  We study the problem of best arm identification with a fairness constraint in
a given causal model. The goal is to find a soft intervention on a given node
to maximize the outcome while meeting a fairness constraint by counterfactual
estimation with only partial knowledge of the causal model. The problem is
motivated by ensuring fairness on an online marketplace. We provide theoretical
guarantees on the probability of error and empirically examine the
effectiveness of our algorithm with a two-stage baseline.
