Local Convergence of Adaptive Gradient Descent Optimizers
This work addresses a theoretical gap for researchers and practitioners using adaptive optimizers in deep learning, though it is incremental as it builds on existing analysis methods.
The paper tackles the lack of complete convergence analysis for the ADAM optimizer by developing a method for local convergence analysis in batch mode, providing necessary hyperparameter conditions for ADAM and showing local convergence for most other adaptive gradient descent algorithms.
Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis exists for ADAM. The contribution of this paper is a method for the local convergence analysis in batch mode for a deterministic fixed training set, which gives necessary conditions for the hyperparameters of the ADAM algorithm. Due to the local nature of the arguments the objective function can be non-convex but must be at least twice continuously differentiable. Then we apply this procedure to other adaptive gradient descent algorithms and show for most of them local convergence with hyperparameter bounds.