The convergence theorems basically say that optimizing for P[t] converges to optimizing for T[t+d] for some sufficient timespan d.
The idea of a convergence theorem showing that optimizing any objective leads to empowerment has been brought up a bunch of times in these discussions, as in this quote. Is there some well-known proof/paper where this is shown? AFAICT the original empowerment do not show any proof like this (may have missed it). Is this based off of Alex Turner’s work (https://arxiv.org/pdf/1912.01683.pdf) which results in a different measure than information theoretic empowerment (but intuitively related), or something else?
The idea of a convergence theorem showing that optimizing any objective leads to empowerment has been brought up a bunch of times in these discussions, as in this quote. Is there some well-known proof/paper where this is shown? AFAICT the original empowerment do not show any proof like this (may have missed it). Is this based off of Alex Turner’s work (https://arxiv.org/pdf/1912.01683.pdf) which results in a different measure than information theoretic empowerment (but intuitively related), or something else?
Excellent post btw.