[Paper Review] AEGD: Adaptive Gradient Decent with Energy.

Hailiang Liu, Xuping Tian|arXiv (Cornell University)|Oct 10, 2020

Stochastic Gradient Optimization Techniques57 references4 citations

TL;DR

AEGD is a novel first-order optimization algorithm that uses adaptive quadratic energy updates to ensure unconditional energy stability and fast convergence, even with large step sizes. It requires minimal hyperparameter tuning and outperforms SGD with momentum in generalization for deep neural networks while being robust to initial conditions.

ABSTRACT

In this paper, we propose AEGD, a new algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive updates of quadratic energy. As long as an objective function is bounded from below, AEGD can be applied, and it is shown to be unconditionally energy stable, irrespective of the step size. In addition, AEGD enjoys tight convergence rates, yet allows a large step size. The method is straightforward to implement and requires little tuning of hyper-parameters. Experimental results demonstrate that AEGD works well for various optimization problems: it is robust with respect to initial data, capable of making rapid initial progress, shows comparable and most times better generalization performance than SGD with momentum for deep neural networks. The implementation of the algorithm can be found at this https URL.

Motivation & Objective

• To develop a first-order optimization algorithm that ensures unconditional energy stability regardless of step size.
• To enable fast convergence with large step sizes while maintaining robustness to initial data.
• To reduce hyperparameter tuning requirements compared to existing methods like SGD with momentum.
• To improve generalization performance in deep neural networks compared to standard stochastic gradient methods.

Proposed method

• AEGD introduces adaptive updates based on a quadratic energy function that evolves during optimization.
• The energy function is dynamically adjusted to ensure the objective function remains bounded from below.
• The algorithm guarantees energy stability independent of the step size, enabling larger learning rates.
• It uses a gradient-based update rule that incorporates energy adaptation to accelerate convergence.
• The method is designed to be simple to implement with minimal hyperparameter configuration.
• The energy adaptation mechanism ensures robustness to initialization and rapid initial progress in optimization.

Experimental results

Research questions

• RQ1 Can a first-order optimization method achieve unconditional energy stability regardless of step size?
• RQ2 Does adaptive energy-based update improve convergence speed and generalization in deep neural networks?
• RQ3 Can AEGD maintain performance with large step sizes while avoiding divergence?
• RQ4 How does AEGD compare to SGD with momentum in terms of generalization and robustness to initialization?

Key findings

• AEGD is unconditionally energy stable, meaning it remains stable for any step size, which is a significant theoretical advantage.
• The algorithm achieves tight convergence rates, enabling rapid initial progress in optimization.
• AEGD demonstrates comparable or better generalization performance than SGD with momentum on deep neural networks.
• The method is robust to initial data, showing consistent performance across different initialization settings.
• AEGD requires minimal hyperparameter tuning, making it practical for real-world deep learning applications.
• The implementation is straightforward and publicly available, supporting reproducibility and adoption.