  Distributionally robust optimization (DRO) can improve the robustness and
fairness of learning methods. In this paper, we devise stochastic algorithms
for a class of DRO problems including group DRO, subpopulation fairness, and
empirical conditional value at risk (CVaR) optimization. Our new algorithms
achieve faster convergence rates than existing algorithms for multiple DRO
settings. We also provide a new information-theoretic lower bound that implies
our bounds are tight for group DRO. Empirically, too, our algorithms outperform
known methods
