66 citations · 450 across the 76 of their papers we have counts for
15 papers · 1 filter
Inexact Tensor Methods and Their Application to Stochastic Convex Optimization
Artem Agafonov, Dmitry Kamzolov, Pavel Dvurechensky +2
We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide…
Tensor methods for strongly convex strongly concave saddle point problems and strongly monotone variational inequalities
Petr Ostroukhov, Rinat Kamalov, Pavel Dvurechensky +1
In this paper we propose three -th order tensor methods for -strongly-convex-strongly-concave saddle point problems (SPP). The first method is based on the assumption of -…
Recent Theoretical Advances in Non-Convex Optimization
Marina Danilova, Pavel Dvurechensky, Alexander Gasnikov +4
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in dat…
Distributed Optimization with Quantization for Computing Wasserstein Barycenters
Roman Krawtschenko, César A. Uribe, Alexander Gasnikov +1
We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we p…
Generalized Self-Concordant Analysis of Frank-Wolfe algorithms
Pavel Dvurechensky, Kamil Safin, Shimrit Shtern +1
Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computati…
Numerical methods in large-scale optimization: inexact oracle and primal-dual analysis
Pavel Dvurechensky
This is a short summary of already published results on accelerated first and zero-order optimization methods, as well as accelerated methods for problems with linear constraints.…
Zeroth-Order Algorithms for Smooth Saddle-Point Problems
Abdurakhmon Sadiev, Aleksandr Beznosikov, Pavel Dvurechensky +1
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using sto…
Zeroth-order methods for noisy Hölder-gradient functions
Innokentiy Shibaev, Pavel Dvurechensky, Alexander Gasnikov
In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use the Gaussian sm…
Stochastic Saddle-Point Optimization for Wasserstein Barycenters
Daniil Tiapkin, Alexander Gasnikov, Pavel Dvurechensky
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads…
Accelerated meta-algorithm for convex optimization
Alexander Gasnikov, Darina Dvinskikh, Pavel Dvurechensky +5
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general s…
Multimarginal Optimal Transport by Accelerated Alternating Minimization
Nazarii Tupitsa, Pavel Dvurechensky, Alexander Gasnikov +1
We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $…
On the Optimal Combination of Tensor Optimization Methods
Dmitry Kamzolov, Alexander Gasnikov, Pavel Dvurechensky
We consider the minimization problem of a sum of a number of functions having Lipshitz -th order derivatives with different Lipschitz constants. In this case, to accelerate opti…
Self-Concordant Analysis of Frank-Wolfe Algorithms
Pavel Dvurechensky, Petr Ostroukhov, Kamil Safin +2
Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learn…
Oracle Complexity Separation in Convex Optimization
Anastasiya Ivanova, Evgeniya Vorontsova, Dmitry Pasechnyuk +4
Many convex optimization problems have structured objective function written as a sum of functions with different types of oracles (full gradient, coordinate derivative, stochastic…
Inexact Relative Smoothness and Strong Convexity for Optimization and Variational Inequalities by Inexact Model
Fedor Stonyakin, Alexander Tyurin, Alexander Gasnikov +7
In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and vari…