Most importanly, it is almost inevitable they must run on a fam of computers basically mean it becomes a service. Can we ever create a robot who can self-learn but with the super brain power locally without having to call a service for an answer?
TPU's are available for rent. Also, apparently AlphaGo became 10x more efficient in a year. Who's to say other Go engines won't continue improving efficiency?
Between software and hardware improvements I think it's likely that we'll see very strong Go engines on desktop computers in a few years.
Public means API? AlphaGo is very specialized in solving Go game. Google, Amazon and IBM have services for various services like image recongition and speech recongition. Startups like Clarifi also exists in that space.
The closest to a generalized AI service would probably be Watson from IBM (but I don't have experiment with it sadly so I am not sure about the usage experience).
Public in the sense of non proprietary, in this case most likely universities.
My question was more : Google probably based its tools on existing tools, and those most likely come from universities (research paper, computer infrastructures, etc.). So what are those tools, where are they ?