Additive Control Variates Dominate Self-Normalisation in Off-Policy Evaluation

TL;DR

This paper proves that additive control variates outperform self-normalisation in off-policy evaluation, providing theoretical justification for shifting to optimal baseline corrections.

Contribution

It establishes that $eta^ extstar$-IPS with an optimal additive baseline asymptotically dominates SNIPS in mean squared error, filling a theoretical gap.

Findings

$eta^ extstar$-IPS asymptotically dominates SNIPS in MSE

SNIPS is equivalent to a sub-optimal additive baseline

Theoretical analysis justifies using optimal baseline corrections

Abstract

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 $\beta^\star$-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.