komponisto comments on A simple counterexample to deBlanc 2007? - Less Wrong

3 Post author: PhilGoetz 30 May 2011 05:09AM

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Comment author: komponisto 30 May 2011 06:08:09AM *  2 points [-]

Peter de Blanc ... claims to show that a utility function can have a value only if the utility function is bounded.

This is important because it implies that, if a utility function is unbounded, it is useless.

From the LW wiki (emphasis added):

Peter de Blanc has proven that if an agent assigns a finite probability to all computable hypotheses...and assigns unboundedly large finite utilities over percept sequences...then the sum in the expected utility formula does not converge.

Peter de Blanc's paper [is] sometimes misinterpreted as showing that any agent with an unbounded finite utility function over outcomes is not consistent, but this has yet to be demonstrated.

Comment author: RichardKennaway 30 May 2011 10:53:17AM *  1 point [-]

What distinction is being drawn in the wiki article between percept sequences and outcomes? The agent's perceptions are its only clue to the outcomes it has achieved, so a utility function over outcomes reduces, via the agent's posterior distribution of outcomes given perceptions, to one over perceptions.

ETA: I'm itching to add a {{by whom}} tag after "sometimes" and {{citation needed}} after "misinterpreted", but I don't think the LW wiki supports those. The implication of the sentence is that some people have interpreted the paper that way and at least one person has argued that this is incorrect, but who and where?

Comment author: PhilGoetz 30 May 2011 06:12:46AM *  0 points [-]

The percept sequences paper is his 2009 paper. That wiki page does refer to his 2007 paper; that may be an error.

It is in any case clear in the 2007 paper that the entities in the sum are possible worlds, and possible actions; and that it is the utility function that is unbounded. "Percepts" in this paper are the result of evaluating a possible-world function on a possible-action. None of this terminological quibbling affects anything I wrote.

As I quoted above, the 2007 paper says, "A computable utility function will have convergent expected utilities iff that function is bounded." Please dissect the difference between that, and the statement I made that you are criticizing, if you think my statement is a misinterpretation. (I just now changed my statement to "a utility function can have an expected value", but I assume you realize that was what I meant.)

Comment author: komponisto 30 May 2011 06:31:20AM *  0 points [-]

As I quoted above, the 2007 paper says, "A computable utility function will have convergent expected utilities iff that function is bounded." Please dissect the difference between that, and the statement I made that you are criticizing, if you think my statement is a misinterpretation.

In that case, the difference is the word "computable". Not that that affects your argument, since as I understood it your proposed counterexample is the identity function.