Variants of RMSProp and Adagrad with Logarithmic Regret Bounds
This work addresses the need for more efficient optimization algorithms in machine learning, particularly for training deep neural networks, by providing incremental improvements to adaptive gradient techniques.
The paper tackles the problem of improving adaptive gradient methods for online convex optimization by analyzing RMSProp and proposing two new variants, SC-Adagrad and SC-RMSProp, which achieve logarithmic regret bounds for strongly convex functions and outperform existing methods in experiments.
Adaptive gradient methods have become recently very popular, in particular as they have been shown to be useful in the training of deep neural networks. In this paper we have analyzed RMSProp, originally proposed for the training of deep neural networks, in the context of online convex optimization and show $\sqrt{T}$-type regret bounds. Moreover, we propose two variants SC-Adagrad and SC-RMSProp for which we show logarithmic regret bounds for strongly convex functions. Finally, we demonstrate in the experiments that these new variants outperform other adaptive gradient techniques or stochastic gradient descent in the optimization of strongly convex functions as well as in training of deep neural networks.