Mathematics

Economic growth

Gene

Statistics

Mathematical optimization

Regular polygon

Covariate

Probability distribution

Limit (mathematics)

Convex optimization

Mathematical analysis

Minimax

Econometrics

Economics

Chemistry

Robust optimization

Geometry

Convergence (economics)

Computer science

Biochemistry

Robustness (evolution)

The Annals of Statistics

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 providing good performance against perturbations to the data-generating distribution. We give a convex formulation for the problem, providing several convergence guarantees. We prove finite-sample minimax upper and lower bounds, showing that distributional 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.

Learning models with uniform performance via distributionally robust optimization