arXiv subjects

Olga Yufereva

Publications and source records attributed to Olga Yufereva.

4 recordsLinked to original sources

arXiv2024

Convergence Analysis of Ensemble Filters for Linear Stochastic Systems with Poisson-Sampled Observations

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov type diffusion process with additive Gaussian noise in observation model, which is used to describe the evolution of the individual particles in the ensemble. These particles are coupled through the empirical covariance and require less computations for implementation than the optimal ones based on solving Riccati differential equations. Using appropriate analysis tools, we show that the empirical mean and the sample covariance of the ensemble filter converges to the mean and covariance of the optimal filter if the mean sampling rate of the observation process satisfies certain bounds and as the number of particles tends to infinity.

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arXiv2023

Decentralized Convex Optimization on Time-Varying Networks with Application to Wasserstein Barycenters

Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are motivated by examples when only a subset of sensors can make an observation at each time step, and yet, the goal is to average signals (e.g., satellite pictures of some area) by approximating their barycenter. We embed this problem into a class of non-smooth dual-friendly distributed optimization problems over time-varying networks, and develop a first-order method for this class. We prove non-asymptotic accelerated in the sense of Nesterov convergence rates and explicitly characterise their dependence on the parameters of the network and its dynamics. In the experiments, we demonstrate the efficiency of the proposed algorithm when applied to the Wasserstein barycenter problem.

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arXiv2019

Approximate Capture in Gromov-Hausdorff Closed Spaces

We consider the Lion and Man game, i.e., a two-person pursuit-evasion game with equal players' top speeds. We assume that capture radius is positive and chosen in advance. The main aim of the paper is describing pursuer's winning strategies in general compact metric spaces that are close to the given one in the sense of Gromov-Hausdorff distance. We prove that the existence of $α$-capture by a time $T$ in one compact geodesic space implies the existence of $(α+ (20T +8)\sqrt{\varepsilon})$-capture by this time $T$ in any compact geodesic space that is $\varepsilon$-close to the given space. It means that capture radii (in a nearby spaces) tends to the given one as the distance between spaces tends to zero. Thus, this result justifies calculations on graphs instead of complicated spaces.

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arXiv2017

Lion and Man Game in Compact Spaces

The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with a positive capture radius). We assume that Lion wins if he manages the capture independently of the initial positions of the players and the evader's strategy. We prove that the discrete-time simple pursuit strategy is a Lion's winning strategy in a compact geodesic space satisfying the betweenness property. In particular, it means that Lion wins in compact CAT(0)-spaces, Ptolemy spaces, Buseman convex spaces or any geodesic space with convex metric. We also do not need to use such properties as finite dimension, smoothness, boundary regularity or contractibility of the loops.

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