Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.
On the Convergence of Adam and Beyond
Sashank J. Reddi,Satyen Kale,Surinder Kumar
Published 2018 in International Conference on Learning Representations
ABSTRACT
PUBLICATION RECORD
- Publication year
2018
- Venue
International Conference on Learning Representations
- Publication date
2018-02-15
- Fields of study
Mathematics, Computer Science
- Identifiers
- External record
- Source metadata
Semantic Scholar
CITATION MAP
EXTRACTION MAP
CLAIMS
- No claims are published for this paper.
CONCEPTS
- No concepts are published for this paper.
REFERENCES
Showing 1-10 of 10 references · Page 1 of 1