AEGD: Adaptive Gradient Descent with Energy

• URL: http://arxiv.org/abs/2010.05109v2
• Date: Fri, 1 Oct 2021 14:40:23 GMT
• Title: AEGD: Adaptive Gradient Descent with Energy
• Authors: Hailiang Liu and Xuping Tian
• Abstract summary: We propose AEGD, a new algorithm for first-order gradient non-energy objective functions variable. We show energy-dependent AEGD for both non-energy convergence and desired small step size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the step size. We prove energy-dependent convergence rates of AEGD for both non-convex and convex objectives, which for a suitably small step size recovers desired convergence rates for the batch gradient descent. We also provide an energy-dependent bound on the stationary convergence of AEGD in the stochastic non-convex setting. The method is straightforward to implement and requires little tuning of hyper-parameters. Experimental results demonstrate that AEGD works well for a large variety of optimization problems: it is robust with respect to initial data, capable of making rapid initial progress. The stochastic AEGD shows comparable and often better generalization performance than SGD with momentum for deep neural networks.

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