Regret Guarantees for Model-Free Cooperative Filtering under Asynchronous Observations

TL;DR

This paper introduces a novel online learning algorithm with regret guarantees for predicting dynamical systems from asynchronous streaming data, outperforming traditional model-based methods under certain conditions.

Contribution

It develops a new autoregressive model and provides theoretical regret bounds for model-free cooperative filtering with asynchronous observations.

Findings

Regret bound of O(log^3 N) relative to optimal predictor

Conditions under which the method outperforms model-based predictors

Theoretical analysis exploiting innovation orthogonality and persistent excitation

Abstract

Predicting the output of a dynamical system from streaming data is fundamental to real-time feedback control and decision-making. We first derive an autoregressive representation that relates future local outputs to asynchronous past outputs. Building on this structure, we propose an online least-squares algorithm to learn this autoregressive model for real-time prediction. We then establish a regret bound of O(log^3 N) relative to the optimal model-based predictor, which holds for marginally stable systems. Moreover, we provide a sufficient condition characterized via a symplectic matrix, under which the proposed cooperative online learning method provably outperforms the optimal model-based predictor that relies solely on local observations. From a technical standpoint, our analysis exploits the orthogonality of the innovation process under asynchronous data structure and the persistent excitation of the Gram matrix despite delay-induced asymmetries. Overall, these results offer both theoretical guarantees and practical algorithms for model-free cooperative prediction with asynchronous observations, thereby enriching the theory of online learning for dynamical systems.