In display advertising, predicting the conversion rate, that is, the probability that a user takes a predefined action on an advertiser's website, such as purchasing goods is fundamental in estimating the value of displaying the advertisement. However, there is a relatively long time delay between a click and its resultant conversion. Because of the delayed feedback, some positive instances at the training period are labeled as negative because some conversions have not yet occurred when training data are gathered. As a result, the conditional label distributions differ between the training data and the production environment. This situation is referred to as a feedback shift. We address this problem by using an importance weight approach typically used for covariate shift correction. We prove its consistency for the feedback shift. Results in both offline and online experiments show that our proposed method outperforms the existing method.

What is the most statistically efficient way to do off-policy optimization with batch data from bandit feedback? For log data generated by contextual bandit algorithms, we consider offline estimators for the expected reward from a counterfactual policy. Our estimators are shown to have lowest variance in a wide class of estimators, achieving variance reduction relative to standard estimators. We then apply our estimators to improve advertisement design by a major advertisement company. Consistent with the theoretical result, our estimators allow us to improve on the existing bandit algorithm with more statistical confidence compared to a state-of-theart benchmark.

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