(This originated as a comment on the post "Embedded World-Models," but it makes a broadly applicable point and is substantial enough to be a post, so I thought I'd make it a post as well.)

This post feels quite similar to things I have written in the past to justify my lack of enthusiasm about idealizations like AIXI and logically-omniscient Bayes. But I would go further: I think that grappling with embeddedness properly will inevitably make theories of this general type irrelevant or useless, so that "a theory like this, except for embedded agents" is not a thing that we can reasonably want. To specify what I mean, I'll use this paragraph as a jumping-off point:

Embedded agents don’t have the luxury of stepping outside of the universe to think about how to think. What we would like would be a theory of rational belief for situated agents which provides foundations that are similarly as strong as the foundations Bayesianism provides for dualistic agents.

Most "theories of rational belief" I have encountered -- including Bayesianism in the sense I think is meant here -- are framed at the level of an evaluator outside the universe, and have essentially no content when we try to transfer them to individual embedded agents. This is because these theories tend to be derived in the following way:

We want a theory of the best possible behavior for agents.
We have some class of "practically achievable" strategies $S$ , which can actually be implemented by agents. We note that an agent's observations provide some information about the quality of different strategies $s \in S$ . So if it were possible to follow a rule like $R \equiv$ "find the best $s \in S$ given your observations, and then follow that $s$ ," this rule would spit out very good agent behavior.
Usually we soften this to a performance-weighted average rather than a hard argmax, but the principle is the same: if we could search over all of $S$ , the rule $R$ that says "do the search and then follow what it says" can be competitive with the very best $s \in S$ . (Trivially so, since it has access to the best strategies, along with all the others.)
But usually $R \notin S$ . That is, the strategy "search over all practical strategies and follow the best ones" is not a practical strategy. But we argue that this is fine, since we are constructing a theory of ideal behavior. It do

...

nostalgebraist

nostalgebraist's Posts

nostalgebraist's Comments