Distributionally Robust Optimization via Ball Oracle Acceleration
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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 ϵ-accurate solution with O(Nϵ^-2/3 + ϵ^-2) first-order oracle queries to individual loss functions. Compared to existing algorithms for this problem, we improve complexity by a factor of up to ϵ^-4/3.
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