Why are you minmaxing over expected values of policies, instead of over outcomes? Isn't the worst case for the "tails only" policy "I'm in COPY and the coin is heads", not "'I'm in COPY"?
Basically I don't understand why "past me, who is screaming at me from the sidelines that it matters whether I pick tails or not" once I see that the coin comes up heads is actually correct and the "me" who's indifferent is wrong; one man's modus ponens is another man's modus tollens.
Here's another example that makes my intuition go "ouch" - suppose that choosing heads in ... (read more)
You could say the same thing for Bayesianism. Priors are subjective, so why should my beliefs be related to past-me beliefs by the Bayes rule? Indeed, some claim they shouldn't be. But it's still interesting to ask what happens if past-me has the power to enforce eir opinions. What if I'm able to make sure that my descendant agents will act optimally from my subjective point of view? Then you need dynamic consistency: for classical Bayesianism it's the Bayes rule, and for infra-Bayesianism it's our new updating rule.
Certainly if you're interested in learning algorithms, then dynamic consistency seems like a very useful property. Our learning desiderata (regret bounds) are defined from the point of view of the prior, so an algorithm designed for that purpose should remain consistent with this starting point.
On the other hand, we can also imagine situations where past-me has a reason to trust present-me's reasoning better than eir own reasoning, in which case some kind of "radical probabilism" is called for. For example, in Turing reinforcement learning, the agent can update on evidence coming from computational experiments. If we consider the beliefs of such an agent about the external environment only, they would change in a way inconsistent with the usual rule. But it's still true that the updates are not systematically biased: if you already knew where you will update, you would already have updated. And ofc if we do treat the "virtual evidence" explicitly, we return to the standard update rule.
1Diffractor
Maximin over outcomes would lead to the agent devoting all its efforts towards avoiding the worst outcomes, sacrificing overall utility, while maximin over expected value pushes towards policies that do acceptably on average in all of the environments that it may find itself in.
Regarding "why listen to past me", I guess to answer this question I'd need to ask about your intuitions on Counterfactual mugging. What would you do if it's one-shot? What would you do if it's repeated? If you were told about the problem beforehand, would you pay money for a commitment mechanism to make future-you pay up the money if asked? (for +EV)
Why are you minmaxing over expected values of policies, instead of over outcomes? Isn't the worst case for the "tails only" policy "I'm in COPY and the coin is heads", not "'I'm in COPY"?
Basically I don't understand why "past me, who is screaming at me from the sidelines that it matters whether I pick tails or not" once I see that the coin comes up heads is actually correct and the "me" who's indifferent is wrong; one man's modus ponens is another man's modus tollens.
Here's another example that makes my intuition go "ouch" - suppose that choosing heads in ... (read more)