I was having a great deal of difficulty installing the keras and tensorflow packages. It turns out the problem was that I (in an earlier attempt to get python integration working) had set the Python interpreter variable using Global Options > Python from the RStudio IDE.
This then meant that reticulate was not properly using miniconda to install tensorflow and keras. (Thanks to Tomasz Kalinowski for helping me debug this).
There seems to be a lot of real-estate on this page, and as reticulate seems to be set up to work with these virutal environments, it might be useful to add a recommendation to install Anaconda/miniconda on this page. This would help somebody like me who is much more of a R person than a python person.