# Adam: A Method for Stochastic Optimization

@article{Kingma2015AdamAM, title={Adam: A Method for Stochastic Optimization}, author={Diederik P. Kingma and Jimmy Ba}, journal={CoRR}, year={2015}, volume={abs/1412.6980} }

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. [...] Key Method The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence… Expand

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A set of mild sufficient conditions are provided that guarantee the convergence for the Adam-type methods and it is proved that under these derived conditions, these methods can achieve the convergence rate of order $O(\log{T}/\sqrt{T})$ for nonconvex stochastic optimization. Expand

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An alternative easy-to-check sufficient condition is introduced, which merely depends on the parameters of the base learning rate and combinations of historical second-order moments, to guarantee the global convergence of generic Adam/RMSProp for solving large-scale non-convex stochastic optimization. Expand

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This work provides proofs that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives, and gives bounds on the running time of these algorithms. Expand

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