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Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm
The first algorithm analyzed has better dependence on $\varepsilon$ in the complexity bound, but also is not specific to entropic regularization and can solve the OT problem with different regularizers.
A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks
- César A. Uribe, Soomin Lee, A. Gasnikov, A. Nedić
- Computer Science, MathematicsInformation Theory and Applications Workshop (ITA…
- 3 September 2018
This work 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.
Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case
- A. Gasnikov, E. Krymova, Anastasia A. Lagunovskaya, Ilnura N. Usmanova, Fedor A. Fedorenko
- Computer ScienceAutom. Remote. Control.
- 1 February 2017
The aim of this paper is to derive the converge rate of the proposed methods and to determine a noise level which does not significantly affect the convergence rate.
On the Complexity of Approximating Wasserstein Barycenters
- Alexey Kroshnin, N. Tupitsa, D. Dvinskikh, P. Dvurechensky, A. Gasnikov, César A. Uribe
- Computer ScienceICML
- 24 May 2019
The complexity of approximating the Wasserstein barycenter of m discrete measures, or histograms of size n, is studied by contrasting two alternative approaches that use entropic regularization, and a novel proximal-IBP algorithm is proposed which is seen as a proximal gradient method.
Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping
The first non-trivial high-probability complexity bounds for SGD with clipping without light-tails assumption on the noise are derived and derive for this method closing the gap in the theory of stochastic optimization with heavy-tailed noise.
Optimal Tensor Methods in Smooth Convex and Uniformly ConvexOptimization
- A. Gasnikov, P. Dvurechensky, Eduard A. Gorbunov, E. Vorontsova, Daniil Selikhanovych, César A. Uribe
- Computer Science, MathematicsCOLT
- 3 February 2019
A new tensor method is proposed, which closes the gap between the lower and upper iteration complexity bounds for convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, and it is shown that in practice it is faster than the best known accelerated Tensor method.
Primal–dual accelerated gradient methods with small-dimensional relaxation oracle
- Y. Nesterov, A. Gasnikov, S. Guminov, P. Dvurechensky
- Computer ScienceOptimization Methods and Software
- 16 September 2018
It is demonstrated how in practice one can efficiently use the combination of line-search and primal-duality by considering a convex optimization problem with a simple structure (for example, linearly constrained).
Stochastic Intermediate Gradient Method for Convex Problems with Stochastic Inexact Oracle
The first method is an extension of the Intermediate Gradient Method proposed by Devolder, Glineur and Nesterov for problems with deterministic inexact oracle and can be applied to problems with composite objective function, both deterministic and stochastic inexactness of the oracle, and allows using a non-Euclidean setup.
Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters
- P. Dvurechensky, D. Dvinskikh, A. Gasnikov, César A. Uribe, Angelia Nedi'c
- Computer Science, MathematicsNeurIPS
- 11 June 2018
A novel accelerated primal-dual stochastic gradient method is developed and applied to the decentralized distributed optimization setting to obtain a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem.
Mirror Descent and Convex Optimization Problems with Non-smooth Inequality Constraints
- A. Bayandina, P. Dvurechensky, A. Gasnikov, F. Stonyakin, A. Titov
- Computer Science, Mathematics
- 18 October 2017
One of its focus is to propose a Mirror Descent with adaptive stepsizes and adaptive stopping rule for problems with objective function, which is not Lipschitz, e.g., is a quadratic function.