  Adaptive learning rate algorithms such as RMSProp are widely used for
training deep neural networks. RMSProp offers efficient training since it uses
first order gradients to approximate Hessian-based preconditioning. However,
since the first order gradients include noise caused by stochastic
optimization, the approximation may be inaccurate. In this paper, we propose a
novel adaptive learning rate algorithm called SDProp. Its key idea is effective
handling of the noise by preconditioning based on covariance matrix. For
various neural networks, our approach is more efficient and effective than
RMSProp and its variant.
