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Vladimir_Nesov comments on Counterfactual Calculation and Observational Knowledge - Less Wrong
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Comments (183)
I don't understand what this refers to. (Which branch is that? What do you mean by "replace"? Does your 'odd' refer to calculator-shows-odd or it's-actually-odd or 'let's-write-"odd"-on-the-test-sheet etc.?)
Also, updateless decision-maker reasons about strategies, which describe responses to all possible observations, and in this sense updateless analysis does take possible observations into account.
(The downside of long replies and asynchronous communication: it's better to be able to interrupt after a few words and make sure we won't talk past each other for another hour.)
Here's another attempt at explaining your error (as it appears to me):
In the terminology of Wei Dai's original post an updateless agent considers the consequences of a program S(X) returning Y on input X, where X includes all observations and memories, and the agent is updateless in respect to things included in X. For an ideal updateless agent this X includes everything, including the memory of having seen the calculator come up even. So it does not make sense for such an agent to consider the unconditional strategy of choosing even, and doing so does not properly model an updating agent choosing even after seeing even, it models an updating agent choosing even without having seen anything.
An obvious simplification of an (computationally extremely expensive) updateless agent would be to simplify X. If X is made up of the parts X1 and X2 and X1 is identical for all instances of S being called, then it makes sense to incorporate X1 into a modified version of S, S' (more precisely the part of S or S' that generates the world programs S or S' tries to maximize). In that case a normal Bayesian update would be performed (UDT is not a blanket rejection of Bayesianism, see Wei Dai's original post). S' would be updateless with resepct to X2, but not with respect to X1. If X1 is indeed always part of the argument when S is called S' should always give back the same output as S.
Your utility implies an S' with respect to having observed "even", but without the corresponding update, so it generates faulty world programs, and a different utility expectation than the original S or a correctly simplified version S'' (which in this case is not updateless because there is nothing else to be updateless towards).
(This question seems to depend on resolving this first.)
The updateless analogue to the updater strategy "ask Omega to fill in the answer "even" in counterfactual worlds because you have seen the calculator result "even"" is "ask Omega to fill in the answer the calculator gives whereever Omega shows up". As an updateless decision maker you don't know that the calculator showed "even" in your world because "your world" doesn't even make sense to an updateless reasoner. The updateless replacing strategy is a fixed strategy that has a particular observation as parameter. An updateless strategy without parameter would be equivalent to an updater strategy of asking Omega to write in "even" in other worlds before seeing any calculator result.
Updateless strategies describe how you react to observations. You do react to observations in updateless strategies. In our case, we don't even need that, since all observations are fixed by the problem statement: you observe "even", case closed. The strategies you consider specify what you write down on your own "even" test sheet, and what you write on the "odd" counterfactual test sheet, all independently of observations.
The "updateless" aspect is in not forgetting about counterfactuals and using prior probabilities everywhere, instead of updated probabilities. So, you use P(Odd n "odd") to describe the situation where Q is Odd and the counterfactual calculator shows "odd", instead of using P(Odd n "odd"|"even"), which doesn't even make sense.
Holding observations fixed but not updating on them is simply a misapplication of UDT. For an ideal updateless agent no observation is fixed and everything (every memory and observation) part of the variable input X. See this comment
A misapplication, strictly speaking, but not "simply". Without restricting your attention to particular situations, while ignoring other situations, you won't be able to consider any thought experiments. For any thought experiment I show you, you'll say that you have to compute expected utility over all possible thought experiments, and that would be end of it.
So in applying UDT in real life, it's necessary to stipulate the problem statement, the boundary event in which all relevant possibilities are contained, and over which we compute expected utility. You, too, introduced such an event, you just did it a step earlier than what's given in the problem statement, by paying attention to the term "observation" attached to the calculator, and the fact that all other elements of the problem are observations also.
(On unrelated note, I have doubts about correctness of your work with that broader event too, see this comment.)
Yes, of course. But you perform normal Bayesian updates for everything else (everything you hold fixed). Holding something fixed and not updating leads to errors.
Simple example: An urn with either 90% red and 10% blue balls or 90% blue and 10% red balls (0.5 prior for either). You have drawn a red ball and put it back. What's the updateless expected utility of drawing another ball, assuming you get 1 util for drawing a ball in the same color and -2 utils for drawing a ball in a different color? Calculating as getting 1 util for red balls and -2 for blue, but not updating on the observation of having drawn a red ball suggests that it's -0.5, when in fact it's 0.46.
EDIT: miscalculated the utilities, but the general thrust is the same.
P(RedU)=P(BlueU)=P(red)=P(blue)=0.5
P(red|RedU)=P(RedU|red)=P(blue|BlueU)=P(BlueU|blue)=0.9
P(blue|RedU)=P(RedU|blue)=P(BlueU|red)=P(Red|BlueU)=0.1
U_updating=P(RedU|red)*P(red|RedU)*1 + P(BlueU|red)*Pred(|BlueU)*1 - P(RedU|red)*P(blue|RedU)*2 - P(BlueU|red)*P(blue|BlueU)*2 = 0.9*0.9+0.1*0.1-0.9*0.1*2*2= 0.46
U_semi_updateless=P(red)*1-P(blue)*2=-0.5
U_updateless= P(red)(P(RedU|red)*P(red|RedU)*1 + P(BlueU|red)*Pred(|BlueU)*1 - P(RedU|red)*P(blue|RedU)*2 - P(BlueU|red)*P(blue|BlueU)*2) +P(blue)(P(BlueU|blue)*P(blue|BlueU)*1 + P(RedU|blue)*P(blue|RedU)*1 - P(BlueU|blue)*P(red|BlueU)*2 - P(RedU|blue)*P(red|RedU)*2) =0.5*(0.9*0.9+0.1*0.1-0.9*0.1*2*2)+0.5* (0.9*0.9+0.1*0.1-0.9*0.1*2*2)=0.46
(though normally you'd probably come up with U_updateless in a differently factored form)
EDIT3: More sensible/readable factorization of U_updateless:
P(RedU)((P(red|RedU)(P(red|RedU)*1-P(blue|RedU)*2)+(P(blue|RedU)(P(blue|RedU)*1-P(red|RedU)*2)) + P(BlueU)((P(blue|BlueU)(P(blue|BlueU)*1-P(red|BlueU)*2)+(P(red|BlueU)(P(red|BlueU)*1-P(blue|BlueU)*2))
No, controlling something and updating it away leads to errors. Fixed terms in expected utility don't influence optimality, you just lose ability to consider the influence of various strategies on them. Here, the strategies under considerations don't have any relevant effects outside the problem statement.
(I'll look into your example another time.)
Just to make sure: You mean something like updating on the box being empty in transparent Newcomb's here, right? Not relevant as far as I can see.
I admit that I did not anticipate you replying in this way and even though I think I understand what you are saying I still don't understand why. This is the main source of my uncertainty on whether I'm right at this point. It seems increasingly clear that at least one of us doesn't properly understand UDT. I hope we can clear this up and if it turns out the misunderstanding was on my part I commit to upvoting all comments by you that contributed to enlightening me about that.
Unless I completely misunderstand you that's a completely different context for/meaning of "fixed term" and while true not at all relevant here. I mean fixed in the sense of knowing the utilities of red and blue balls in the example I gave.
Also leads to errors, obviously. And I'm not doing that anyway. Something leading to errors is extremely weak evidence against something else also leading to error, so how is this relevant?
This is the very error which UDT (at least, this aspect of it) is correction for.
That still doesn't make it evidence for something different not being an error. (and formal UDT is not the only way to avoid that error)
More generally, you can have updateless analysis being wrong on any kind of problem, simply by incorporating an observation into the problem statement and then not updating on it.
Huh? If you don't update, you don't need to update, so to speak. By not forgetting about events, you do take into account their relative probability in the context of the sub-events relevant for your problem. Examples please.
here