Distributionally Robust Optimization via Ball Oracle Acceleration

Abstract

We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that queries a ball optimization oracle, i.e., a subroutine that minimizes the objective within a small ball around the query point. Our main contribution is efficient implementations of this oracle for DRO objectives. For DRO with $N$ non-smooth loss functions, the resulting algorithms find an $\epsilon$-accurate solution with $\tilde{O}\left(N{\epsilon }^{-2/3}+{\epsilon }^{-2}\right)$ first-order oracle queries to individual loss functions. Compared to existing algorithms for this problem, we improve complexity by a factor of up to ${\epsilon }^{-4/3}$.