A novel decoupled method for distributed saddle problems achieves optimal communication complexity via multi-stage residual norm minimization, with a matching lower bound and extension to variational inequalities.
arXiv preprint arXiv:2410.14369 , year=
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Anchoring is realized as operator-side Tikhonov regularization before applying the base method, recovering Halpern iteration from Picard and producing new regularized forward-step, EG, and PEG variants with O(1/k) or O(1/sqrt(k)) residual rates under monotone Lipschitz assumptions.
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Efficient Gradient Methods for Distributed Saddle Problems
A novel decoupled method for distributed saddle problems achieves optimal communication complexity via multi-stage residual norm minimization, with a matching lower bound and extension to variational inequalities.
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A Unifying View of Anchoring via Operator-Side Tikhonov Regularization
Anchoring is realized as operator-side Tikhonov regularization before applying the base method, recovering Halpern iteration from Picard and producing new regularized forward-step, EG, and PEG variants with O(1/k) or O(1/sqrt(k)) residual rates under monotone Lipschitz assumptions.