A variance-reduced cubic Newton method with homotopy refinement finds (ε, √(L₂ε))-SOSP in finite-sum non-convex problems with total oracle complexity n + Õ(n^{1/2} ε^{-3/2}) under average smoothness assumptions.
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Decentralized Cubic Newton method for convex optimization that matches exact centralized iteration complexity with polylogarithmic extra communication rounds under gradient L1-smoothness and Hessian L2-Lipschitz continuity.
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Cubic Regularized Newton Method with Variance Reduction for Finite-sum Non-convex Problems
A variance-reduced cubic Newton method with homotopy refinement finds (ε, √(L₂ε))-SOSP in finite-sum non-convex problems with total oracle complexity n + Õ(n^{1/2} ε^{-3/2}) under average smoothness assumptions.
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Decentralized Inexact Cubic Newton Method with Consensus Procedure
Decentralized Cubic Newton method for convex optimization that matches exact centralized iteration complexity with polylogarithmic extra communication rounds under gradient L1-smoothness and Hessian L2-Lipschitz continuity.