You can’t turn off just the ads and they aren’t ads as such, they offer different products from avast! in case you might be interested in them. Though, i agree, they can be annoying if you aren’t interested and i also hate the big white button in the VPS update popup but they refuse to make it look better.
Only way that i know to get rid of it is to disable the VPS update popup altogether.
Settings → Updating → scroll down and expand last section, uncheck the second checkbox out of three which is for the updating popup. This way you won’t even see the popup anymore.