Counterfactual Ranking Evaluation with Flexible Click Models

Evaluating a new ranking policy using data logged by a previously deployed policy requires a counterfactual (off-policy) estimator that corrects for presentation and selection biases. Some estimators (e.g., the position-based model) perform this correction by making strong assumptions about user behavior, which can lead to high bias if the assumptions are not met. Other estimators (e.g., the itemposition model) rely on randomization to avoid these assumptions, but they often suffer from high variance. In this paper, we develop a new counterfactual estimator, called Interpol, that provides a tunable trade-off in the assumptions it makes, thus providing a novel ability to optimize the bias-variance trade-off. We analyze the bias of our estimator, both theoretically and empirically, and show that it achieves lower error than both the position-based model and the item-position model, on both synthetic and real datasets. This improvement in accuracy not only benefits offline evaluation of ranking policies, we also find that Interpol improves learning of new ranking policies when used as the training objective for learning-to-rank.