Additive Control Variates Dominate Self-Normalisation in Off-Policy Evaluation
This provides a theoretical justification for shifting from self-normalization to optimal baseline corrections, potentially improving evaluation accuracy in ranking and recommendation systems.
The paper tackled the problem of variance reduction in off-policy evaluation for ranking and recommendation systems, proving that an estimator with an optimal additive baseline asymptotically dominates the standard self-normalized method in Mean Squared Error.
Off-policy evaluation (OPE) is essential for assessing ranking and recommendation systems without costly online interventions. Self-Normalised Inverse Propensity Scoring (SNIPS) is a standard tool for variance reduction in OPE, leveraging a multiplicative control variate. Recent advances in off-policy learning suggest that additive control variates (baseline corrections) may offer superior performance, yet theoretical guarantees for evaluation are lacking. This paper provides a definitive answer: we prove that $β^\star$-IPS, an estimator with an optimal additive baseline, asymptotically dominates SNIPS in Mean Squared Error. By analytically decomposing the variance gap, we show that SNIPS is asymptotically equivalent to using a specific -- but generally sub-optimal -- additive baseline. Our results theoretically justify shifting from self-normalisation to optimal baseline corrections for both ranking and recommendation.