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arXiv · 2604.25468

Distributed adaptive estimation for stochastic large regression models

Die Gan·Siyu Xie·Zhixin Liu·Xuebo Zhang
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Abstract

This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least squares algorithm to estimate the unknownsystem parameters, where the growth rate of regressors'dimension is characterized by a non-decreasing positivefunction. The almost sure convergence of the proposedalgorithm is established under a cooperative excitationcondition, which incorporates the temporal information andthe spatial information to reflect the cooperative effectamong multiple agents. Moreover, we analyze the predic-tion error by establishing the asymptotic upper boundof the accumulated regret without any excitation condi-tions. The main difficulty of theoretical analysis lies in howto analyze properties of the product of non-independentand non-stationary random matrices, whose dimensionschange over time simultaneously. Some techniques, suchas stochastic Lyapunov function, double-array martingaletheory and algebraic graph theory, are employed to dealwith the above issue. Our theoretical results are derivedwithout imposing independence or stationarity assump-tions on the regression vectors, thereby not excluding thecorrelated feedback signals.

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Die Gan, Siyu Xie, Zhixin Liu, Xuebo Zhang. 2026-04-28. Distributed adaptive estimation for stochastic large regression models. https://arxiv.org/abs/2604.25468

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