# Towards Accelerated Rates for Distributed Optimization over Time-Varying Networks

@inproceedings{Rogozin2021TowardsAR, title={Towards Accelerated Rates for Distributed Optimization over Time-Varying Networks}, author={Alexander Rogozin and Vladislav Lukoshkin and Alexander V. Gasnikov and D. Kovalev and Egor Shulgin}, booktitle={OPTIMA}, year={2021} }

We study the problem of decentralized optimization over time-varying networks with strongly convex smooth cost functions. In our approach, nodes run a multi-step gossip procedure after making each gradient update, thus ensuring approximate consensus at each iteration, while the outer loop is based on accelerated Nesterov scheme. The algorithm achieves precision $\varepsilon > 0$ in $O(\sqrt{\kappa_g}\chi\log^2(1/\varepsilon))$ communication steps and $O(\sqrt{\kappa_g}\log(1/\varepsilon…

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## 12 Citations

ADOM: Accelerated Decentralized Optimization Method for Time-Varying Networks

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This work designs two optimal algorithms, one of which is a variant of the recently proposed algorithm ADOM enhanced via a multi-consensus subroutine and a novel algorithm, called ADOM+, which is optimal in the case when access to the primal gradients is assumed.

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The widely used accelerated gradient tracking is revisits and extended to time-varying graphs and the dependence on the network connectivity constants can be further improved to O(1) and O( γ 1−σγ ) for the computation and communication complexities, respectively.

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An Accelerated Method For Decentralized Distributed Stochastic Optimization Over Time-Varying Graphs

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This work proposes the first accelerated (in the sense of Nesterov’s acceleration) method that simultaneously attains optimal up to a logarithmic factor communication and oracle complexity bounds for smooth strongly convex distributed stochastic optimization.

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This work proposes a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph, and derives global complexity bounds for convex and strongly convex losses.

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Optimal Gradient Tracking (OGT) is the first single-loop decentralized gradient-type method that is optimal in both gradient computation and communication complexities.

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## References

SHOWING 1-10 OF 37 REFERENCES

A Sharp Convergence Rate Analysis for Distributed Accelerated Gradient Methods

- Computer Science
- 2018

Two algorithms based on the framework of the accelerated penalty method with increasing penalty parameters are presented, which achieves the near optimal complexities for both computation and communication.

Variance Reduced EXTRA and DIGing and Their Optimal Acceleration for Strongly Convex Decentralized Optimization

- Computer Science
- 2020

The widely used EXTRA and DIGing methods with variance reduction (VR) are extended, and the accelerated VR-EXTRA and VR-DIGing with both the optimal stochastic gradient computation complexity and communication complexity are proposed.

An Optimal Algorithm for Decentralized Finite Sum Optimization

- Computer ScienceSIAM Journal on Optimization
- 2021

A lower bound of complexity is given to show that ADFS is optimal among decentralized algorithms, which uses local stochastic proximal updates and decentralized communications between nodes to derive ADFS.

Revisiting EXTRA for Smooth Distributed Optimization

- Computer Science, MathematicsSIAM J. Optim.
- 2020

A sharp complexity analysis for EXTRA with the improved improved Catalyst framework is given and the strong convexity is absent and communication complexities of the accelerated EXTRA are only worse by the factors.

Optimal Algorithms for Smooth and Strongly Convex Distributed Optimization in Networks

- Computer ScienceICML
- 2017

The efficiency of MSDA against state-of-the-art methods for two problems: least-squares regression and classification by logistic regression is verified.

Optimal Algorithms for Non-Smooth Distributed Optimization in Networks

- Mathematics, Computer ScienceNeurIPS
- 2018

The error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions, and the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate are provided.

Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs

- Mathematics, Computer ScienceSIAM J. Optim.
- 2017

This paper introduces a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient method and a gradient tracking technique that converges to a global and consensual minimizer over time-varying graphs.

Accelerated Distributed Nesterov Gradient Descent

- Computer ScienceIEEE Transactions on Automatic Control
- 2020

This paper considers the distributed optimization problem over a network, where the objective is to optimize a global function formed by a sum of local functions, using only local computation and…

A dual approach for optimal algorithms in distributed optimization over networks

- Computer Science, MathematicsOptim. Methods Softw.
- 2021

This work studies dual-based algorithms for distributed convex optimization problems over networks, and proposes distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional optimal cost related to the spectral properties of the network.

EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization

- Computer ScienceSIAM J. Optim.
- 2015

A novel decentralized exact first-order algorithm (abbreviated as EXTRA) to solve the consensus optimization problem and uses a fixed, large step size, which can be determined independently of the network size or topology.