one trouble might be that this robot isn't equipped to handle improper distributions. So if you hand it an infinitude of finite simple groups and tell it to choose one, it assigns everything a probability of zero and chooses according to whatever algorithm it uses to choose between things that have identical utility.

I don't think this is too hard to fix. The robot could have a unit of improper prior (epsilon) that it remembers is larger than zero but smaller than any positive real.

Of course, this doesn't tell you what to do when asked to guess whether the order of the correct finite simple group is even, which might be a pretty big drawback.