I've read two interpretations of Akaike's Information Criterion (AIC) that seem to be in conflict, and I was hoping that someone could help me understand how to reconcile them.
Interpretation 1: AIC's approximation to the model's KL divergence is only accurate up to an unknown constant, so AIC is useless for estimating predictive error in a more absolute way. This is what Burnham and Anderson say about it.
Interpretation 2: AIC is an approximation to the out-of-sample prediction error, which is on the same absolute scale as cross-validation. This is the approach that Gelman and Vehtari take.
So who's right? Can they both be correct?