We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing, with a focus on functionals that arise in causal inference. We study the setting where probability distributions are not known a priori but need to be estimated from data. These estimated distributions lead to empirical Gateaux derivatives, and we study the relationships between empirical, numerical, and analytical Gateaux derivatives.

We additionally assume that the agent cannot interact with the environment but has access to the action-labeled transition data collected by some agents with unknown qualities.

Long-term fairness is an important factor of consideration in designing and deploying learning-based decision systems in high-stake decision-making contexts.