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Deterministic Gradient-Descent Learning of Linear Regressions: Adaptive Algorithms, Convergence Analysis and Noise
This study introduces a deterministic weight learning method for linear regression, guaranteeing convergence for online applications. Adaptive hyperparameters are derived to compensate for measurement noise, enhancing learning performance.
Area of Science:
- Machine Learning
- Control Theory
Background:
- Weight learning is fundamental to machine learning, with most algorithms using stochastic frameworks or loss minimization.
- Guaranteed asymptotic convergence for online weight learning is rarely achieved.
- Linear regression is a foundational machine learning model.
Purpose of the Study:
- To develop a deterministic analysis for weight learning in linear regression for online applications.
- To guarantee asymptotic convergence for first-order and second-order learning algorithms.
- To analyze noise influence and derive adaptive hyperparameters for measurement noise compensation.
Main Methods:
- A deterministic analysis method based on LaSalle's invariance principle.
- Derivation of convergence conditions without stochastic arguments.
- Development of adaptive hyperparameters and tuning rules.
Main Results:
- Guaranteed convergence conditions for both first-order and second-order weight learning algorithms.
- A framework for analyzing the influence of measurement noise.
- Derived adaptive hyperparameters and tuning rules for noise compensation.
Conclusions:
- The deterministic approach offers guaranteed convergence for online weight learning.
- Adaptive hyperparameters effectively compensate for measurement noise.
- This method demonstrates superior learning capability compared to popular algorithms.
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