Timezone: »
Poster
Optimal Gradient Sliding and its Application to Optimal Distributed Optimization Under Similarity
Dmitry Kovalev · Aleksandr Beznosikov · Ekaterina Borodich · Alexander Gasnikov · Gesualdo Scutari
We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we proposed an inexact accelerated gradient sliding method that can skip the gradient computation for one of these components while still achieving optimal complexity of gradient calls of $p$ and $q$, that is, $\mathcal{O}(\sqrt{L_p/\mu})$ and $\mathcal{O}(\sqrt{L_q/\mu})$, respectively. This result is much sharper than the classic black-box complexity $\mathcal{O}(\sqrt{(L_p+L_q)/\mu})$, especially when the difference between $L_p$ and $L_q$ is large. We then apply the proposed method to solve distributed optimization problems over master-worker architectures, under agents' function similarity, due to statistical data similarity or otherwise. The distributed algorithm achieves for the first time lower complexity bounds on both communication and local gradient calls, with the former having being a long-standing open problem. Finally the method is extended to distributed saddle-problems (under function similarity) by means of solving a class of variational inequalities, achieving lower communication and computation complexity bounds.
Author Information
Dmitry Kovalev (UCLouvain)
Aleksandr Beznosikov (Moscow Institute of Physics and Technology)
Ekaterina Borodich (MIPT)
Alexander Gasnikov (Moscow Institute of Physics and Technology)
Gesualdo Scutari (Purdue University)
More from the Same Authors
-
2021 : Decentralized Personalized Federated Learning: Lower Bounds and Optimal Algorithm for All Personalization Modes »
Abdurakhmon Sadiev · Ekaterina Borodich · Darina Dvinskikh · Aleksandr Beznosikov · Alexander Gasnikov -
2021 : Decentralized Personalized Federated Learning: Lower Bounds and Optimal Algorithm for All Personalization Modes »
Abdurakhmon Sadiev · Ekaterina Borodich · Darina Dvinskikh · Aleksandr Beznosikov · Alexander Gasnikov -
2021 : Random-reshuffled SARAH does not need a full gradient computations »
Aleksandr Beznosikov · Martin Takac -
2021 : Decentralized Personalized Federated Min-Max Problems »
Ekaterina Borodich · Aleksandr Beznosikov · Abdurakhmon Sadiev · Vadim Sushko · Alexander Gasnikov -
2022 : Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods »
Aleksandr Beznosikov · Eduard Gorbunov · Hugo Berard · Nicolas Loizou -
2022 : Effects of momentum scaling for SGD »
Dmitry A. Pasechnyuk · Alexander Gasnikov · Martin Takac -
2022 Spotlight: Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling »
Dmitry Kovalev · Alexander Gasnikov · Peter Richtarik -
2022 Spotlight: Communication Acceleration of Local Gradient Methods via an Accelerated Primal-Dual Algorithm with an Inexact Prox »
Abdurakhmon Sadiev · Dmitry Kovalev · Peter Richtarik -
2022 Spotlight: The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization »
Dmitry Kovalev · Alexander Gasnikov -
2022 Spotlight: Distributed Methods with Compressed Communication for Solving Variational Inequalities, with Theoretical Guarantees »
Aleksandr Beznosikov · Peter Richtarik · Michael Diskin · Max Ryabinin · Alexander Gasnikov -
2022 Spotlight: Optimal Algorithms for Decentralized Stochastic Variational Inequalities »
Dmitry Kovalev · Aleksandr Beznosikov · Abdurakhmon Sadiev · Michael Persiianov · Peter Richtarik · Alexander Gasnikov -
2022 Spotlight: Lightning Talks 4A-1 »
Jiawei Huang · Su Jia · Abdurakhmon Sadiev · Ruomin Huang · Yuanyu Wan · Denizalp Goktas · Jiechao Guan · Andrew Li · Wei-Wei Tu · Li Zhao · Amy Greenwald · Jiawei Huang · Dmitry Kovalev · Yong Liu · Wenjie Liu · Peter Richtarik · Lijun Zhang · Zhiwu Lu · R Ravi · Tao Qin · Wei Chen · Hu Ding · Nan Jiang · Tie-Yan Liu -
2022 Spotlight: Optimal Gradient Sliding and its Application to Optimal Distributed Optimization Under Similarity »
Dmitry Kovalev · Aleksandr Beznosikov · Ekaterina Borodich · Alexander Gasnikov · Gesualdo Scutari -
2022 Spotlight: The First Optimal Algorithm for Smooth and Strongly-Convex-Strongly-Concave Minimax Optimization »
Dmitry Kovalev · Alexander Gasnikov -
2022 Spotlight: Decentralized Local Stochastic Extra-Gradient for Variational Inequalities »
Aleksandr Beznosikov · Pavel Dvurechenskii · Anastasiia Koloskova · Valentin Samokhin · Sebastian Stich · Alexander Gasnikov -
2022 Poster: DGD^2: A Linearly Convergent Distributed Algorithm For High-dimensional Statistical Recovery »
Marie Maros · Gesualdo Scutari -
2022 Poster: Communication Acceleration of Local Gradient Methods via an Accelerated Primal-Dual Algorithm with an Inexact Prox »
Abdurakhmon Sadiev · Dmitry Kovalev · Peter Richtarik -
2022 Poster: Acceleration in Distributed Sparse Regression »
Marie Maros · Gesualdo Scutari -
2022 Poster: Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noise »
Eduard Gorbunov · Marina Danilova · David Dobre · Pavel Dvurechenskii · Alexander Gasnikov · Gauthier Gidel -
2022 Poster: The First Optimal Algorithm for Smooth and Strongly-Convex-Strongly-Concave Minimax Optimization »
Dmitry Kovalev · Alexander Gasnikov -
2022 Poster: A Damped Newton Method Achieves Global $\mathcal O \left(\frac{1}{k^2}\right)$ and Local Quadratic Convergence Rate »
SlavomÃr Hanzely · Dmitry Kamzolov · Dmitry Pasechnyuk · Alexander Gasnikov · Peter Richtarik · Martin Takac -
2022 Poster: The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization »
Dmitry Kovalev · Alexander Gasnikov -
2022 Poster: Optimal Algorithms for Decentralized Stochastic Variational Inequalities »
Dmitry Kovalev · Aleksandr Beznosikov · Abdurakhmon Sadiev · Michael Persiianov · Peter Richtarik · Alexander Gasnikov -
2022 Poster: Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling »
Dmitry Kovalev · Alexander Gasnikov · Peter Richtarik -
2022 Poster: Distributed Methods with Compressed Communication for Solving Variational Inequalities, with Theoretical Guarantees »
Aleksandr Beznosikov · Peter Richtarik · Michael Diskin · Max Ryabinin · Alexander Gasnikov -
2022 Poster: Decentralized Local Stochastic Extra-Gradient for Variational Inequalities »
Aleksandr Beznosikov · Pavel Dvurechenskii · Anastasiia Koloskova · Valentin Samokhin · Sebastian Stich · Alexander Gasnikov -
2021 : Poster Session 2 (gather.town) »
Wenjie Li · Akhilesh Soni · Jinwuk Seok · Jianhao Ma · Jeffery Kline · Mathieu Tuli · Miaolan Xie · Robert Gower · Quanqi Hu · Matteo Cacciola · Yuanlu Bai · Boyue Li · Wenhao Zhan · Shentong Mo · Junhyung Lyle Kim · Sajad Fathi Hafshejani · Chris Junchi Li · Zhishuai Guo · Harshvardhan Harshvardhan · Neha Wadia · Tatjana Chavdarova · Difan Zou · Zixiang Chen · Aman Gupta · Jacques Chen · Betty Shea · Benoit Dherin · Aleksandr Beznosikov -
2021 Poster: Distributed Saddle-Point Problems Under Data Similarity »
Aleksandr Beznosikov · Gesualdo Scutari · Alexander Rogozin · Alexander Gasnikov -
2021 Poster: Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks »
Dmitry Kovalev · Elnur Gasanov · Alexander Gasnikov · Peter Richtarik -
2020 Poster: Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping »
Eduard Gorbunov · Marina Danilova · Alexander Gasnikov -
2020 Poster: Linearly Converging Error Compensated SGD »
Eduard Gorbunov · Dmitry Kovalev · Dmitry Makarenko · Peter Richtarik -
2020 Spotlight: Linearly Converging Error Compensated SGD »
Eduard Gorbunov · Dmitry Kovalev · Dmitry Makarenko · Peter Richtarik -
2020 Poster: Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization »
Dmitry Kovalev · Adil Salim · Peter Richtarik -
2019 Poster: RSN: Randomized Subspace Newton »
Robert Gower · Dmitry Kovalev · Felix Lieder · Peter Richtarik -
2019 Poster: Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates »
Adil Salim · Dmitry Kovalev · Peter Richtarik -
2019 Spotlight: Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates »
Adil Salim · Dmitry Kovalev · Peter Richtarik -
2018 Poster: Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters »
Pavel Dvurechenskii · Darina Dvinskikh · Alexander Gasnikov · Cesar Uribe · Angelia Nedich -
2018 Spotlight: Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters »
Pavel Dvurechenskii · Darina Dvinskikh · Alexander Gasnikov · Cesar Uribe · Angelia Nedich -
2016 Poster: Learning Supervised PageRank with Gradient-Based and Gradient-Free Optimization Methods »
Lev Bogolubsky · Pavel Dvurechenskii · Alexander Gasnikov · Gleb Gusev · Yurii Nesterov · Andrei M Raigorodskii · Aleksey Tikhonov · Maksim Zhukovskii