23 accepted papers
Recent advancements in machine learning have improved performance while also increasing computational demands. While federated and distributed setups address these issues, their structures remain vulnerable to malicious influences. In this paper, we address a specific threat: Byzantine attacks, wher
Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To address this issue, we reformulate PINN training as a nonconvex-…
This paper deals with stochastic optimization problems involving Markovian noise with a zero-order oracle. We present and analyze a novel derivative-free method for solving such problems in strongly convex smooth and non-smooth settings with both one-point and two-point feedback oracles. Using a ran…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems and, unlike most previous work, we take into account the complex Markov nature of the noise. We
Large language models have achieved major advances across domains, yet training them remains extremely resource-intensive. We revisit Sign-SGD, which serves both as a memory-efficient optimizer for single-node training and as a gradient compression mechanism for distributed learning. This paper addr…
Sign-based optimization methods, such as SignSGD and Signum, have become essential for modern Deep Learning due to their 1) high performance 2) low memory footprint and 3) communication efficiency. Despite their success, these methods suffer from distinct limitations in the terminal phase of trainin…
Modern machine learning problems are frequently formulated in federated learning domain and incorporate inherently heterogeneous data. Weighting methods operate efficiently in terms of iteration complexity and represent a common direction in this setting. At the same time, they do not address direct…
In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge. Several techniques have been developed to overcome this prob…
Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability…
With the increase in the number of parameters in large language models, the training process increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation…
Variational inequalities (VIs) have emerged as a universal framework for solving a wide range of problems. A broad spectrum of applications include optimization, equilibrium analysis, reinforcement learning, and the rapidly evolving field of generative adversarial networks (GANs). Stochastic methods
In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependen…
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient i…
The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many practical problems helped the method to gain popularity in the commu…
This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our approach covers scenarios for both non-convex and strongly co…
Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, and fixed point problems as special cases. Therefore, variational inequalities are used in various applications ranging from equilibrium search to adversarial learning. With the increasing s…
Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominent algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. The success of the method led to several advanced extensions of the classical SGDA, including va…
We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentral…
Variational inequalities in general and saddle point problems in particular are increasingly relevant in machine learning applications, including adversarial learning, GANs, transport and robust optimization. With increasing data and problem sizes necessary to train high performing models across var…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including machine learning problems. This work concentrates on the dece…
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 ca…
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on opt…
We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type--master/workers (thus centralized) architectures and mesh (thus decentralized) networks. The local functions at each node are assumed to be \textit{similar}, due to statistical…