Opposite Online Learning via Sequentially Integrated Stochastic Gradient Descent Estimators

Stochastic gradient descent algorithm (SGD) has been popular in various fields of artificial intelligence as well a prototype online learning algorithms. This article proposes novel and general framework one-sided testing for streaming data based on SGD, which determines whether the unknown parameter is greater than certain positive constant. We construct online-updated test statistic sequentially by integrating selected batch-specific estimator or its opposite, referred to opposite learning. The estimators are chosen strategically according proposed sequential tactics designed two-armed bandit process. Theoretical results prove advantage strategy ensuring distribution be optimal under null hypothesis also supply theoretical evidence power enhancement compared with classical statistic. In application, method appealing statistical inference because it scalable any model. Finally, superior finite-sample performance evaluated simulation studies.