Regret Guarantees for Model-Free Cooperative Filtering under Asynchronous Observations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911490001338368 |
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| author | Qian, Jiachen Zheng, Yang |
| author_facet | Qian, Jiachen Zheng, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05661 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regret Guarantees for Model-Free Cooperative Filtering under Asynchronous Observations Qian, Jiachen Zheng, Yang Systems and Control 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. |
| title | Regret Guarantees for Model-Free Cooperative Filtering under Asynchronous Observations |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.05661 |