Preconditioned Stochastic Gradient Descent.

Area of Science:

• Machine Learning
• Optimization Algorithms

Background:

• Stochastic Gradient Descent (SGD) is widely used but suffers from slow convergence and tuning difficulties.
• Existing preconditioning methods for SGD are often specialized or overly complex.

Purpose of the Study:

• To develop a new adaptive preconditioner for SGD that enhances convergence speed and stability.
• To create a method applicable to both convex and non-convex optimization problems with noisy gradients.

Main Methods:

• An adaptive preconditioner is estimated to match stochastic gradient perturbation amplitudes with parameter perturbation amplitudes, inspired by Newton's method.
• The preconditioner is designed to work with exact or noisy gradients, applicable to convex and non-convex settings.
• Efficient estimation techniques are developed, with simplifications for large-scale applications.

Main Results:

• The proposed preconditioner effectively dampens gradient noise, stabilizing SGD.
• The method demonstrates efficiency in solving challenging problems, including deep and recurrent neural network training.
• No manual tuning was required for the preconditioned SGD to achieve efficient results.

Conclusions:

• The novel adaptive preconditioner significantly improves SGD performance by accelerating convergence and enhancing stability.
• This approach offers a practical and efficient solution for complex optimization tasks in machine learning.
• The method's applicability to large-scale problems and its robustness across different optimization landscapes are key advantages.