Statistical Parity with Exponential Weights

Statistical parity is one of the most foundational constraints in algorithmic fairness and privacy. In this paper, we show that statistical parity can be enforced efficiently in the contextual bandit setting while retaining strong performance guarantees. Specifically, we present a meta-algorithm that transforms any efficient implementation of Hedge (or, equivalently, any discrete Bayesian inference algorithm) into an efficient contextual bandit algorithm that guarantees exact statistical parity on every trial. Compared to any comparator that satisfies the same statistical parity constraint, the algorithm achieves the same asymptotic regret bound as running the equivalent instance of Exp4 for each group. We also address the scenario where the target parity distribution is unknown and must be estimated online. Finally, using online-to-batch conversion, we extend our approach to the batch classification setting - achieving exact statistical parity there as well, whilst attaining excellent generalisation bounds. We believe these batch bounds to be a significant contribution to the literature in their own right.