If someone creates a Juju Charm https://jujucharms.com for this, then you can use the pre-configured service on any of the major public clouds.
We work with the ubuntu team on juju.
We are working very closely with canonical/IBM on the whole DL stack[1]. You will also see some stuff from us and nvidia here within the next month or so on making cuda a bit easier to setup in a normal data science "stack" eg: jvm/python hybrid product stacks. Cudnn has tricky licensing but it shouldn't be that bad to automate setting up the cuda part.
[1]: https://insights.ubuntu.com/2016/04/25/making-deep-learning-...
I will work out what we are allowed to do licemse wise. Reach out to adam@skymind.io if that is interesting.