Adaptive prediction theory combining offline and online learning

TL;DR

This paper presents a theoretical framework for combining offline and online learning in nonlinear stochastic systems, providing bounds on generalization error and a meta-LMS algorithm for adaptation, with proven superior prediction performance.

Contribution

It introduces a novel two-stage learning framework with theoretical error bounds and an online adaptation algorithm for nonlinear systems, bridging offline and online learning.

Findings

Established an upper bound on generalization error for nonlinear least-squares estimation.

Proposed a meta-LMS algorithm for online adaptation to parameter drift.

Demonstrated superior prediction performance over purely offline or online methods.

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.