To be honest, I don’t really know what “Bayesianism as a conceptual framework” is, or if it even exists at all. Bayes theorem is an equation, and Bayesianism to the rest of the world is a formalization of probability based on Bayes theorem. It’s certainly not this comical strawman of a hypothetical general AI that doesn’t understand that its prediction algorithms take time to run.
I agree that I am not critiquing “Bayesianism to the rest of the world”, but rather a certain philosophical position that I see as common amongst people reading this site. For example, I interpret Eliezer as defending that position here (note that the first paragraph is sarcastic):
Clearly, then, a Carnot engine is a useless tool for building a real-world car. The second law of thermodynamics, obviously, is not applicable here. It’s too hard to make an engine that obeys it, in the real world. Just ignore thermodynamics—use whatever works.
This is the sort of confusion that I think reigns over they who still cling to the Old Ways.
No, you can’t always do the exact Bayesian calculation for a problem. Sometimes you must seek an approximation; often, indeed. This doesn’t mean that probability theory has ceased to apply, any more than your inability to calculate the aerodynamics of a 747 on an atom-by-atom basis implies that the 747 is not made out of atoms. Whatever approximation you use, it works to the extent that it approximates the ideal Bayesian calculation—and fails to the extent that it departs.
Also, insofar as AIXI is a “hypothetical general AI that doesn’t understand that its prediction algorithms take time to run”, I think “strawman” is a little inaccurate.
Anyway, thanks for the comment. I’ve updated the first paragraph to make the scope of this essay clearer.
Somehow you and I are taking the exact opposite conclusions from that paragraph. He is explicitly noting that your interpretation is incorrect—that approximations are necessary because of time constraints. All he is saying is that underneath, the best possible action is determined by Bayesian arithmetic, even if it’s better on net to choose the approximation because of compute constraints. Just because general relativity is more “true” than newtonian mechanics, doesn’t mean that it’s somehow optimal to use it to track the trajectory of mortar fire.
To be honest, I don’t really know what “Bayesianism as a conceptual framework” is, or if it even exists at all. Bayes theorem is an equation, and Bayesianism to the rest of the world is a formalization of probability based on Bayes theorem. It’s certainly not this comical strawman of a hypothetical general AI that doesn’t understand that its prediction algorithms take time to run.
I agree that I am not critiquing “Bayesianism to the rest of the world”, but rather a certain philosophical position that I see as common amongst people reading this site. For example, I interpret Eliezer as defending that position here (note that the first paragraph is sarcastic):
Also, insofar as AIXI is a “hypothetical general AI that doesn’t understand that its prediction algorithms take time to run”, I think “strawman” is a little inaccurate.
Anyway, thanks for the comment. I’ve updated the first paragraph to make the scope of this essay clearer.
Somehow you and I are taking the exact opposite conclusions from that paragraph. He is explicitly noting that your interpretation is incorrect—that approximations are necessary because of time constraints. All he is saying is that underneath, the best possible action is determined by Bayesian arithmetic, even if it’s better on net to choose the approximation because of compute constraints. Just because general relativity is more “true” than newtonian mechanics, doesn’t mean that it’s somehow optimal to use it to track the trajectory of mortar fire.