Recent advances have enabled oracle classifiers that can classify across many classes and input distributions with high accuracy without retraining. However, these classifiers are relatively heavyweight, so that applying them to classify video is costly. We show that day-to-day video exhibits highly skewed class distributions over the short term, and that these distributions can be classified by much simpler models. We formulate the problem of detecting the short-term skews online and exploiting models based on it as a new sequential decision making problem dubbed the Online Bandit Problem, and present a new algorithm to solve it. When applied to recognizing faces in TV shows and movies, we realize end-to-end classification speedups of 2.4-7.8x/2.6-11.2x (on GPU/CPU) relative to a state-of-the-art convolutional neural network, at competitive accuracy.