Learning Models with Uniform Performance via Distributionally Robust Optimization

A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that learns a model that provides good performance against perturbations to the data-generating distribution. We give a convex optimization formulation for the problem, providing several convergence guarantees. We prove finite-sample minimax upper and lower bounds, showing that distributinoal robustness sometimes comes at a cost in convergence rates. We give limit theorems for the learned parameters, where we fully specify the limiting distribution so that confidence intervals can be computed. On real tasks including generalizing to unknown subpopulations, fine-grained recognition, and providing good tail performance, the distributionally robust approach often exhibits improved performance.