  Off-policy evaluation (OPE) aims to estimate the benefit of following a
counterfactual sequence of actions, given data collected from executed
sequences. However, existing OPE estimators often exhibit high bias and high
variance in problems involving large, combinatorial action spaces. We
investigate how to mitigate this issue using factored action spaces i.e.
expressing each action as a combination of independent sub-actions from smaller
action spaces. This approach facilitates a finer-grained analysis of how
actions differ in their effects. In this work, we propose a new family of
"decomposed" importance sampling (IS) estimators based on factored action
spaces. Given certain assumptions on the underlying problem structure, we prove
that the decomposed IS estimators have less variance than their original
non-decomposed versions, while preserving the property of zero bias. Through
simulations, we empirically verify our theoretical results, probing the
validity of various assumptions. Provided with a technique that can derive the
action space factorisation for a given problem, our work shows that OPE can be
improved "for free" by utilising this inherent problem structure.
