Theoretical Analysis of Momentum LMS Algorithm for Non-Stationary Data Streams
Researchers have developed theoretical stability and regret bounds for the Momentum Least Mean Squares (MLMS) algorithm when processing sequentially arriving data with changing distributions. The work addresses a gap in existing theory by analyzing how momentum affects algorithm behavior in non-stationary settings, which is common in real-world streaming applications. This matters because it provides theoretical guarantees for an algorithm that can adapt to changing data without expensive retraining.
A new theoretical analysis of the Momentum Least Mean Squares (MLMS) algorithm extends classical learning theory to handle non-stationary data streams where distributions drift over time. The paper derives tracking performance and regret bounds for MLMS in time-varying stochastic linear systems, addressing a significant theoretical challenge: momentum introduces second-order dynamics that require analyzing products of random matrices, making stability analysis substantially more complex than classical first-order LMS. The algorithm maintains computational and memory efficiency independent of stream length while processing each sample in a single pass. Experiments on both synthetic and real-world data demonstrate that MLMS achieves rapid adaptation and robust tracking in agreement with theoretical predictions, particularly in nonstationary settings. These results highlight the algorithm's potential for modern streaming and online learning applications where data distributions continuously evolve.
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- arXiv cs.LGCenter
Momentum LMS Theory beyond Stationarity: Stability, Tracking, and Regret
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