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Linearly Converging Error Compensated SGD
P. 20889–20900.
Eduard Gorbunov, Kovalev D., Makarenko D., Richtarik P.
In book
Curran Associates, Inc., 2020.
Beznosikov A., Kormakov G., Grigorievskiy A. et al., Journal of Optimization Theory and Applications 2026 Vol. 209 Article 18
The objective of Vertical Federated Learning (VFL) is to collectively train a model using features available on different devices while sharing the same users. This paper focuses on the saddle point reformulation of the VFL problem via the classical Lagrangian function. We first demonstrate how this formulation can be solved using deterministic methods.More importantly, we explore various stochastic modifications to ...
Added: June 17, 2026
Vasilev A., Kapitanov A., Roman Solovyev et al., PeerJ Computer Science 2026 Vol. 12 Article 3724
This article introduces MinMAE, a novel activation calibration method for Post-Training Quantization (PTQ) that significantly reduces accuracy loss in Convolutional Neural Networks (CNN). Motivated by the need for high-fidelity quantization without costly retraining, MinMAE directly minimizes the Mean Absolute Error (MAE) between original and dequantized activations, making it robust to outliers that degrade standard methods. ...
Added: May 3, 2026
Borodich E., Gasnikov A., Kovalev D., , in: Volume 267: International Conference on Machine Learning, 13-19 July 2025, Vancouver Convention Center, Vancouver, CanadaVol. 267.: [б.и.], 2025. P. 5045–5100.
Added: November 18, 2025
Demidovich Y., Petr Ostroukhov, Malinovsky G. et al., , in: The Thirteenth International Conference on Learning Representations: ICLR 2025.: ICLR, 2025.
Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0,L_1)$-smoothness assumption, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. However, in the context of Federated Learning, only a few ...
Added: July 15, 2025
Kornilov N., Gasnikov A., Dvurechensky P. et al., Computational Management Science 2023 Article 37
We present two easy-to-implement gradient-free/zeroth-order methods to optimize a stochastic non-smooth function accessible only via a black-box. The methods are built upon efficient first-order methods in the heavy-tailed case, i.e., when the gradi- ent noise has infinite variance but bounded (1 + 𝜅)-th moment for some 𝜅 ∈ (0, 1]. The first algorithm is based ...
Added: February 7, 2025
Gladin E., Alkousa M., Gasnikov A., Automation and Remote Control 2021 Vol. 82 P. 1679–1691
The article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of the two groups of variables. It is shown that the proposed approaches based on Vaidya’s method, the fast gradient method, and the accelerated gradient method with variance reduction have linear convergence. It ...
Added: November 29, 2024
Gladin E., Gasnikov A., Ermakova E., Mathematical notes 2022 Vol. 112 No. 1 P. 183–190
The paper deals with a general problem of convex stochastic optimization in a space of small dimension (for example, 100 variables). It is known that for deterministic problems of convex optimization in small dimensions, the methods of centers of gravity type (for example, Vaidya’s method) provide the best convergence. For stochastic optimization problems, the question ...
Added: November 29, 2024
Gladin E., Gasnikov A., Dvurechensky P., Journal of Optimization Theory and Applications 2025 Vol. 204 No. 1 Article 1
Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy certificates produce a simple way to recover an approximate primal solution and estimate its accuracy. In this paper, we generalize accuracy certificates for the ...
Added: November 29, 2024
Gladin E., Зайнуллина К. Э., Компьютерные исследования и моделирование 2021 Т. 13 № 6 С. 1137–1147
The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a variety of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are usually used to solve such problems. We propose to use the ellipsoid method with mini-batching, which converges linearly and can ...
Added: November 29, 2024
Gladin E., Borodich E., Computer Research and Modeling 2022 Vol. 14 No. 2 P. 257–275
The paper is devoted to convex-concave saddle point problems where the objective is a sum of a large number of functions. Such problems attract considerable attention of the mathematical community due to the variety of applications in machine learning, including adversarial learning, adversarial attacks and robust reinforcement learning, to name a few. The individual functions ...
Added: November 29, 2024
Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
Added: November 29, 2024
Brosse N., Durmus A., Meyn S. et al., Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 4 P. 693–738
A new method is introduced for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. These control variates are obtained by minimizing the asymptotic variance associated with the Langevin diffusion over a family of functions. To motivate our approach, we then show that the asymptotic ...
Added: October 13, 2024
Puchkin N., Gorbunov E., Kutuzov N. et al., , in: Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024), 2-4 May 2024, Palau de Congressos, Valencia, Spain. PMLR: Volume 238Vol. 238.: Valencia: PMLR, 2024. P. 856–864.
We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than 𝑂(𝐾^{−2(𝛼−1)/𝛼}), when the stochastic gradients have finite 𝛼-th moment, 𝛼∈(1,2]. In particular, our analysis allows the noise norm to have an unbounded expectation. To achieve these results, we stabilize stochastic gradients, ...
Added: April 22, 2024
Alashqar B., Gasnikov A., Dvinskikh D. et al., Computational Mathematics and Mathematical Physics 2023 Vol. 63 P. 1600–1653
This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in l1-norm or l2-norm) of a small radius centered at this point, and then the original problem is reduced to a smooth problem (whose ...
Added: March 27, 2024
Kornilov N., Shamir O., Lobanov A. et al., , in: Advances in Neural Information Processing Systems 36 (NeurIPS 2023).: Curran Associates, Inc., 2023. P. 64083–64102.
Added: March 26, 2024
Schechtman S., Tiapkin D., Muehlebach M. et al., , in: Proceedings of Machine Learning Research: Volume 195: The Thirty Sixth Annual Conference on Learning Theory, 12-15 July 2023, Bangalore, IndiaVol. 195: The Thirty Sixth Annual Conference on Learning Theory, 12-15 July 2023, Bangalore, India.: PMLR, 2023. P. 1228–1258.
We consider the problem of minimizing a non-convex function over a smooth manifold M. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM), which only requires computing a projection onto a vector space. ODCGM is infeasible but the iterates are constantly pulled towards the manifold, ensuring the convergence of ODCGM towards M. ...
Added: December 1, 2023
Belomestny D., Kaledin M., Golubev A., /. 2022.
Policy-gradient methods in Reinforcement Learning(RL) are very universal and widely applied in practice but their performance suffers from the high variance of the gradient estimate. Several procedures were proposed to reduce it including actor-critic(AC) and advantage actor-critic(A2C) methods. Recently the approaches have got new perspective due to the introduction of Deep RL: both new control ...
Added: April 14, 2023
Cardoso G., Samsonov S., Thin A. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 716–729.
Added: February 1, 2023
Beznosikov A., Richtarik P., Diskin M. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 14013–14029.
Added: January 27, 2023