DR-FERMI is a distributionally robust stochastic optimization framework for handling distribution shifts in fair empirical risk minimization tasks. The distribution shift happens when the distribution of the test data (target domain) is different from the distribution of the training data (source domain). The main advantage of DR-FERMI over the previous methods is that it does not assume the availability of the causal graph describing the interaction of non-sensitive predictors, sensitive attributes, and the target variable. Further, we do not consider specific types of distribution shifts such as demographic shifts, covariate shifts, or label shifts in formulating the problem and developing algorithms.
A common assumption of algorithmic fairness approaches is that the training data has the same distribution as the test data. However, such an assumption might not hold in many practical problems. For instance, ACS PUMS Data is a collection of new datasets distributed over different states. Learning a fair model (demographic parity of equalized odds) in one US state, such as California, does not guarantee that the model remains fair in other states. In other words, fairness is not transferable from the source domain (training data) to the target domain (test data) when the distribution of the data shifts in the test phase.
The Distributionally Robust Fair Empirical Risk Minimization with Exponential Renyi Mutual Information (ERMI) as the measure of fairness violation seeks to optimize the following problem:
Where the uncertainty set over the matrix Q is defined as Lp balls around the empirical Q estimated by the training data:
The implementation of DR-FERMI on the ACS Data for L1 and L2 norms are avalable at DR-FERMI_ACS Data.ipynb notebook. One can consider each one of the US states as the training data and learn the fair model on that dataset. The evaluation will be done at each 10 epochs on all states. The results on 4 different datasets as the training data is depicted below. For more experiments and plots please see the paper.
