# Distributed Proximal Splitting Algorithms with Rates and Acceleration

@inproceedings{Condat2021DistributedPS, title={Distributed Proximal Splitting Algorithms with Rates and Acceleration}, author={Laurent Condat and Grigory Malinovsky and Peter Richt{\'a}rik}, booktitle={Frontiers in Signal Processing}, year={2021} }

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…

## 12 Citations

### Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists

- Computer Science
- 2019

This overview of recent proximal splitting algorithms presents them within a unified framework, which consists in applying splitting methods for monotone inclusions in primal-dual product spaces, with well-chosen metrics, and emphasizes that when the smooth term in the objective function is quadratic, convergence is guaranteed with larger values of the relaxation parameter than previously known.

### Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms

- Computer Science, MathematicsArXiv
- 2020

New primal-dual algorithms to minimize the sum of three convex functions, each having its own oracle, are introduced, which prove convergence to an exact solution with sublinear or linear rates, depending on strong convexity properties.

### RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates

- Computer Science, Mathematics
- 2022

A new primal–dual algorithm is proposed, in which the dual update is randomized; equivalently, the proximity operator of one of the function in the problem is replaced by a stochastic oracle.

### Dualize, Split, Randomize: Toward Fast Nonsmooth Optimization Algorithms

- MathematicsJournal of Optimization Theory and Applications
- 2022

We consider minimizing the sum of three convex functions, where the first one F is smooth, the second one is nonsmooth and proximable and the third one is the composition of a nonsmooth proximable…

### An Optimal Algorithm for Strongly Convex Minimization under Affine Constraints

- Computer Science, MathematicsAISTATS
- 2022

This work considers the task of minimizing a smooth strongly convex function F ( x ) under the affine constraint K x = b, with an ora-cle providing evaluations of the gradient of F and multiplications by K and its transpose and proposes an accelerated primal–dual algorithm achieving these lower bounds.

### Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness

- Computer Science, Mathematics
- 2021

An adaptive restart scheme is developed and verified that restarts improve the ability of PDHG, EGM, and ADMM to high accuracy solutions to LP problems, and applies to the strictly more general class of sharp primal-dual problems.

### DADAO: Decoupled Accelerated Decentralized Asynchronous Optimization for Time-Varying Gossips

- Computer ScienceArXiv
- 2022

DADAO is a novel decentralized asynchronous stochastic algorithm to minimize a sum of L -smooth and µ -strongly convex functions distributed over a time-varying connectivity network of size n . We…

### ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!

- Computer ScienceICML
- 2022

ProxSkip is a surprisingly simple and provably provably effective method for minimizing the sum of a smooth and an expensive nonsmooth proximable function and offers an effec-tive acceleration of communication complexity.

### Distributed Forward-Backward Methods without Central Coordination

- Mathematics, Computer ScienceArXiv
- 2021

In this work, we propose and analyse forward-backward-type algorithms for finding a zero in the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion…

### EF-BV: A Unified Theory of Error Feedback and Variance Reduction Mechanisms for Biased and Unbiased Compression in Distributed Optimization

- Computer ScienceArXiv
- 2022

The general approach works with a new, larger class of compressors, which has two parameters, the bias and the variance, and includes unbiased and biased compressors as particular cases, and proves its linear convergence under certain conditions.

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### Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists

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- 2019

This overview of recent proximal splitting algorithms presents them within a unified framework, which consists in applying splitting methods for monotone inclusions in primal-dual product spaces, with well-chosen metrics, and emphasizes that when the smooth term in the objective function is quadratic, convergence is guaranteed with larger values of the relaxation parameter than previously known.

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This overview of recent proximal splitting algorithms within a unified framework, which consists in applying splitting methods for monotone inclusions in primal-dual product spaces, with well-chosen metric, is presented.

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New primal-dual algorithms to minimize the sum of three convex functions, each having its own oracle, are introduced, which prove convergence to an exact solution with sublinear or linear rates, depending on strong convexity properties.

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