Apple Tasting Revisited: Bayesian Approaches to Partially Monitored Online Binary Classification
Abstract
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 Pólya-Gamma augmentation have superior empirical performance to existing methods.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.14412
- arXiv:
- arXiv:2109.14412
- Bibcode:
- 2021arXiv210914412G
- Keywords:
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- Computer Science - Machine Learning
- E-Print:
- Update to Theorem 1 and experimental work