Efficient Offline Learning of Ranking Policies via Top-$k$ Policy Decomposition

Abstract

Many recommender systems such as for e-commerce and news platforms aim to provide users with rankings they are likely to interact with. Off-Policy Learning (OPL) of ranking policies enables us to learn new ranking policies using only historical logged data. However, ranking settings make OPL remarkably challenging because their action spaces consist of permutations of unique items, being extremely large. Existing methods primarily use either policy- or regression-based approaches. The policy-based approach, which typically uses importance-weighted policy gradients, can suffer from high variance due to large action spaces. The regression-based approach, on the other hand, estimates the expected reward using conventional machine learning methods, avoiding variance issues but potentially suffering from severe bias. To circumvent these issues of existing methods, we propose a new OPL method for ranking, named Ranking Policy Optimization via Top-$k$ Policy Decomposition (R-POD), which combines the policy- and regression-based approaches in an effective fashion. Specifically, R-POD decomposes a ranking policy into a first-stage policy for selecting top-$k$ actions and a second-stage policy for choosing the bottom actions given the top-$k$ actions. It learns the first-stage policy using a new policy gradient estimator and the second-stage policy via the regression-based approach. This method can substantially reduce variance, since it applies importance weighting only to the top-$k$ actions. We also demonstrate that our policy-gradient estimator for the first-stage policy is unbiased under a conditional pairwise correctness condition, which only requires that the expected reward differences of pairs of rankings sharing the same top-$k$ actions can be estimated correctly.