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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.19981 |
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Table of Contents:
- Stochastic gradient (SG) methods are fundamental to system identification and machine learning, enabling online parameter estimation in large-scale and streaming-data settings. As a classical identification method, the SG algorithm has been extensively studied for decades. Under non-persistent excitation, the strongest currently available convergence result assumes that the condition number of the Fisher information matrix is \(O((\log r_n)^α)\), where \(r_n = 1 + \sum_{i=1}^n \|φ_i\|^2\). Existing theory establishes strong consistency when \(α\le 1/3\), whereas the same condition with \(α> 1\) is insufficient to guarantee strong consistency. We prove that strong consistency holds throughout the range \(0 \le α< 1\). The proof is based on a new algebraic framework that yields substantially sharper matrix norm bounds. This result nearly resolves the four-decade-old Chen--Guo conjecture by establishing strong consistency throughout the previously open range \(1/3 < α< 1\).