192 citations · 220 across the 13 of their papers we have counts for
14 papers
Exact Permutation Recovery Under Unknown Scalar Affine Transformation
Tigran Galstyan, Avetik Karagulyan, Arshak Minasyan
We study the problem of matching two sets of noisy feature vectors when underlying true features are related by an unknown scalar affine transformation. Our method comprises two pr…
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
Arnak S. Dalalyan, Avetik Karagulyan
We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result sho…
SPAM: Stochastic Proximal Point Method with Momentum Variance Reduction for Non-convex Cross-Device Federated Learning
Avetik Karagulyan, Egor Shulgin, Abdurakhmon Sadiev +1
Cross-device training is a crucial subfield of federated learning, where the number of clients can reach into the billions. Standard approaches and local methods are prone to issue…
Applying statistical learning theory to deep learning
Cédric Gerbelot, Avetik Karagulyan, Stefani Karp +3
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how diff…
Variance Reduced Distributed Non-Convex Optimization Using Matrix Stepsizes
Hanmin Li, Avetik Karagulyan, Peter Richtárik
Matrix-stepsized gradient descent algorithms have been shown to have superior performance in non-convex optimization problems compared to their scalar counterparts. The det-CGD alg…
Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited
Lu Yu, Avetik Karagulyan, Arnak Dalalyan
We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in . In this context, if no additional density…
Det-CGD: Compressed Gradient Descent with Matrix Stepsizes for Non-Convex Optimization
Hanmin Li, Avetik Karagulyan, Peter Richtárik
This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-v…
ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compression
Avetik Karagulyan, Peter Richtárik
Federated sampling algorithms have recently gained great popularity in the community of machine learning and statistics. This paper studies variants of such algorithms called Error…
Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Condition
Lukang Sun, Avetik Karagulyan, Peter Richtarik
Stein Variational Gradient Descent (SVGD) is an important alternative to the Langevin-type algorithms for sampling from probability distributions of the form $π(x) \propto \exp(-V(…
Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets
Avetik Karagulyan, Arnak S. Dalalyan
We study the problem of sampling from a probability distribution on defined via a convex and smooth potential function. We consider a continuous-time diffusion-type p…
Bounding the error of discretized Langevin algorithms for non-strongly log-concave targets
Arnak S. Dalalyan, Avetik Karagulyan, Lionel Riou-Durand
In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the…
Non-Asymptotic Guarantees For Sampling by Stochastic Gradient Descent
Avetik Karagulyan
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or…
User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Arnak S. Dalalyan, Avetik G. Karagulyan
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approxi…
Existence of positive solutions for an approximation of stationary mean-field games
Nojood Almayouf, Elena Bachini, Andreia Chapouto +22
Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a pr…