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Marginal Density Ratio for Off-Policy Evaluation in Contextual Bandits
Muhammad Faaiz Taufiq · Arnaud Doucet · Rob Cornish · Jean-Francois Ton

Thu Dec 14 08:45 AM -- 10:45 AM (PST) @ Great Hall & Hall B1+B2 #1013
Off-Policy Evaluation (OPE) in contextual bandits is crucial for assessing new policies using existing data without costly experimentation. However, current OPE methods, such as Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators, suffer from high variance, particularly in cases of low overlap between target and behaviour policies or large action and context spaces. In this paper, we introduce a new OPE estimator for contextual bandits, the Marginal Ratio (MR) estimator, which focuses on the shift in the marginal distribution of outcomes $Y$ instead of the policies themselves. Through rigorous theoretical analysis, we demonstrate the benefits of the MR estimator compared to conventional methods like IPW and DR in terms of variance reduction. Additionally, we establish a connection between the MR estimator and the state-of-the-art Marginalized Inverse Propensity Score (MIPS) estimator, proving that MR achieves lower variance among a generalized family of MIPS estimators. We further illustrate the utility of the MR estimator in causal inference settings, where it exhibits enhanced performance in estimating Average Treatment Effects (ATE). Our experiments on synthetic and real-world datasets corroborate our theoretical findings and highlight the practical advantages of the MR estimator in OPE for contextual bandits.

Author Information

Muhammad Faaiz Taufiq (University of Oxford)
Arnaud Doucet (Oxford)
Rob Cornish (University of Oxford)
Jean-Francois Ton (Bytedance)

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