Learning from eXtreme bandit feedback

We study the problem of batch learning from bandit feedback in the setting of extremely large action spaces. Learning from extreme bandit feedback is ubiquitous in recommendation systems, in which billions of decisions are made over millions of choices in a single day, yielding massive observational data. In these large-scale real-world applications, supervised learning approaches such as eXtreme Multi-label Classification (XMC) remain the standard approach despite the bias inherent in the data collection process. Conversely, previously developed importance sampling approaches are unbiased but suffer from impractical variance when dealing with a large number of actions. In this paper, we introduce a selective importance sampling estimator (sIS) with more favorable bias-variance tradeoff. Specifically, sIS is obtained by performing importance sampling on the conditional expectation of the reward with respect to a small subset of actions for each instance (a form of Rao-Blackwellization). We employ this estimator in a novel algorithmic procedure—named Policy Optimization for eXtreme Models (POXM)—for learning from bandit feedback on XMC tasks. In POXM, the selected actions for the sIS estimator are the top-p actions of the logging policy, where p is adjusted from the data and is significantly smaller than the size of the action space. We use a supervised-to-bandit conversion on three XMC datasets to benchmark our POXM method against BanditNet, a previously applied partial matching pruning strategy as well as a supervised learning baseline. Whereas BanditNet sometimes improves marginally over the logging policy, our experiments show that POXM systematically and significantly improves over all baselines.