Speaker: 甘叠，复旦大学

Title: Distributed adaptive estimation for stochastic large regression models

Language: Chinese

Time & Venue: 2026.10.22 16:30-17:15 Zoom会议 64135181073

Abstract: We study the distributed adaptive estimation problems for stochastic large regression models with an infinite number of parameters. By constructing a recursive local cost function, we propose a novel distributed recursive least squares algorithm to estimate the unknown system parameters, where the growth rate of regressors’ dimension is characterized by a non-decreasing positive function. The almost sure convergence of the proposed algorithm is established under a cooperative excitation condition, which incorporates the temporal information and the spatial information to reflect the cooperative effect among multiple agents. Moreover, we analyze the prediction error by establishing the asymptotic upper bound of the accumulated regret without any excitation conditions. The main difficulty of theoretical analysis lies in how to analyze properties of the product of non-independent and non-stationary random matrices, whose dimensions change over time simultaneously. Some techniques, such as stochastic Lyapunov function, double-array martingale theory and algebraic graph theory, are employed to deal with the above issue. Our theoretical results are derived without imposing independence or stationarity assumptions on the regression vectors, thereby not excluding the correlated feedback signals.