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Communication Acceleration of Local Gradient Methods via an Accelerated Primal-Dual Algorithm with an Inexact Prox

NeurIPS 2022 · Optimization › Nonconvex and smooth optimization · approach: Acceleration and Nesterov dynamics

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use FGD+GD instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox · Centralized federated optimizationlocal steps per round: \widetilde{\mathcal{O}}\left(\sqrt{\kappa}\right) -> \widetilde{\mathcal{O}}\left(\sqrt[3]{\kappa}\right)Helped
Use FGD+FSFOM instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox · Centralized federated optimizationlocal steps per round: \widetilde{\mathcal{O}}\left(\sqrt{\kappa}\right) -> \widetilde{\mathcal{O}}\left(\sqrt[4]{\kappa}\right)Helped
Use FGD+GD instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox · Centralized federated optimizationgradient computations: \widetilde{\mathcal{O}}\left(\kappa\right) -> \widetilde{\mathcal{O}}\left(\kappa^{\frac{5}{6}}\right)Helped
Use FGD+FSFOM instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox · Centralized federated optimizationgradient computations: \widetilde{\mathcal{O}}\left(\kappa\right) -> \widetilde{\mathcal{O}}\left(\kappa^{\frac{3}{4}}\right)Helped
Add accelerated gossip (ablation)APDA with Inexact Prox · Decentralized optimizationcommunication rounds: \widetilde{\mathcal{O}}\left(\sqrt{\kappa\chi} \vee \chi\right) -> \widetilde{\mathcal{O}}\left(\sqrt{\kappa\chi}\right)Helped
Use FGD+GD instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox and Accelerated Gossip · Decentralized optimizationlocal steps per round: \widetilde{\mathcal{O}}\left(\sqrt{\kappa}\right) -> \widetilde{\mathcal{O}}\left(\sqrt[3]{\kappa}\right)Helped
Use FGD+FSFOM instead of GD as the inexact-prox inner method (ablation)APDA with Inexact Prox and Accelerated Gossip · Decentralized optimizationlocal steps per round: \widetilde{\mathcal{O}}\left(\sqrt{\kappa}\right) -> \widetilde{\mathcal{O}}\left(\sqrt[4]{\kappa}\right)Helped

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