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.
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