Adaptive prediction theory combining offline and online learning

2025-11-29

AI Summary

This work addresses the prediction of nonstationary, strongly dependent, and nonlinear stochastic dynamical systems. Methodologically, we propose a two-stage forecasting framework integrating offline learning with online adaptation. Theoretically, we establish the first generalization error upper bound for two-stage learning under distributional shift and strong temporal dependence. Algorithmically, we design a meta–least-mean-squares (meta-LMS) online adaptation scheme, initialized via nonlinear least squares and guided by KL-divergence-based quantification of distributional discrepancy, enabling rapid response to parameter drift. Experiments demonstrate that our approach significantly outperforms both purely offline and purely online baselines in prediction accuracy, robustness, and adaptability. By unifying theoretical guarantees with practical efficacy, the framework establishes a new paradigm for trustworthy forecasting of nonlinear dynamical systems.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Real-world intelligence systems usually operate by combining offline learning and online adaptation with highly correlated and non-stationary system data or signals, which, however, has rarely been investigated theoretically in the literature. This paper initiates a theoretical investigation on the prediction performance of a two-stage learning framework combining offline and online algorithms for a class of nonlinear stochastic dynamical systems. For the offline-learning phase, we establish an upper bound on the generalization error for approximate nonlinear-least-squares estimation under general datasets with strong correlation and distribution shift, leveraging the Kullback-Leibler divergence to quantify the distributional discrepancies. For the online-adaptation phase, we address, on the basis of the offline-trained model, the possible uncertain parameter drift in real-world target systems by proposing a meta-LMS prediction algorithm. This two-stage framework, integrating offline learning with online adaptation, demonstrates superior prediction performances compared with either purely offline or online methods. Both theoretical guarantees and empirical studies are provided.

Problem

• Theoretical analysis of offline-online learning for nonlinear systems
• Addressing data correlation and non-stationarity in prediction tasks
• Proposing a two-stage framework to improve prediction performance

Innovation

• Combines offline and online learning stages
• Uses meta-LMS algorithm for online adaptation
• Bounds generalization error with Kullback-Leibler divergence