  We consider the off-policy evaluation (OPE) problem in contextual bandits,
where the goal is to estimate the value of a target policy using the data
collected by a logging policy. Most popular approaches to the OPE are variants
of the doubly robust (DR) estimator obtained by combining a direct method (DM)
estimator and a correction term involving the inverse propensity score (IPS).
Existing algorithms primarily focus on strategies to reduce the variance of the
DR estimator arising from large IPS. We propose a new approach called the
Doubly Robust with Information borrowing and Context-based switching (DR-IC)
estimator that focuses on reducing both bias and variance. The DR-IC estimator
replaces the standard DM estimator with a parametric reward model that borrows
information from the 'closer' contexts through a correlation structure that
depends on the IPS. The DR-IC estimator also adaptively interpolates between
this modified DM estimator and a modified DR estimator based on a
context-specific switching rule. We give provable guarantees on the performance
of the DR-IC estimator. We also demonstrate the superior performance of the
DR-IC estimator compared to the state-of-the-art OPE algorithms on a number of
benchmark problems.
