[1412.6980] Adam: A Method for Stochastic Optimization
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Computer Science > Machine Learning
arXiv:1412.6980 (cs)
[Submitted on 22 Dec 2014 (v1), last revised 30 Jan 2017 (this version, v9)]
Title:Adam: A Method for Stochastic Optimization
Authors:Diederik P. Kingma, Jimmy Ba
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Abstract: We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions, based on adaptive estimates of lower-order
moments. The method is straightforward to implement, is computationally
efficient, has little memory requirements, is invariant to diagonal rescaling
of the gradients, and is well suited for problems that are large in terms of
data and/or parameters. 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 properties of the
algorithm and provide a regret bound on the convergence rate that is comparable
to the best known results under the online convex optimization framework.
Empirical results demonstrate that Adam works well in practice and compares
favorably to other stochastic optimization methods. Finally, we discuss AdaMax,
a variant of Adam based on the infinity norm.
Comments: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, 2015
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:1412.6980 [cs.LG]
(or
arXiv:1412.6980v9 [cs.LG] for this version)
Submission history
From: Diederik P Kingma M.Sc. [view email]
[v1]
Mon, 22 Dec 2014 13:54:29 UTC (280 KB)
[v2]
Sat, 17 Jan 2015 20:26:06 UTC (283 KB)
[v3]
Fri, 27 Feb 2015 21:04:48 UTC (289 KB)
[v4]
Tue, 3 Mar 2015 17:51:27 UTC (289 KB)
[v5]
Thu, 23 Apr 2015 16:46:07 UTC (289 KB)
[v6]
Tue, 23 Jun 2015 19:57:17 UTC (958 KB)
[v7]
Mon, 20 Jul 2015 09:43:23 UTC (519 KB)
[v8]
Thu, 23 Jul 2015 20:27:47 UTC (526 KB)
[v9]
Mon, 30 Jan 2017 01:27:54 UTC (490 KB)
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