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