Control Variates for Slate Off-Policy Evaluation

TL;DR

This paper introduces new control variate-based estimators for off-policy evaluation in slate recommendation systems, improving accuracy over existing methods by optimizing estimator risk.

Contribution

It develops a broad class of unbiased estimators using control variates, including and extending the pseudoinverse estimator, with theoretical risk guarantees.

Findings

New estimators outperform PI and self-normalized PI in experiments

The approach provides risk improvement guarantees

Validated on real-world and synthetic data

Abstract

We study the problem of off-policy evaluation from batched contextual bandit data with multidimensional actions, often termed slates. The problem is common to recommender systems and user-interface optimization, and it is particularly challenging because of the combinatorially-sized action space. Swaminathan et al. (2017) have proposed the pseudoinverse (PI) estimator under the assumption that the conditional mean rewards are additive in actions. Using control variates, we consider a large class of unbiased estimators that includes as specific cases the PI estimator and (asymptotically) its self-normalized variant. By optimizing over this class, we obtain new estimators with risk improvement guarantees over both the PI and the self-normalized PI estimators. Experiments with real-world recommender data as well as synthetic data validate these improvements in practice.