Adam: A Method for Stochastic Optimization

TL;DR

Adam is a new stochastic optimization algorithm that adaptively estimates moments of gradients, offering efficiency, invariance, and robustness for large-scale, noisy, and sparse problems, with strong theoretical and empirical support.

Contribution

This paper introduces Adam, a novel adaptive gradient optimization method with theoretical convergence guarantees and practical advantages over existing algorithms.

Findings

Adam converges faster than traditional methods in experiments.

Adam performs well on large-scale and noisy datasets.

Theoretical analysis shows Adam has favorable convergence properties.

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.