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Problem-Parameter-Free Decentralized Nonconvex Stochastic Optimization

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arxiv 2402.08821 v1 pith:5ZIH5DLR submitted 2024-02-13 math.OC cs.DC

Jiaxiang Li , Xuxing Chen , Shiqian Ma , Mingyi Hong This is my paper
classification math.OCcs.DC
keywords decentralizedknowledgenonconvexusuallyd-nasaoptimizationparametersproblem
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Existing decentralized algorithms usually require knowledge of problem parameters for updating local iterates. For example, the hyperparameters (such as learning rate) usually require the knowledge of Lipschitz constant of the global gradient or topological information of the communication networks, which are usually not accessible in practice. In this paper, we propose D-NASA, the first algorithm for decentralized nonconvex stochastic optimization that requires no prior knowledge of any problem parameters. We show that D-NASA has the optimal rate of convergence for nonconvex objectives under very mild conditions and enjoys the linear-speedup effect, i.e. the computation becomes faster as the number of nodes in the system increases. Extensive numerical experiments are conducted to support our findings.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Affine W-certificate bundle-level methods (BLW/A-BLW) attain optimal parameter-free rates under unknown Hölder smoothness and growth for convex first-order optimization.

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    New adaptive decentralized algorithms select stepsizes from local curvature estimates derived from a Lyapunov function, delivering sublinear convergence for convex problems and linear rates for strongly convex ones.

  3. Adaptive Stepsize Selection in Decentralized Convex Optimization

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    A fully local adaptive step-size scheme achieves linear (strongly convex) and sublinear (convex) convergence rates, matching tuned nonadaptive decentralized methods.

  4. Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach

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    A projection-based zeroth-order federated learning algorithm on Riemannian manifolds achieves sublinear convergence with linear speedup, using only Euclidean random perturbations.

  5. A Parameter-free Decentralized Algorithm for Composite Convex Optimization

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    A local backtracking rule for stepsizes in decentralized composite convex optimization is shown to preserve robust convergence without global network information.

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