Thanks, you’re right. There’s this long thread, but I’ll try to explain the issues here more concisely. I think the theorems have the following limitations that were not reasonably explained in the paper (and some accompanying posts):
The theorems are generally not applicable for stochastic environments (despite the paper and some relatedposts suggesting otherwise).
The theorems may not be applicable if there are cycles in the state graph of the MDP (other than self-loops in terminal states); for example:
The theorems are not applicable in states from which a reversible action can be taken.
The theorems are not applicable in states from which only one action (that is not POWER-seeking) allows to reach a cycle of a given length.
I’m not arguing that the theorems don’t prove anything useful. I’m arguing that it’s very hard for the readers of the paper (and some accompanying posts) to understand what the theorems actually prove. Readers need to understand about 20 formal definitions that build on each other to understand the theorems. I also argue that the lack of explanations about what the theorems actually prove, and some of the informal claims that were made about the theorems, are not reasonable (and cause the theorems to appear more impressive). Here’s an example for such an informal claim (taken from this post):
This isn’t exactly what Ofer is complaining about, but one take on the issue, that math can be overstated, poorly socialized, misleading or overbearing, is a common critique in domains that use a lot of applied math (theoretical econ, interdisciplinary biology) that borrows from pure math, physics, etc.
It depends on things (well, sort of your ideology, style, and academic politics TBH) but I think the critique can often be true.
Thanks, you’re right. There’s this long thread, but I’ll try to explain the issues here more concisely. I think the theorems have the following limitations that were not reasonably explained in the paper (and some accompanying posts):
The theorems are generally not applicable for stochastic environments (despite the paper and some related posts suggesting otherwise).
The theorems may not be applicable if there are cycles in the state graph of the MDP (other than self-loops in terminal states); for example:
The theorems are not applicable in states from which a reversible action can be taken.
The theorems are not applicable in states from which only one action (that is not POWER-seeking) allows to reach a cycle of a given length.
I’m not arguing that the theorems don’t prove anything useful. I’m arguing that it’s very hard for the readers of the paper (and some accompanying posts) to understand what the theorems actually prove. Readers need to understand about 20 formal definitions that build on each other to understand the theorems. I also argue that the lack of explanations about what the theorems actually prove, and some of the informal claims that were made about the theorems, are not reasonable (and cause the theorems to appear more impressive). Here’s an example for such an informal claim (taken from this post):
To onlookers, I want to say that:
This isn’t exactly what Ofer is complaining about, but one take on the issue, that math can be overstated, poorly socialized, misleading or overbearing, is a common critique in domains that use a lot of applied math (theoretical econ, interdisciplinary biology) that borrows from pure math, physics, etc.
It depends on things (well, sort of your ideology, style, and academic politics TBH) but I think the critique can often be true.
Although to be fair, this particular one critique seems much more specific and it seems like Ofer might be talking past Alex Turner and his meaning (but I have no actual idea of the math or the claims)
The tone of the original post is pretty normal or moderate, and isn’t “casting shade”.
but it might be consistent with issues like:
this person has some agenda that is unhelpful and unreasonable;
they are just a gadfly;
they don’t really “get it” but know enough to fool themselves and pick at things forever.
But these issues apply to my account too. I think the tone is pretty good to me.