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Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexity

NeurIPS 2022 · Optimization › Nonconvex and smooth optimization · approach: Complexity of nonconvex first-order methods

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use adaptive selection of component functions with combined cutting-plane and interior-point updatesDecomposable convex optimization · Decomposable convex optimizationgradient oracle calls: O(nd \log(1/\epsilon)) -> O(m\log(m/\epsilon))Helped
Apply the proposed decomposable optimization algorithm to decomposable submodular minimizationDecomposable submodular minimization · Decomposable submodular minimizationevaluation oracle calls: \widetilde{O}(n k^6 \log (1/\epsilon)) -> O(n k^2 \log(nk/\epsilon))Helped

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