  In real-world recommender systems and search engines, optimizing ranking
decisions to present a ranked list of relevant items is critical. Off-policy
evaluation (OPE) for ranking policies is thus gaining a growing interest
because it enables performance estimation of new ranking policies using only
logged data. Although OPE in contextual bandits has been studied extensively,
its naive application to the ranking setting faces a critical variance issue
due to the huge item space. To tackle this problem, previous studies introduce
some assumptions on user behavior to make the combinatorial item space
tractable. However, an unrealistic assumption may, in turn, cause serious bias.
Therefore, appropriately controlling the bias-variance tradeoff by imposing a
reasonable assumption is the key for success in OPE of ranking policies. To
achieve a well-balanced bias-variance tradeoff, we propose the Cascade Doubly
Robust estimator building on the cascade assumption, which assumes that a user
interacts with items sequentially from the top position in a ranking. We show
that the proposed estimator is unbiased in more cases compared to existing
estimators that make stronger assumptions. Furthermore, compared to a previous
estimator based on the same cascade assumption, the proposed estimator reduces
the variance by leveraging a control variate. Comprehensive experiments on both
synthetic and real-world data demonstrate that our estimator leads to more
accurate OPE than existing estimators in a variety of settings.
