i doubt there is a cloud based software for compositing right now.
there are several issues to consider: compositing uses a lot of footage and transfering that over the internet to the cloud based computer takes time. even if you upload all your footage before you start it will take a long time, we speaking here of several GBs of data (depending of shot length and how many elements you have)
then you often (speaking of VFX work) decide to add a nother element to the shot and now you have to upload that again. in the mean time you have to wait and cant work anymore.
so you wont get a speed increase when you compute your effects on a remote computer.
as the other guy said before: there are some cheap (or free) alternatives in software which will get you started and become familiar with the principles of compositing.