Related papers: Constructive approaches to concentration inequalit…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
The well-known Bennett-Hoeffding bound for sums of independent random variables is refined, by taking into account truncated third moments, and at that also improved by using, instead of the class of all increasing exponential functions,…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…
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…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…
We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…