Optimal and Adaptive Off-policy Evaluation in Contextual Bandits
This addresses the challenge of evaluating policies in contextual bandits for applications like recommendation systems, though it is incremental as it builds on existing estimators.
The paper tackles the off-policy evaluation problem in contextual bandits without a consistent reward model, establishing a minimax lower bound on mean squared error that is matched by IPS and DR estimators, and proposes the SWITCH estimator that empirically outperforms prior methods by orders of magnitude.
We study the off-policy evaluation problem---estimating the value of a target policy using data collected by another policy---under the contextual bandit model. We consider the general (agnostic) setting without access to a consistent model of rewards and establish a minimax lower bound on the mean squared error (MSE). The bound is matched up to constants by the inverse propensity scoring (IPS) and doubly robust (DR) estimators. This highlights the difficulty of the agnostic contextual setting, in contrast with multi-armed bandits and contextual bandits with access to a consistent reward model, where IPS is suboptimal. We then propose the SWITCH estimator, which can use an existing reward model (not necessarily consistent) to achieve a better bias-variance tradeoff than IPS and DR. We prove an upper bound on its MSE and demonstrate its benefits empirically on a diverse collection of data sets, often outperforming prior work by orders of magnitude.