  Machine learning models (e.g., speech recognizers) are usually trained to
minimize average loss, which results in representation disparity---minority
groups (e.g., non-native speakers) contribute less to the training objective
and thus tend to suffer higher loss. Worse, as model accuracy affects user
retention, a minority group can shrink over time. In this paper, we first show
that the status quo of empirical risk minimization (ERM) amplifies
representation disparity over time, which can even make initially fair models
unfair. To mitigate this, we develop an approach based on distributionally
robust optimization (DRO), which minimizes the worst case risk over all
distributions close to the empirical distribution. We prove that this approach
controls the risk of the minority group at each time step, in the spirit of
Rawlsian distributive justice, while remaining oblivious to the identity of the
groups. We demonstrate that DRO prevents disparity amplification on examples
where ERM fails, and show improvements in minority group user satisfaction in a
real-world text autocomplete task.
