arXiv subjects

Xiaozheng Fu

Publications and source records attributed to Xiaozheng Fu.

3 recordsLinked to original sources

arXiv2026

Continuous-Time Decentralized Online Estimation With Additive Noises

We study a decentralized online estimation problem with additive communication noises over the fixed digraph. Each node has a linear measurement of an unknown parameter with random measurement matrices and runs a continuous-time online estimation algorithm. We transform the convergence analysis of the algorithm into the stability analysis of the non-autonomous linear stochastic differential equation (SDE) with random time-varying coefficients, and develop the asymptotic stability by numerical approximation theory. Based on the stability results, we show that the algorithm gains can be properly designed to ensure mean square convergence if the measurement matrices and the communication graph satisfy the stochastic spatial-temporal persistence of excitation condition. Furthermore, a special case where the measurement matrices contain a Markov chain is investigated, and the theoretical results are demonstrated by a numerical example.

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arXiv2025

Decentralized Online Regularized Learning Over Random Time-Varying Graphs

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. It is not required that the regression matrices and graphs satisfy special statistical assumptions such as mutual independence, spatio-temporal independence or stationarity. We develop the nonnegative supermartingale inequality of the estimation error, and prove that the estimations of all nodes converge to the unknown true parameter vector almost surely if the algorithm gains, graphs and regression matrices jointly satisfy the sample path spatio-temporal persistence of excitation condition. Especially, this condition holds by choosing appropriate algorithm gains if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely. In addition, we prove that the regret upper bound is $O(T^{1-τ}\ln T)$, where $τ\in (0.5,1)$ is a constant depending on the algorithm gains.

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arXiv2024

Distributed Stochastic Optimization With Unbounded Subgradients Over Randomly Time-Varying Networks

Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a communication link. We consider the distributed subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes. By stochastic Lyapunov method, convex analysis, algebraic graph theory and martingale convergence theory, we prove that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely.

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