Dr. FERMI: A Stochastic Distributionally Robust Fair Empirical Risk Minimization Framework

Abstract

While training fair machine learning models has been studied extensively in recent years, most developed methods rely on the assumption that the training and test data have similar distributions. In the presence of distribution shifts, fair models may behave unfairly on test data. There have been some developments for fair learning robust to distribution shifts to address this shortcoming. However, most proposed solutions are based on the assumption of having access to the causal graph describing the interaction of different features. Moreover, existing algorithms require full access to data and cannot be used when small batches are used (stochastic/batch implementation). This paper proposes the first stochastic distributionally robust fairness framework with convergence guarantees that do not require knowledge of the causal graph. More specifically, we formulate the fair inference in the presence of the distribution shift as a distributionally robust optimization problem under $L_p$ norm uncertainty sets with respect to the Exponential Renyi Mutual Information (ERMI) as the measure of fairness violation. We then discuss how the proposed method can be implemented in a stochastic fashion. We have evaluated the presented framework's performance and efficiency through extensive experiments on real datasets consisting of distribution shifts.