Distributed Proximal Splitting Algorithms with Rates and Acceleration

By Laurent Condat, Grigory Malinovsky, Peter Richtárik. 2020

24 citations recorded by the source corpus.

We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the solution, as well as new accelerated versions, using varying stepsizes. In addition, we propose distributed variants of these algorithms, which can be accelerated as well. While most existing results are ergodic, our nonergodic results significantly broaden our understanding of primal–dual optimization algorithms.

Subfields: Artificial Intelligence, Computational Mechanics, Numerical Analysis

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Citations in the corpus

Distributed Fixed Point Methods with Compressed Iterates (2019, methodology): “V˜u algorithm to tackle the minimization of F + G + H ◦ L [13].”
Federated Learning Based on Dynamic Regularization (2021, methodology): “Another line of distributed optimization methods (Konečnỳ et al., 2016; Makhdoumi & Ozdaglar, 2017; Shamir et al., 2014; Yuan & Ma, 2020; Pathak & Wainwright, 2020; Liang et al., 2019; Li et al., 2020c; Condat et al., 2020) could be considered in this setting.”
Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, background): “t PD3O and PDDY have recently been accelerated in the case of deterministic gradients [16].”