Variance Reduced Advantage Estimation with $\delta$ Hindsight Credit Assignment

Hindsight Credit Assignment (HCA) refers to a recently proposed family of methods for producing more efficient credit assignment in reinforcement learning. These methods work by explicitly estimating the probability that certain actions were taken in the past given present information. Prior work has studied the properties of such methods and demonstrated their behaviour empirically. We extend this work by introducing a particular HCA algorithm which has provably lower variance than the conventional Monte-Carlo estimator when the necessary functions can be estimated exactly. This result provides a strong theoretical basis for how HCA could be broadly useful.