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Andrew Veprikov

Publications and source records attributed to Andrew Veprikov.

2 recordsLinked to original sources
arXiv2025

Methods for Optimization Problems with Markovian Stochasticity and Non-Euclidean Geometry

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 also consider the geometry of the problem in an arbitrary non-Euclidean setting, and propose four methods based on the Mirror Descent iteration technique. Theoretical analysis is provided for smooth and convex minimization problems and variational inequalities with Lipschitz and monotone operators. The convergence guarantees obtained are optimal for first-order stochastic methods, as evidenced by the lower bound estimates provided in this paper.

math.OC↗
arXiv2023

Non-Smooth Setting of Stochastic Decentralized Convex Optimization Problem Over Time-Varying Graphs

Distributed optimization has a rich history. It has demonstrated its effectiveness in many machine learning applications, etc. In this paper we study a subclass of distributed optimization, namely decentralized optimization in a non-smooth setting. Decentralized means that $m$ agents (machines) working in parallel on one problem communicate only with the neighbors agents (machines), i.e. there is no (central) server through which agents communicate. And by non-smooth setting we mean that each agent has a convex stochastic non-smooth function, that is, agents can hold and communicate information only about the value of the objective function, which corresponds to a gradient-free oracle. In this paper, to minimize the global objective function, which consists of the sum of the functions of each agent, we create a gradient-free algorithm by applying a smoothing scheme via $l_2$ randomization. We also verify in experiments the obtained theoretical convergence results of the gradient-free algorithm proposed in this paper.

math.OC↗