Distributed adaptive estimation for stochastic large regression models

Researchers Die Gan, Siyu Xie, Zhixin Liu, and Xuebo Zhang have introduced a novel distributed adaptive estimation algorithm for stochastic large regression models that can handle an infinite number of parameters. Their approach, detailed in a paper submitted to IEEE Transactions on Automatic Control, constructs a recursive local cost function to enable a distributed recursive least squares (RLS) algorithm. This allows multiple agents to collaboratively estimate unknown system parameters even as the dimension of regressors grows over time, characterized by a non-decreasing positive function. The algorithm's almost sure convergence is proven under a cooperative excitation condition that integrates both temporal information (time-series data) and spatial information (data from different agents), reflecting how agents work together to improve estimation.

The theoretical backbone of this work tackles a major challenge: analyzing products of non-independent and non-stationary random matrices whose dimensions change simultaneously. The team employs advanced techniques including stochastic Lyapunov functions, double-array martingale theory, and algebraic graph theory to handle this complexity. A key strength is that their results do not require independence or stationarity assumptions on regression vectors, meaning the algorithm works with correlated feedback signals common in real-world systems like sensor networks or autonomous vehicle coordination. Additionally, they analyze prediction error by establishing an asymptotic upper bound on accumulated regret without any excitation conditions, offering robustness guarantees even in less ideal scenarios. This work pushes the frontier of distributed machine learning and control systems, potentially enabling more scalable and resilient estimation in IoT, robotics, and smart infrastructure.