Eliezer_Yudkowsky comments on Universal agents and utility functions - Less Wrong

29 Post author: Anja 14 November 2012 04:05AM

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Comment author: Eliezer_Yudkowsky 25 November 2012 12:26:12AM 2 points [-]

Game theory motivated surreal numbers. Game theory != decision theory.

Comment author: timtyler comment score below threshold [+] (7 children)

Comment author: Eliezer_Yudkowsky 25 November 2012 01:33:38AM 2 points [-]

They're entirely different fields of math, and for good reason (most decisions are not about adversarial games). Plugging surreal numbers into decision theory as (probabilistic) utility-weights is a completely different project from their standard use in (deterministic) game theory to determine who wins a game.

Comment author: timtyler 25 November 2012 02:24:57AM * -1 points [-]

Game theory hasn't been confined to adversarial interactions for decades, and - as far as I know - it was never confined to deterministic interactions in the first place. Game theory and decision theory massively overlap - and the differences are not too significant, IMO. In particular, the reason why surreal numbers are useful when deciding what move to make in a game of go is the exact same reason why they are useful when making other kinds of decisions.

Comment author: Benja 25 November 2012 08:12:50PM * 3 points [-]

Except that surreal numbers were invented for and are useful for combinatorial game theory, which is confined to adversarial and deterministic interactions.

[ETA: Ok, this was unclear: I'm saying that this is how they are useful in the context of analyzing Go, and this is the only context where they are useful in this way; I'm agreeing with the grandparent that trying to use surreal numbers as probabilities or utilities is not even remotely related, not saying that they couldn't possibly be used like that.]

In particular, the reason why surreal numbers are useful when deciding what move to make in a game of go is the exact same reason why they are useful when making other kinds of decisions.

Well--

I believe I understand the issues involved well enough that my correct answer to this is not to ask what you could possibly mean by that, but simply to say:

No. That's nonsense.

Comment author: timtyler 25 November 2012 09:20:29PM * 0 points [-]

That doesn't have the form of a proper argument. It's like arguing that, because Viagra was invented as a treatment for hypertension, it isn't useful for anything else.

Surreal numbers solve the problem of adding values - in cases where 0 < A < B and any number of A < B. Such scenarios don't require determinism or adversaries - those are are irrelevant.

Comment author: Benja 25 November 2012 09:42:19PM * -1 points [-]

That doesn't have the form of a proper argument. It's like arguing that, because Viagra was invented as a treatment for hypertension, it isn't useful for anything else.

No, it's like if someone says that the reason Viagra helps with erectile dysfunction is "completely different" from the reason it helps with hypertension, and you claim that no, the reason is in fact "exactly the same", and then a third person says "No. That's nonsense." and then you explain lucidly how it is in fact the same reason and everybody laughs at that other person...

Oh wait, your reply wasn't to explain why the reason is the same, it was to explain how everybody else is missing the important fact that Viagra helps with erectile dysfunction.

[ETA: Wait, I see how the first paragraph of my earlier post could sound like I was missing the point that surreal numbers can be used like that; edited to clarify.] [ETA2: But I'd still like to hear that lucid explanation and get the attendant egg on my face, if there is one. There isn't one, though.]

Comment author: Oscar_Cunningham 25 November 2012 12:35:36PM * 1 point [-]

The usage that I thought was standard was to use "decision theory" and "game theory" synonymously and then use "combinatorial game theory" to refer in particular to the games which are deterministic and have perfect knowledge e.g. Chess, Tic-tac-toe and Nim. It's combinatorial game theory for which Conway used the theory of the surreals, and I haven't heard of any use of them in game theory outside of this.

EDIT: On second thoughts, "decision theory" and "game theory" aren't synonyms; game theory is the subset of decision theory involving interactions with other agents.

Comment author: timtyler 25 November 2012 02:00:33PM 0 points [-]

Yes, but see:

Individual decision problems with stochastic outcomes are sometimes considered "one-player games".

Also, "decisions in situations where there's at least one agent around" is a pretty daft way to define a field of enquiry, IMO.

Eliezer_Yudkowsky comments on Universal agents and utility functions - Less Wrong

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