I don't see exactly how that would work - it can't build paper clips during the first week, so u(p(t))=0 during that period. Therefore it should behave exactly as if nothing special happened on Tuesday?
And my comment on turning itself off for Tuesday was more that the Monday AI wouldn't want it's infrastructure ruined by the Tuesday version, and would just turn itself off to prevent that.
I see - I thought you meant it would run for a week building infrastructure, and then be able to build paperclips on the first Monday you named.
I'm not sure what you WANT it to do, really. Do you want it to actually sabotage itself on Tuesday, or do you want it to keep on building infrastructure for later paperclip construction?
Under the system I built, it would do absolutely nothing different on Tuesday and continue to build infrastructure because it anticipates wanting more paperclips by the time it is able to build them at the end of the week. It wants ...
A putative new idea for AI control; index here.
A simple and easy design for a u-maximising agent that turns into a u-minimising one.
Let X be some boolean random variable outside the agent's control, that will be determined at some future time t (based on a cosmic event, maybe?). Set it up so that P(X=1)=ε, and for a given utility u, consider the utility:
Before t, the expected value of (2/ε)X is 2, so u# = u. Hence the agent is a u-maximiser. After t, the most likely option is X=0, hence a little bit of evidence to that effect is enough to make u# into a u-minimiser.
This isn't perfect corrigibility - the agent would be willing to sacrifice a bit of u-value (before t) in order to maintain its flexibility after t. To combat this effect, we could instead use:
If Ω is large, then the agent is willing to pay very little u-value to maintain flexibility. However, the amount of evidence of X=0 that it needs to become a u-minimiser is equally proportional to Ω, so X better be a clear and convincing event.