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Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimization

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arxiv 1911.07596 v2 pith:IMC6IU5Z submitted 2019-11-18 math.OC cs.LGstat.ML

classification math.OCcs.LGstat.ML
keywords adaptiveconvergenceadamalgorithmoptimizationstepassumptionbeen
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Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent this convergence issue. In this work, we study the ADAM algorithm for smooth nonconvex optimization under a boundedness assumption on the adaptive learning rate. The bound on the adaptive step size depends on the Lipschitz constant of the gradient of the objective function and provides safe theoretical adaptive step sizes. Under this boundedness assumption, we show a novel first order convergence rate result in both deterministic and stochastic contexts. Furthermore, we establish convergence rates of the function value sequence using the Kurdyka-Lojasiewicz property.

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Cited by 3 Pith papers

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  1. Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks

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    Bounded trajectories of a broad class of GD optimizers (Adam, RMSprop, NAG, Adan, etc.) converge with polynomial rates to critical points of KL objectives with locally Lipschitz gradients, covering analytic-activation...

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    Adam can achieve the accelerated momentum convergence rate locally on smooth strongly convex problems when its momentum and step size are tuned to the condition number, while RMSprop is shown to converge at the slower...

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