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# Psy-Kosh comments on Decision theory: Why Pearl helps reduce “could” and “would”, but still leaves us with at least three alternatives - Less Wrong

29 06 September 2009 06:10AM

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Comment author: 08 September 2009 05:50:14PM *  0 points [-]

What I meant is that for TDT, the agent, for lack of a better word, decides what the outcome for a certain abstract algorithm is. (Specifically, the abstract algorithm that it is using to decide that.)

The agent can reason about other systems computing the related algorithms producing related output, so it knows that what it chooses will be reflected in those other systems.

But, I'd want it to be able to take into account the fact that the algorithm it's actually computing is not necessarally the algorithm it thinks it is computing. That is, due to hardware error or whatever, it may produce an output other than what the abstract calculation it thought it was doing would have produced... thus breaking the correlation it was assuming.

ie, I just want some way for the agent to be able to take into account in all this the possibility of errors in the hardware and so on, and in the raw TDT there didn't seem to be a convenient way to do that. Adding in an extra layer of indirection, setting up the causal net as saying "my innards" control a selector which determines which abstract algorithm is actually being computed would SEEM to fix that in a way that, to me, seems to actually fit what's actually going on.

If we assume a weaker "Omega", that can't predict, say, a stray cosmic ray hitting you and causing you to make a 1 bit error or whatever in your decision algorithm, even though it has a copy of your exact algorithm, then that's where what I'm talking about comes in. In that case, your output would derive from the same abstract computation as Omega's prediction for your output.

Imagine the set of all possible algorithms feed into a "my selector node", and also into omega's "prediction selector node"... then "my innards" are viewed as selecting which of those determine the output. But a stray cosmic ray comes in, influences the computation... that is, influences which algorithm the "selector" selects.

A stray cosmic ray can't actually alter an abstract platonic algorithm. Yet it is able to influence the output. So we have to have some way of shoving into TDT the notion of "stuff that actually physically messes with the computation"

Does that clarify what I'm saying here, or am I describing it poorly, or am I just really wrong about all this?

Comment author: 08 September 2009 06:29:55PM *  0 points [-]

Okay, I think I see what you're saying: There is the possibility of something making your action diverge from the Platonic computation you think you're instantiating, and that would interfere with the relationship between the choice you make and the Platonic algorithm.

On top of that, you say that there should be a "My innards" node between the platonic algorithm node and the action node.

However, you claim Omega can't detect this kind of interference. Therefore, the inteference is independent of the implicit interference with all the other nodes and does not need to be represented. (See my remark about how Pearl networks implicitly have an error term parent for every node, and only need to be explicity represented when two or more of these error parents are not independent.)

Also, since it would still be an uninterrupted path from Platonic to choice, the model doesn't gain anything by this intermediate steps; Pearl nets allow you to collapse these into one edge/node.

And, of course, it doesn't make much of a difference for Omega's accuracy anyway...

Comment author: 08 September 2009 06:57:19PM *  1 point [-]

Yeah, I think you've got the point of the problem I'm trying to deal with, though I'm not sure I communicated my current view of the structure of what the solution should be. For one thing, I said that my initial plan, platonic algorithm pointing to innards pointing to output was wrong.

There may potentially be platonic algorithm pointing to innards representing the notion of "intent of the original programmer" or whatever, but I figured more importantly is an inversion is that.

Ie, start with innards... the initial code/state/etc "selects" a computation from the platonic space of all possible computations. But, say, a stray cosmic ray may interfere with the computation. This would be analogous to an external factor poking the selector, shifting which abstract algorithm is the one being computed. So then "omega" (in quotes because am assuming a slightly less omniscient being than usually implied by the name) would be computing the implications of one algorithm, while your output would effectively be the output if a different algorithm. So that weakens the correlation that justifies PD coopoperation, Newcomb one-boxing, etc etc etc etc...

I figure the "innards -> selector from the space of algorithms" structure would seem to be the right way to represent this possibility. It's not exactly just logical uncertainty.

So, I don't quite follow how this is collapsible. ie, It's not obvious to me that the usual error terms help with this specific issue without the extra node. Unless, maybe, we allow the "output" node to be separate from the "algorithm" node and let us interpret the extra uncertianty term from the output node as something that (weakly) decouples the output from the abstract algorithm...

Comment author: 09 September 2009 02:58:20PM 0 points [-]

So then "omega" (in quotes because am assuming a slightly less omniscient being than usually implied by the name) would be computing the implications of one algorithm, while your output would effectively be the output if a different algorithm. So that weakens the correlation that justifies PD coopoperation, Newcomb one-boxing, etc etc etc etc...

Yes, but like I said the first time around, this would be a rare event, rare enough to be discounted if all that Omega cares about is maximizing the chance of guessing correctly. If Omega has some other preferences over the outcomes (a "safe side" it wants to err on), and if the chance is large enough, it may have to change its choice based on this possibility.

So, here's what I have your preferred representation as:

"Platonic space of algorithms" and "innards" both point to "selector" (the actual space of algorithms influences the selector, I assume); "innards" and "Platonic space" also together point to "Omega's prediction", but selector does not, because your omega can't see the things that can cause it to err. Then, "Omega's prediction" points to box content and selector points to your choice. Then, of course, box content and your choice point to payout.

Further, you say the choice the agent makes is at the innards node.

Is that about right?

Comment author: 09 September 2009 03:17:54PM 0 points [-]

Even if rare, the decision theory used should at least be able to THINK ABOUT THE IDEA of a hardware error or such. Even if it dismisses it as not worth considering, it should at least have some means of describing the situation. ie, I am capable of at least considering the possibility of me having brain damage or whatever. Our decision theory should be capable of no less.

Sorry if I'm unclear here, but my focus isn't so much on omega as trying to get a version of TDT that can at least represent that sort of situation.

You seem to more or less have it right. Except I'd place the choice more at the selector or at the "node that represents the specific abstract algorithm that actually gets used"

As per TDT, choose as if you get to decide what the output for the abstract algorithm should be. The catch is that here there's a bit of uncertainty as to which abstract algorithm is being computed. So if, due to cosmic ray striking and causing a bitflip at a certain point in the computation, you end up actually computing algorithm 1B while omega models you as being algorithm 1A, then that'd be potentially a weakening of the dependence. (Again, just using the Newcomb problem simply as a way of talking about this.)

Comment author: 09 September 2009 03:37:12PM 0 points [-]

You seem to more or less have it right. Except I'd place the choice more at the selector or at the "node that represents the specific abstract algorithm that actually gets used".

Okay, so there'd be another node between "algorithm selector" and "your choice of box"; that would still be an uninterrupted path (chain) and so doesn't affect the result.

The problem, then, is that if you take the agent's choice as being at "algorithm selector", or any descendant through "your choice of box", you've d-separated "your choice of box" from "Omega's prediction", meaning that Omega's prediction is conditionally independent of "your choice of box", given the agent's choice. (Be careful to distinguish "your choice of box" from where we're saying the agent is making a choice.)

But then, we know that's not true, and it would reduce your model to the "innards CSA" that AnnaSalamon gave above. (The parent of "your choice of box" has no parents.)

So I don't think that's an accurate representation of the situation, or consistent with TDT. So the agent's choice must be occuring at the "innards node" in your graph.

(Note: this marks the first time I've drawn a causal Bayesian network and used the concept of d-separation to approach a new problem. w00t! And yes, this would be easier if I uploaded pictures as I went.)

Comment author: 09 September 2009 04:25:18PM 0 points [-]

Okay, so there'd be another node between "algorithm selector" and "your choice of box";

Not sure where you're getting that extra node from. The agent's choice is the output of the abstract algorithm they actually end up computing as a result of all the physical processes that occur.

Abstract algorithm space feeds into both your algorithm selector node and the algorithm selector node in "omega"'s model of you. That's where the dependence comes from.

So given logical uncertainty about the output of the algorithm, wouldn't they be d-connected? They'd be d-separated if the choice was already known... but if it was, there'd be nothing left to choose, right? No uncertainties to be dependent on each other in the first place.

Actually, maybe I ought draw a diagram of what I have in mind and upload to imgur or whatever.

Comment author: 10 September 2009 04:24:05AM 0 points [-]

Alright, after thinking about your points some more, and refining the graph, here's my best attempt to generate one that includes your concerns: Link.

Per AnnaSalamon's convention, the agent's would-node-surgery is in a square box, with the rest elliptical and the payoff octagonal. Some nodes included for clarity that would normally be left out. Dotted lines indicate edges that are cut for surgery when fixing "would" node. One link I wasn't sure about has a "?", but it's not that important.

Important points: The cutting of parents for the agent's decision preserves d-connection between box choice and box content. Omega observes innards and attempted selection of algorithm but retains uncertainty as to how the actual algorithm plays out. Innards contribute to hardware failures to accurately implement algorithm (as do [unshown] exogenous factors).

And I do hope you follow up, given my efforts to help you spell out your point.

Comment author: 10 September 2009 04:31:27AM 0 points [-]

Just placing this here now as sort of a promise to follow up. Just that I'm running on insufficient sleep, so can only do "easy stuff" at the moment. :) I certainly plan on following up on our conversation in more detail, once I get a good night's sleep.

Comment author: 10 September 2009 05:03:09AM 0 points [-]

Understood. Looking forward to hearing your thoughts when you're ready :-)

Comment author: 09 September 2009 05:15:43PM *  0 points [-]

Okay, I think there are some terminological issues to sort out here, resulting from our divergence from AnnaSalamon's original terminology.

The discussion I thought we were having corresponds to the CSA's calculation of "woulds". And when you calculate a would, you surgically set the output of the node, which means cutting the links to its parents.

Is this where we are? Are you saying the "would" should be calculated from surgery on the "algorithm selector" node (which points to "choice of box")? Because in that case, the links to "algorithm selector" from "algorithm space" and "innards" are cut, which d-separates them. (ETA: to clarify: d-separates "box choice" from Omega and its descendants.)

OTOH, even if you follow my suggestion and do surgery on "innards", the connection between "box choice" and "omega's prediction" is only a weak link -- algorithm space is huge.

Perhaps you also want an arrow from "algorithm selector" to "omega's prediction" (you don't need a separate node for "Omega's model of your selector" because it chains). Then, the possible difference between the box choice and omega's prediction emerges from the independent error term pointing to box choice (which accounts for cosmic rays, hardware errors, etc.) There is a separate (implicit) "error parent" for the "Omega's prediction" node, which accounts for shortcomings of Omega's model.

This preserves d-connection (between box choice and box content) after a surgery on "algorithm selector". Is that what you're aiming for?

(Causal Bayes nets are kinda fun!)