Thoughts on the 5-10 Problem

Yes, you could make the code more robust by allowing the agent to act once its found a proof that any action is superior. Then, it might find a proof like

U(F) = 5

U(~F) = 10

10 > 5

U(~F) > U(F)

However, there's no guarantee that this will be the first proof it finds.

When I say "look for a proof", I mean something like "for each of the first 10^(10^100)) Godel numbers, see if it encodes a proof. If so, return that action.

In simple cases like the one above, it likely will find the correct proof first. However, as the universe gets more complicated (as our universe is), there is a greater chance that a spurious proof will be found first.

Doesn't that mean the agent never makes a decision?