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Distributionally Robust Optimization via Ball Oracle Acceleration

Yair Carmon · Danielle Hausler

Hall J (level 1) #837

Keywords: [ Monteiro-Svaiter acceleration ] [ Distributionally Robust Optimization ] [ Oracle complexity ] [ multilevel monte-carlo ] [ algorithm design ] [ Convex Optimization ] [ entropy regularization ] [ accelerated methods ] [ Theory ]

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 $\widetilde{O}\left(N\epsilon^{-2/3} + \epsilon^{-2}\right)$ first-order oracle queries to individual loss functions. Compared to existing algorithms for this problem, we improve complexity by a factor of up to $\epsilon^{-4/3}$.

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