We propose deviation-based learning, a new approach to training recommender systems. In the beginning, the recommender and rational users have different pieces of knowledge, and the recommender needs to learn the users' knowledge to make better recommendations. The recommender learns users' knowledge by observing whether each user followed or deviated from her recommendations. We show that learning frequently stalls if the recommender always recommends a choice: users tend to follow the recommendation blindly, and their choices do not reflect their knowledge. Social welfare and the learning rate are improved drastically if the recommender abstains from recommending a choice when she predicts that multiple arms will produce a similar payoff.

The extensive use of private and personally identifiable information in modern statistical (and machine learning) applications can present an obstacle to individuals contributing their data to research. As just one example, when considering contribution to biobanks Kaufman et al. (2009) reported 90% of respondents had privacy concerns. Addressing these concerns is paramount if the participation rate in biomedical and genetic research is to be increased, especially for government and industry where public trust is lower (Kaufman et al., 2009). Indeed, industry is on the brink on embarking on biomedical applications on a scale never before witnessed via the impending wave of so-called'wearable devices' such as smart watches, which present serious privacy concerns. Companies hope to market the ability to monitor and track vital health signs round the clock, perhaps fitting classification models to alert different health concerns of interest.