Wei_Dai comments on Values vs. parameters - Less Wrong

9 Post author: PhilGoetz 17 May 2011 05:53AM

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Comment author: Wei_Dai 17 May 2011 05:01:39PM 2 points [-]

I have one heuristic that I think is pretty good for telling when something is not a value: If it's mathematically wrong, it's an error, not a value. So my inclination is to point out that exponential time-discounting is correct. All other forms of time-discounting lead to inconsistencies. You can time-discount exponentially; or you can not time-discount at all, as Eliezer suggested; or you can be in error.

I think this is a good heuristic, but my inclination is to say that it's a logical error to think that non-exponential time-discounting is an "error" and that either exponential discounting and no time-discounting must be part of our values because they are not "errors".

Besides what I said in this reply to Eliezer, another way to avoid inconsistencies without going to exponential discounting is to discount via absolute time as opposed to time relative to "now". Humans do not work this way, of course, but you can program it into an AI if you wanted to.

Comment author: PhilGoetz 17 May 2011 06:10:23PM *  0 points [-]

Besides what I said in this reply to Eliezer,

I'll have to think about that. It's a little too deep for me to process right now.

discount via absolute time as opposed to time relative to "now".

I don't think that will work. Can you explain it in more detail? Distorting time won't prevent reversals of preference just because it makes some plotted curves match.

Comment author: pengvado 21 May 2011 03:19:10AM *  1 point [-]

Distorting time won't prevent reversals of preference just because it makes some plotted curves match.

If your discounting factor is f(t-now) for some function f, then f needs to be translation invariant (modulo positive affine scaling), on pain of preference reversals. The requirement of translation invariance is directly due to the fact that f gets translated by the varying values of "now". For two possible events x1 and x2, the agent compares U(x1)*f(t1-now) vs U(x2)*f(t2-now), where U is the non-discounted utility function, and if the result of that comparison depends on the value of "now" you have problems.

However, if your discounting factor is f(t) simpliciter, then f isn't translated and thus doesn't need to be translation invariant. No single event is ever valued according to multiple different outputs of f. The agent will derive the same preference between any two events regardless of when it computes the decision.

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