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We consider a variant of online binary classification where a learnersequentially assigns labels ($0$ or $1$) to items with unknown true class. If,but only if, the learner chooses label $1$ they immediately observe the truelabel of the item. The learner faces a trade-off between short-termclassification accuracy and long-term information gain. This problem haspreviously been studied under the name of the `apple tasting' problem. Werevisit this problem as a partial monitoring problem with side information, andfocus on the case where item features are linked to true classes via a logisticregression model. Our principal contribution is a study of the performance ofThompson Sampling (TS) for this problem. Using recently developedinformation-theoretic tools, we show that TS achieves a Bayesian regret boundof an improved order to previous approaches. Further, we experimentally verifythat efficient approximations to TS and Information Directed Sampling viaP\'{o}lya-Gamma augmentation have superior empirical performance to existingmethods.

Apple Tasting Revisited: Bayesian Approaches to Partially Monitored Online Binary Classification