  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.
