Adaptive Gradient Descent for Convex and Non-Convex Stochastic Optimization

Darina Dvinskikh; Aleksandr Ogaltsov; Alexander Gasnikov; Pavel Dvurechensky; Alexander Tyurin; Vladimir Spokoiny

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arXiv · 1911.08380

Adaptive Gradient Descent for Convex and Non-Convex Stochastic Optimization

Darina Dvinskikh·Aleksandr Ogaltsov·Alexander Gasnikov·Pavel Dvurechensky·Alexander Tyurin·Vladimir Spokoiny

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Abstract

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of the gradient and variance of the stochastic approximation for the gradient. We consider an accelerated and non-accelerated gradient descent for convex problems and gradient descent for non-convex problems. In the experiments we demonstrate superiority of our methods to existing adaptive methods, e.g. AdaGrad and Adam.

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Darina Dvinskikh, Aleksandr Ogaltsov, Alexander Gasnikov, Pavel Dvurechensky, Alexander Tyurin, Vladimir Spokoiny. 2020-06-12. Adaptive Gradient Descent for Convex and Non-Convex Stochastic Optimization. https://arxiv.org/abs/1911.08380

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