Always Valid Risk Monitoring for Online Matrix Completion

We consider an online matrix completion problem with continuous monitoring, a setting where decision-makers seek to recover a structured matrix from noisy partial measurements (matrix completion), while the decision-makers are allowed to terminate the experiment whenever they wish, and the result still maintains statistical validity (continuous monitoring). Such a setting arises naturally in industrial practice but remains challenging in the literature, preventing practitioners from effectively deploying matrix completion methodology in modern online service industries. Risk control of learned models in continuously-monitored online experiments is in emerging demand from industrial practice because the opportunity cost of lengthy experiments is high and regrettable (Johari et al. [2021]). Indeed, it is desirable to detect the true effect size as quickly as possible, or to abolish the running experiment if the effect appears unpromising so that scientists may test other available actions. Besides, optimizing the running time in advance is unfortunately impractical due to the lack in prior knowledge on the seeking effect size and cost elasticity. In modern online experiment practice, the deployment of online statistical learning methodology turns out to be impeded by such dynamic trade-off between maximum effect detection and minimum running time. Resolving such dynamic trade-off is a crucial advancement of real-time data learning methodology, which is pioneered by Wang et al. [2020] in the dynamic pricing setting, but it still remains an open question in the setting of online matrix completion problems.