On the Convergence of the LMS Algorithm with Adaptive Learning Rate for Linear Feedforward Networks

Area of Science:

• Machine Learning
• Artificial Neural Networks
• Optimization Algorithms

Background:

• Training linear feedforward neural networks involves finding an optimal weight matrix.
• The Least Mean Squares (LMS) algorithm is a gradient descent-like method used for this training.
• Previous work showed fixed learning rates lead to convergence to near-optimal matrices.

Purpose of the Study:

• To demonstrate that dynamically decreasing the learning rate improves LMS algorithm convergence.
• To analyze the convergence rate and efficiency of the LMS algorithm with decreasing learning rates.

Main Methods:

• Utilized a gradient descent-like LMS learning algorithm.
• Implemented a dynamically decreasing learning rate schedule during training cycles.
• Analyzed the convergence properties and number of training cycles required for optimality.

Main Results:

• The LMS algorithm with a dynamically decreasing learning rate converges to the optimal weight matrix.
• Achieves an ∊-optimal matrix in O(1/∊) training cycles, significantly faster than the Ω(1/∊ log 1/∊) cycles with fixed rates.
• Established general conditions for learning rates guaranteeing LMS algorithm convergence.

Conclusions:

• Dynamically adjusting the learning rate is crucial for efficient and guaranteed convergence in neural network training.
• The proposed method offers a substantial improvement in training speed and optimality.
• Provides theoretical underpinnings for the convergence of LMS algorithms with adaptive learning rates.