵完成问题建立并设计了始终存在的风险绑定过程。这种理论上的进步是通过非染色的martingale浓度和正则低级矩阵回归的新型组合来实现的。我们的结果使更有效的在线算法设计可以评估在线矩阵完成任务的在线实验策略的基础。
Always-valid concentration inequalities are increasingly used as performance measures for online statistical learning, notably in the learning of generative models and supervised learning. Such inequality advances the online learning algorithms design by allowing random, adaptively chosen sample sizes instead of a fixed pre-specified size in offline statistical learning. However, establishing such an always-valid type result for the task of matrix completion is challenging and far from understood in the literature. Due to the importance of such type of result, this work establishes and devises the always-valid risk bound process for online matrix completion problems. Such theoretical advances are made possible by a novel combination of non-asymptotic martingale concentration and regularized low-rank matrix regression. Our result enables a more sample-efficient online algorithm design and serves as a foundation to evaluate online experiment policies on the task of online matrix completion.
