RMSprop is an unpublished, adaptive learning rate optimization algorithm first proposed by Geoff Hinton in lecture 6 of his online class "Neural Networks for Machine Learning". RMSprop and Adadelta have been developed independently around the same time, and both try to resolve Adagrad's diminishing learning rate problem. [1]
The difference between Adadelta and RMSprop is that Adadelta removes the learning rate 
entirely and replaces it by the root mean squared error of parameter updates.
[1] Sebastian Ruder (2016). An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747.