I basically agree with this, although I guess I’d always thought of it in terms of the KL distance incorporating a particular, implicit utility function that happens to be wrong in many cases. It can speak of “better_KL”, but only according to a (sometimes) stupid utility function.
The failure of the KL divergence to incorporate an adequate notion of “betterness” is also demonstrated by the fact that you’d get a different answer if you used an alternative divergence measure. Jensen-Shannon divergence, for example, would give the same answer as instrumental rationality in this example, no? (Though you could obviously construct different examples where it too would diverge from instrumental rationality.)
I basically agree with this, although I guess I’d always thought of it in terms of the KL distance incorporating a particular, implicit utility function that happens to be wrong in many cases. It can speak of “better_KL”, but only according to a (sometimes) stupid utility function.
The failure of the KL divergence to incorporate an adequate notion of “betterness” is also demonstrated by the fact that you’d get a different answer if you used an alternative divergence measure. Jensen-Shannon divergence, for example, would give the same answer as instrumental rationality in this example, no? (Though you could obviously construct different examples where it too would diverge from instrumental rationality.)