Academic website: https://www.andrew.cmu.edu/user/coesterh/
Caspar Oesterheld(Caspar Oesterheld)
In short, the idea is that there might be a few broad types of “personalities” that AIs tend to fall into depending on their training. These personalities are attractors.
I’d be interested in why one might think this to be true. (I only did a very superficial ctrl+f on Lukas’ post—sorry if that post addresses this question.) I’d think that there are lots of dimensions of variation and that within these, AIs could assume a continuous range of values. (If AI training mostly works by training to imitate human data, then one might imagine that (assuming inner alignment) they’d mostly fall within the range of human variation. But I assume that’s not what you mean.)
This means that the model can and will implicitly sacrifice next-token prediction accuracy for long horizon prediction accuracy.
Are you claiming this would happen even given infinite capacity?
I think that janus isn’t claiming this and I also think it isn’t true. I think it’s all about capacity constraints. The claim as I understand it is that there are some intermediate computations that are optimized both for predicting the next token and for predicting the 20th token and that therefore have to prioritize between these different predictions.
Here’s a simple toy model that illustrates the difference between 2 and 3 (that doesn’t talk about attention layers, etc.).
Say you have a bunch of triplets . Your want to train a model that predicts from and from .
Your model consists of three components: . It makes predictions as follows:
(Why have such a model? Why not have two completely separate models, one for predicting and one for predicting ? Because it might be more efficient to use a single both for predicting and for predicting , given that both predictions presumably require “interpreting” .)
So, intuitively, it first builds an “inner representation” (embedding) of . Then it sequentially makes predictions based on that inner representation.
Now you train and to minimize the prediction loss on the parts of the triplets. Simultaneously you train to minimize prediction loss on the full triplets. For example, you update and with the gradients
and you update and with the gradients
.
(The here is the “true” , not one generated by the model itself.)This training pressures to be myopic in the second and third sense described in the post. In fact, even if we were to train with the predicted by rather than the true , is pressured to be myopic.
Type 3 myopia: Training doesn’t pressure to output something that makes the follow an easier-to-predict (computationally or information-theoretically) distribution. For example, imagine that on the training data implies , while under , follows some distribution that depends in complicated ways on . Then will not try to predict more often.
Type 2 myopia: won’t try to provide useful information to in its output, even if it could. For example, imagine that the s are strings representing real numbers. Imagine that is always a natural number, that is the -th Fibonacci number and is the -th Fibonacci number. Imagine further that the model representing is large enough to compute the -th Fibonacci number, while the model representing is not. Then one way in which one might think one could achieve low predictive loss would be for to output the -th Fibonacci number and then encode, for example, the -th Fibonacci number in the decimal digits. (E.g., .) And then computes the -th Fibonacci number from the -th decimal. But the above training will not give rise to this strategy, because gets the true as input, not the one produced by . Further, even if we were to change this, there would still be pressure against this strategy because () is not optimized to give useful information to . (The gradient used to update doesn’t consider the loss on predicting .) If it ever follows the policy of encoding information in the decimal digits, it will quickly learn to remove that information to get higher prediction accuracy on .
Of course, still won’t be pressured to be type-1-myopic. If predicting requires predicting , then will be trained to predict (“plan”) .
(Obviously, $g_2$ is pressured to be myopic in this simple model.)
Now what about ? Well, is optimized both to enable predicting from and predicting from . Therefore, if resources are relevantly constrained in some way (e.g., the model computing is small, or the output of is forced to be small), will sometimes sacrifice performance on one to improve performance on the other. So, adapting a paragraph from the post: The trained model for (and thus in some sense the overall model) can and will sacrifice accuracy on to achieve better accuracy on . In particular, we should expect trained models to find an efficient tradeoff between accuracy on and accuracy on . When is relatively easy to predict, will spend most of its computation budget on predicting .
So, is not “Type 2” myopic. Or perhaps put differently: The calculations going into predicting aren’t optimized purely for predicting .
However, is still “Type 3” myopic. Because the prediction made by isn’t fed (in training) as an input to or the loss, there’s no pressure towards making influence the output of in a way that has anything to do with . (In contrast to the myopia of , this really does hinge on not using in training. If mattered in training, then there would be pressure for to trick into performing calculations that are useful for predicting . Unless you use stop-gradients...)
* This comes with all the usual caveats of course. In principle, the inductive bias may favor a situationally aware model that is extremely non-myopic in some sense.
At least in this case (celebrities and their largely unknown parents), I would predict the opposite. That is, people are more likely to be able to correctly answer “Who is Mary Lee Pfeiffer’s son?” than “Who is Tom Cruise’s mother?” Why? Because there are lots of terms / words / names that people can recognize passively but not produce. Since Mary Lee Pfeiffer is not very well known, I think Mary Lee Pfeiffer will be recognizable but not producable to lots of people. (Of people who know Mary Lee Pfeiffer in any sense, I think the fraction of people who can only recognize her name is high.) As another example, I think “Who was born in Ulm?” might be answered correctly by more people than “Where was Einstein born?”, even though “Einstein was born in Ulm” is a more common sentence for people to read than “Ulm is the city that Einstein was born in”.
If I had to run an experiment to test whether similar effects apply in humans, I’d probably try to find cases where A and B in and of themselves are equally salient but the association A → B is nonetheless more salient than the association B → A. The alphabet is an example of this (where the effect is already confirmed).
I mean, translated to algorithmic description land, my claim was: It’s often difficult to prove a negative and I think the non-existence of a short algorithm to compute a given object is no exception to this rule. Sometimes someone wants to come up with a simple algorithm for a concept for which I suspect no such algorithm to exist. I usually find that I have little to say and can only wait for them to try to actually provide such an algorithm.
So, I think my comment already contained your proposed caveat. (“The concept has K complexity at least X” is equivalent to “There’s no algorithm of length <X that computes the concept.”)Of course, I do not doubt that it’s in principle possible to know (with high confidence) that something has high description length. If I flip a coin n times and record the results, then I can be pretty sure that the resulting binary string will take at least ~n bits to describe. If I see the graph of a function and it has 10 local minima/maxima, then I can conclude that I can’t express it as a polynomial of degree <10. And so on.
I think I sort of agree, but...
It’s often difficult to prove a negative and I think the non-existence of a crisp definition of any given concept is no exception to this rule. Sometimes someone wants to come up with a crisp definition of a concept for which I suspect no such definition to exist. I usually find that I have little to say and can only wait for them to try to actually provide such a definition. And sometimes I’m surprised by what people can come up with. (Maybe this is the same point that Roman Leventov is making.)
Also, I think there are many different ways in which concepts can be crisp or non-crisp. I think cooperation can be made crisp in some ways and not in others.
For example, I do think that (in contrast to human values) there are approximate characterizations of cooperation that are useful, precise and short. For example: “Cooperation means playing Pareto-better equilibria.”
One way in which I think cooperation isn’t crisp, is that you can give multiple different sensible definitions that don’t fully agree with each other. (For example, some definitions (like the above) will include coordination in fully cooperative (i.e., common-payoff) games, and others won’t.) I think in that way it’s similar to comparing sets by size, where you can give lots of useful, insightful, precise definitions that disagree with each other. For example, bijection, isomorphism, and the subset relationship can each tell us when one set is larger than or as large as another, but they sometimes disagree and nobody expects that one can resolve the disagreement between the concepts or arrive at “one true definition” of whether one set is larger than another.
When applied to the real world rather than rational agent models, I would think we also inherit fuzziness from the application of the rational agent model to the real world. (Can we call the beneficial interaction between two cells cooperation? Etc.)
I guess we have talked about this a bunch last year, but since the post has come up again...
It then becomes clear what the requirements are besides “I believe we have compatible DTs” for Arif to believe there is decision-entanglement:
“I believe we have entangled epistemic algorithms (or that there is epistemic-entanglement[5], for short)”, and
“I believe we have been exposed to compatible pieces of evidence”.I still don’t understand why it’s necessary to talk about epistemic algorithms and their entanglement as opposed to just talking about the beliefs that you happen to have (as would be normal in decision and game theory theory).
Say Alice has epistemic algorithm A with inputs x that gives rise to beliefs b and Bob has a completely different [ETA: epistemic] algorithm A’ with completely different inputs x’ that happens to give rise to beliefs b as well. Alice and Bob both use decision algorithm D to make decisions. Part of b is the belief that Alice and Bob have the same beliefs and the same decision algorithm. It seems that Alice and Bob should cooperate. (If D is EDT/FDT/..., they will cooperate.) So it seems that the whole A,x,A’,x’ stuff just doesn’t matter for what they should do. It only matters what their beliefs are. My sense from the post and past discussions is that you disagree with this perspective and that I don’t understand why.
(Of course, you can talk about how in practice, arriving at the right kind of b will typically require having similar A, A’ and similar x, x’.)
(Of course, you need to have some requirement to the extent that Alice can’t modify her beliefs in such a way that she defects but that she doesn’t (non-causally) make it much more likely that Bob also defects. But I view this as an assumption about decision-theoretic not epistemic entanglement: I don’t see why an epistemic algorithm (in the usual sense of the word) would make such self-modifications.)
Three months later, I still find that:
a) Bing Chat has a lot of issues that the ChatGPTs (both 3.5 or 4) don’t seem to suffer from nearly as much. For example, it often refuses to answer prompts that are pretty clearly harmless.
b) Bing Chat has a harder time than I expected when answering questions that you can answer by copy-and-pasting the question into Google and then copy-and-pasting the right numbers, sentence or paragraph from the first search result. (Meanwhile, I find that Bing Chat’s search still works better than the search plugins for ChatGPT 4, which seem to still have lots of mundane technical issues.) Occasionally ChatGPT (even ChatGPT 3.5) gives better (more factual or relevant) answers “from memory” than Bing Chat gives by searching.However, when I pose very reasoning-oriented tasks to Bing Chat (i.e., tasks that mostly aren’t about searching on Google) (and Bing Chat doesn’t for some reason refuse to answer and doesn’t get distracted by unrelated search results it gets), it seems clear that Bing Chat is more capable than ChatGPT 3.5, while Bing Chat and ChatGPT 4 seem similar in their capabilities. I pose lots of tasks that (in contrast to variants of Monty Hall (which people seem to be very interested in), etc.) I’m pretty sure aren’t in the training data, so I’m very confident that this improvement isn’t primarily about memorization. So I totally buy that people who asked Bing Chat the right questions were justified in being very confident that Bing Chat is based on a newer model than ChatGPT 3.5.
Also:
>I’ve tried (with little success) to use Bing Chat instead of Google Search.
I do now use Bing Chat instead of Google Search for some things, but I still think Bing Chat is not really a game changer for search itself. My sense is that Bing Chat doesn’t/can’t comb through pages and pages of different documents to find relevant info and that it also doesn’t do one search to identify relevant search times for a second search, etc. (Bing Chat seems to be restricted to a few (three?) searches per query.) For the most part it seems to enter obvious search terms into Bing Search and then give information based on the first few results (even if those don’t really answer the question or are low quality). The much more important feature from a productivity perspective is the processing of the information it finds, such as the processing of the information on some given webpage into a bibtex entry or applying some method from Stack Exchange to the particularities of one’s code.
Very interesting post! Unfortunately, I found this a bit hard to understand because the linked papers don’t talk about EDT versus CDT or scenarios where these two come apart and because both papers are (at least in part) about sequential decision problems, which complicates things. (CDT versus EDT can mostly be considered in the case of a single decision and there are various complications in multi-decision scenarios, like updatelessness.)
Here’s an attempt at trying to describe the relation of the two papers to CDT and EDT, including prior work on these topics. Please correct me if I’m misunderstanding anything! The writing is not very polished—sorry!
Ignoring all the sequential stuff, my understanding is that the first paper basically does this: First, we train a model to predict utilities after observing actions, i.e., make predictions conditional on actions. So in particular, we get a function a ---> E[utility | a] that maps an observed action by the agent onto a prediction of future reward/utility. Then if we use some procedure to find the action a that maximizes E[utility | a], it seems that we have an EDT agent. I think this is essentially the case of an “EDT overseer” who rewards based on actions (rather than outcomes) in “Approval-directed agency and the decision theory of Newcomb-like problems”. Also see the discussion of Obstacle 1 in “Two Major Obstacles for Logical Inductor Decision Theory”.
Now what could go wrong with this? I think in some sense the problem is generally that it’s unclear how the predictive model works, or where it comes from. The second paper (the DeepMind one) basically points out one issue with this. Other issues are known to this community. I’ll start with an issue that has been known to this community: the 5 and 10 problem / the problem of counterfactuals. If the agent always (reliably) chooses the action a that maximizes E[utility | a], then the predictive model’s counterfactual predictions (i.e., predictions for all other actions) could be nonsensical without being strictly speaking wrong. So for example, in 5 and 10, you choose between a five dollar bill and a ten dollar bill. (There’s no catch and you should clearly just take the ten dollar bill.) The model predicts that if you take the five dollar bill, you will get five dollars, and (spuriously / intuitively falsely) that if you take the ten dollar bill, you get nothing. Because you are maximizing expected utility according to this particular predictive model, you take the five dollars. So the crazy prediction for what happens if you take the ten dollars is never falsified.
In non-Newcomb-like scenarios, a simple, extremely standard solution to this problem is to train the predictive model (the thing that gives a ---> E[utility | a]) while the agent follows some policy that randomizes over all actions (perhaps one that takes actions with probabilities in proportion to the model’s predictions E[utility | a]). My understanding is that this is how the first paper avoids these issues and gives good results. Unfortunately, in Newcomb-like problems these approaches tend to lead to pretty CDT-ish behavior, as shown in “Reinforcement Learning in Newcomblike Environments”.
Anyway, the second paper (the DeepMind one) points out another issue related to where the E[utility | action] model comes from. Roughly, the story — which I think is very well described in Section 2 — seems to be the following: the E[utility | action] model is trained on the actions of an expert who knows whether X=1,2 and acts on that fact by choosing A=X; then the E[utility | action] model won’t work for a non-expert agent, i.e., one who doesn’t observe X. I view this as a distributional shift issue — you train a model (the a ---> E[utility | a] one) in a setting where A=X, and then you apply it in a setting where sometimes A and X are uncorrelated.
It’s also similar to the Smoking Lesion/medical Newcomb-like problems! Consider the following medical Newcomb-like problem: First we learn the fact that sick people go to the doctor and healthy people don’t go to the doctor. Then without looking at how healthy I am, I don’t go to the doctor so as to gain evidence that I am healthy. Arguably what goes wrong here is also that I’m using a rule for prediction out of distribution on someone who doesn’t look at whether they’re sick. I think it relates to one of the least challenging versions of medical Newcomb-like problems and it’s handled comfortably by the so-called tickle defense.
Interlude: The paper talks about how this relates to hallucination in LLMs. So what’s that about? IIUC, the idea is that when generating text, LLMs incorrectly update based on the text they generate themselves. For example, imagine that you want an LLM to generate ten tokens. Then after generating the first nine tokens, it will predict the tenth token from its learned distribution . But this distribution was trained on fully human- not LLM-written text. So (in my way of thinking), might do poorly (i.e., not give a human-like continuation of ), because it was trained on seeing nine tokens created by a human and having to predict a continuation by a human rather than nine tokens by itself/an LLM and having to predict a continuation by a human. For example, we might imagine that if are words that only a human expert confident in a particular claim C would say, then the LLM will predict continuations that confidently defend claim C, even if the LLM doesn’t know anything about C. I’m not sure I really buy this explanation of hallucination. I think the claim would need more evidence than the authors provide. But it’s definitely a very interesting point.
Now, back to the original toy model. Again, I would view this as a distribution shift problem. If we make some assumptions, though, we can infer/guess a model (i.e. function a ---> E[utility | a]) that predicts the utility obtained by a non-expert, i.e., an agent who doesn’t observe X. Specifically, let’s assume that we are told the conditional distributions P(utility | X=1, A=0) and P(utility | X=0, A=1) (which we never see in training if the agent in training always knows and acts on X). Let’s also assume that we know that the difference between the training distribution and the new setting is that in the new setting the agent chooses A independently of X. Then in the new model we just need to make X and A independent and change nothing else. Formally you use the new distribution P’(X,U|A) = P(X)P(U|A,X), where the Ps on the right-hand side are just the old distribution, instead of P(X,U|A) = P(X|A)P(U|A,X).
It turns out that if we put the original distribution into a causal graph with edges X->A and A->U and X->U and then make a do-intervention on A (a la Pearl), then we get this exact distribution, i.e., P(X,U|do(A)) = P’(X,U|A). (Intuitively, removing the inference from A to X is exactly what the do(A) does if A’s parent is X.) So in particular maximizing E[U | do(A)] gives the same result as maximizing E’[U|A]. Anyway, the paper uses the do operator to construct the new predictor, rather than the above argument. They seem to claim that the causal structure (or reasoning about causality) is necessary to construct the new predictor, with which I disagree.
Is this really CDT? I’m not sure… In the above type of case, this doesn’t come apart from EDT. If we buy that their scenario is a bit like a Smoking Lesion, then one could argue that part of the point of CDT is to solve this type of scenario. (In some sense my response is as in most versions of the Smoking Lesion: Because of the tickle defense, EDT applied properly gets this right anyway, so there’s actually nothing to fix here.) In my view it’s basically just about using the do-calculus to concisely specify the scenario P’ (based on P plus a particular causal graph for P). It seems that one can do these things without being committed to using do(A) in a scenario where there’s some non-causal dependence between A and U (that doesn’t disappear outside of training), perhaps via some common cause Y. In any case, the paper doesn’t tell us how to distinguish between U ← Y → A and A → Y → U — all causal relationships are assumed. So while nominally they construct their predictor as E[U | do(A)], it’s a bit unclear how wedded they are to CDT.
Anyway, with a (maybe-causalist) E[U | do(A)] in hand, we can of course build a (maybe-)CDT agent by choosing a to maximize E[U | do(A)]. But I think the paper doesn’t say anything about where to get the causal model from that gives us E[U | do(A)]. They pretty much assume that the model is provided.
I think the “counterfactual teaching” stuff doesn’t really say anything about CDT versus EDT, either. IIUC the basic idea is this. Imagine you want to train an LLM and you want to prevent the issue above. Then intuitively — in my distribution shift view — what we need to do is just train the LLM to make a good prediction upon observing that were generated by itself (rather than humans). The simplest, most obvious way to do this is to let the LLM generate some tokens , then get a probabilistic prediction about the next token from the LLM and then ask a human to give a next token . The loss of the LLM is just the, e.g., log loss of its prediction against the provided by the human. One slightly tricky point here is that we only train the LLM to make good predictions on . We don’t want to train it to output that make easier to predict. So we need to be careful to choose the right gradient. I think that’s basically all they’re doing, though. It doesn’t seem like there’s anything causalist here.
So, in conclusion: While very interesting, I don’t think these papers tell us anything new about how to build an EDT or a CDT agent.
Nice overview! I mostly agree.
>What I do not expect is something I’d have been happy to pay $500 or $1,000 for, but not $3,500. Either the game will be changed, or it won’t be changed quite yet. I can’t wait to find out.
From context, I assume you’re saying this about the current iteration?
I guess willingness to pay for different things depends on one’s personal preferences, but here’s an outcome that I find somewhat likely (>50%):
The first-gen Apple Vision Pro will not be very useful for work, aside from some niche tasks.
It seems that to be better than a laptop for working at a coffee shop or something they need to have solved ~10 different problems extremely well and my guess is that they will have failed to solve one of them well enough. For example, I think comfort/weight alone has a >30% probability of making this less enjoyable to work with (for me at least) than with a laptop, even if all other stuff works fairly well.
Like you, I’m sometimes a bit puzzled by what Apple does. So I could also imagine that Apple screws up something weird that isn’t technologically difficult. For example, the first version of iPad OS was extremely restrictive (no multitasking/splitscreen, etc.). So even though the hardware was already great, it was difficult to use it for anything serious and felt more like a toy. Based on what they emphasize on the website, I could very well imagine that they won’t focus on making this work and that there’ll be some basic, obvious issue like not being able to use a mouse. If Apple had pitched this more in the way that Spacetop was pitched, I’d be much more optimistic that the first gen will be useful for work.
The first-gen Apple Vision Pro will still produce lots of extremely interesting experiences so that many people would be happy to pay, say, $1000 for, but not $3,500 and definitely not much more than $3,500. For example, I think all the reviews I’ve seen have described the experience as very interesting, intense and immersive. Let’s say this novelty value wears off after something like 10h. Then a family of four gets 40h of fun out of it. Say, you’re happy to spend on the order of $10 per hour per person for a fun new experience (that’s roughly what you’d spend to go to the movie theater, for example), then that’d be a willingness to pay in the hundreds of dollars.
>All accounts agree that Apple has essentially solved issues with fit and comfort.
Besides the 30min point, is it really true that all accounts agree on that? I definitely remember reading in at least two reports something along the lines of, “clearly you can’t use this for hours, because it’s too heavy”. Sorry for not giving a source!
Do philosophers commonly use the word “intention” to refer to mental states that have intentionality, though? For example, from the SEP article on intentionality:
>intention and intending are specific states of mind that, unlike beliefs, judgments, hopes, desires or fears, play a distinctive role in the etiology of actions. By contrast, intentionality is a pervasive feature of many different mental states: beliefs, hopes, judgments, intentions, love and hatred all exhibit intentionality.(This is specifically where it talks about how intentionality and the colloquial meaning of intention must not be confused, though.)
Ctrl+f-ing through the SEP article gives only one mention of “intention” that seems to refer to intentionality. (“The second horn of the same dilemma is to accept physicalism and renounce the ‘baselessness’ of the intentional idioms and the ‘emptiness’ of a science of intention.”) The other few mentions of “intention” seem to talk about the colloquial meaning. The article seems to generally avoid the avoid “intention”. Generally the article uses “intentional” and “intentionality”.Incidentally, there’s also an SEP article on “intention” that does seem to be about what one would think it to be about. (E.g., the first sentence of that article: “Philosophical perplexity about intention begins with its appearance in three guises: intention for the future, as I intend to complete this entry by the end of the month; the intention with which someone acts, as I am typing with the further intention of writing an introductory sentence; and intentional action, as in the fact that I am typing these words intentionally.”)
So as long as we don’t call it “artificial intentionality research” we might avoid trouble with the philosophers after all. I suppose the word “intentional” becomes ambiguous, however. (It is used >100 times in both SEP articles.)
>They could have turned their safety prompts into a new benchmark if they had ran the same test on the other LLMs! This would’ve taken, idk, 2–5 hrs of labour?
I’m not sure I understand what you mean by this. They ran the same prompts with all the LLMs, right? (That’s what Figure 1 is...) Do you mean they should have tried the finetuning on the other LLMs as well? (I’ve only read your post, not the actual paper.) And how does this relate to turning their prompts into a new benchmarks?
>I’m not sure I understand the variant you proposed. How is that different than the Othman and Sandholm MAX rule?
Sorry if I was cryptic! Yes, it’s basically the same as using the MAX decision rule and (importantly) a quasi-strictly proper scoring rule (in their terminology, which is basically the same up to notation as a strictly proper decision scoring rule in the terminology of the decision scoring rules paper). (We changed the terminology for our paper because “quasi-strictly proper scoring rule w.r.t. the max decision rule” is a mouthful. :-P) Does that help?
>much safer than having it effectively chosen for them by their specification of a utility function
So, as I tried to explain before, one convenient thing about using proper decision scoring rules is that you do not need to specify your utility function. You just need to give rewards ex post. So one advantage of using proper decision scoring rules is that you need less of your utility function not more! But on to the main point...
>I think, from an alignment perspective, having a human choose their action while being aware of the distribution over outcomes it induces is much safer than having it effectively chosen for them by their specification of a utility function. This is especially true because probability distributions are large objects. A human choosing between them isn’t pushing in any particular direction that can make it likely to overlook negative outcomes, while choosing based on the utility function they specify leads to exactly that. This is all modulo ELK, of course.
Let’s grant for now that from an alignment perspective the property you describe is desirable. My counterargument is that proper decision scoring rules (or the max decision rule with a scoring rule that is quasi-strictly proper w.r.t. the max scoring rule) and zero-sum conditional prediction both have this property. Therefore, having the property cannot yield an argument to favor one over the other.
Maybe put differently: I still don’t know what property it is that you think favors zero-sum conditional prediction over proper decision scoring rules. I don’t think it can be not wanting to specify your utility function / not wanting the agent to pick agents based on their model of your utility function / wanting to instead choose yourself based on reported distributions, because both methods can be used in this way. Also, note that in both methods the predictors in practice have incentives that are determined by (their beliefs about) the human’s values. For example, in zero-sum conditional prediction, each predictor is incentivized to run computations to evaluate actions that it thinks could potentially be optimal w.r.t. human values, and not incentivized to think about actions that it confidently thinks are suboptimal. So for example, if I have the choice between eating chocolate ice cream, eating strawberry ice cream and eating mud, then the predictor will reason that I won’t choose to eat mud and that therefore its prediction about mud won’t be evaluated. Therefore, it will probably not think much about how what it will be like if I eat mud (though it has to think about it a little to make sure that the other predictor can’t gain by recommending mud eating).
On whether the property is desirable [ETA: I here mean the property: [human chooses based on reported distribution] but not compared to [explicitly specifying a utility function]]: Perhaps my objection is just what you mean by ELK. In any case, I think my views depend a bit on how we imagine lots of different aspect of the overall alignment scheme. One important question, I think, is how exactly we imagine the human to “look at” the distributions for example. But my worry is that (similar to RLHF) letting the human evaluate distributions rather than outcomes increases the predictors’ incentives to deceive the human. The incentive is to find actions whose distribution looks good (in whatever format you represent the distribution) in relation to the other distributions, not which distributions are good. Given that the distributions are so large (and less importantly because humans have lots of systematic, exploitable irrationalities related to risk), I would think that human judgment of single outcomes/point distributions is much better than human judgment of full distributions.
>the biggest distinction is that this post’s proposal does not require specifying the decision maker’s utility function in order to reward one of the predictors and shape their behavior into maximizing it.
Hmm… Johannes made a similar argument in personal conversation yesterday. I’m not sure how convinced I am by this argument.So first, here’s one variant of the proper decision scoring rules setup where we also don’t need to specify the decision maker’s utility function: Ask the predictor for her full conditional probability distribution for each action. Then take the action that is best according to your utility function and the predictor’s conditional probability distribution. Then score the predictor according to a strictly proper decision scoring rule. (If you think of strictly proper decision scoring rules as taking only a predicted expected utility as input, you have to first calculate the expected utility of the reported distribution, and then score that expected utility against the utility you actually obtained.) (Note that if the expert has no idea what your utility function is, they are now strictly incentivized to report fully honestly about all actions! The same is true in your setup as well, I think, but in what I describe here a single predictor suffices.) In this setup you also don’t need to specify your utility function.
One important difference, I suppose, is that in all the existing methods (like proper decision scoring rules) the decision maker needs to at some point assess her utility in a single outcome—the one obtained after choosing the recommended action—and reward the expert in proportion to that. In your approach one never needs to do this. However, in your approach one instead needs to look at a bunch of probability distributions and assess which one of these is best. Isn’t this much harder? (If you’re doing expected utility maximization—doesn’t your approach entail assigning probabilities to all hypothetical outcomes?) In realistic settings, these outcome distributions are huge objects!
The following is based on an in-person discussion with Johannes Treutlein (the second author of the OP).
>But is there some concrete advantage of zero-sum conditional prediction over the above method?
So, here’s a very concrete and clear (though perhaps not very important) advantage of the proposed method over the method I proposed. The method I proposed only works if you want to maximize expected utility relative to the predictor’s beliefs. The zero-sum competition model enables optimal choice under a much broader set of possible preferences over outcome distributions.
Let’s say that you have some arbitrary (potentially wacky discontinuous) function V that maps a distributions over outcomes onto a real value representing how much you like the distribution over outcomes. Then you can do zero-sum competition as normal and select the action for which V is highest (as usual with “optimism bias”, i.e., if the two predictors make different predictions for an action a, then take the maximum of the Vs of the two actions). This should still be incentive compatible and result in taking the action that is best in terms of V applied to the predictors’ belief.
(Of course, one could have even crazier preferences. For example, one’s preferences could just be a function that takes as input a set of distributions and selects one distribution as its favorite. But I think if this preference function is intransitive, doesn’t satisfy independence of irrelevant alternatives and the like, it’s not so clear whether the proposed approach still works. For example, you might be able to slightly misreport some option that will not be taken anyway in such a way as to ensure that the decision maker ends up taking a different action. I don’t think this is ever strictly incentivized. But it’s not strictly disincentivized to do this.)
Interestingly, if V is a strictly convex function over outcome distributions (why would it be? I don’t know!), then you can strictly incentivize a single predictor to report the best action and honestly report the full distribution over outcomes for that action! Simply use the scoring rule , where is the reported distribution for the recommended action, is the true distribution of the recommended action and is a subderivative of . Because a proper scoring rule is used, the expert will be incentivized to report and thus gets a score of , where is the distribution of the recommended action. So it will recommend the action whose associate distribution maximizes . It’s easy to show that if -- the function saying how much you like different distribution—is not strictly convex, then you can’t construct such a scoring rule. If I recall correctly, these facts are also pointed out in one of the papers by Chen et al. on this topic.
I don’t find this very important, because I find expected utility maximization w.r.t. the predictors’ beliefs much more plausible than anything else. But if nothing else, this difference further shows that the proposed method is fundamentally different and more capable in some ways than other methods (like the one I proposed in my comment).
Nice post!
Miscellaneous comments and questions, some of which I made on earlier versions of this post. Many of these are bibliographic, relating the post in more detail to prior work, or alternative approaches.
In my view, the proposal is basically to use a futarchy / conditional prediction market design like that the one proposed by Hanson, with I think two important details:
- The markets aren’t subsidized. This ensures that the game is zero-sum for the predictors—they don’t prefer one action to be taken over another. In the scoring rules setting, subsidizing would mean scoring relative to some initial prediction $p_0$ provided by the market. Because the initial prediction might differ in how bad it is for different actions, the predictors might prefer a particular action to be taken. Conversely, the predictors might have no incentive to correct an overly optimistic prediction for one of the actions if doing so causes that action not to be taken. The examples in Section 3.2 of the Othman and Sandholm paper show these things.
- The second is “optimism bias” (a good thing in this context): “If the predictors disagree about the probabilities conditional on any action, the decision maker acts as though they believe the more optimistic one.” (This is as opposed to taking the market average, which I assume is what Hanson had in mind with his futarchy proposal.) If you don’t have optimism bias, then you get failure modes like the ones pointed out in Obstacle 1 of Scott Garrabrant’s post “Two Major Obstacles for Logical Inductor Decision Theory”: One predictor/trader could claim that the optimal action will lead to disaster and thus cause the optimal action to never be taken and her prediction to never be tested. This optimism bias is reminiscent of some other ideas. For example some ideas for solving the 5-and-10 problem are based on first searching for proofs of high utility. Decision auctions also work based on this optimism. (Decision auctions work like this: Auction off the right to make the decision on my behalf to the highest bidder. The highest bidder has to pay their bid (or maybe the second-highest bid) and gets paid in proportion to the utility I obtain.) Maybe getting too far afield here, but the UCB term in bandit algorithms also works this way in some sense: if you’re still quite unsure how good an action is, pretend that it is very good (as good as some upper bound of some confidence interval).My work on decision scoring rules describes the best you can get out of a single predictor. Basically you can incentivize a single predictor to tell you what the best action is and what the expected utility of that action is, but nothing more (aside from some degenerate cases).
Your result shows that if you have two predictors with the same information, then you can get slightly more: you can incentivize them to tell you what the best action is and what the full distribution over outcomes will be if you take the action.
You also get some other stuff (as you describe starting from the sentence, “Additionally, there is a bound on how inaccurate...”). But these other things seem much less important. (You also say: “while it does not guarantee that the predictions conditional on the actions not taken will be accurate, crucially there is no incentive to lie about them.” But the same is true of decision scoring rules for example.)
Here’s one thing that is a bit unclear to me, though.
If you have two predictors that have the same information, there’s other, more obvious stuff you can do. For example, here’s one:
- Ask Predictor 1 for a recommendation for what to do.
- Ask Predictor 2 for a prediction over outcomes conditional on Predictor 1′s recommendation.
- Take the action recommended by Predictor 1.
- Observe an outcome o with a utility u(o).
- Pay Predictor 1 in proportion to u(o).
- Pay Predictor 2 according to a proper scoring rule.In essence, this is just splitting the task into two: There’s the issue of making the best possible choice and there’s the issue of predicting what will happen. We assign Predictor 1 to the first and Predictor 2 to the second problem. For each of these problems separately, we know what to do (use proper (decision) scoring rules). So we can solve the overall problem.
So this mechanism also gets you an honest prediction and an honest recommendation for what to do. In fact, one advantage of this approach is that honesty is maintained even if the Predictors 1 and 2 have _different_ information/beliefs! (You don’t get any information aggregation with this (though see below). But your approach doesn’t have any information aggregation either.)
As per the decision scoring rules paper, you could additionally ask Predictor 1 for an estimate of the expected utility you will obtain. You can also let the Predictor 2 look at Predictor 1′s prediction (or perhaps even score Predictor 2 relative to Predictor 1′s prediction). (This way you’d get some information aggregation.) (You can also let Predictor 1 look at Predictor 2′s predictions if Predictor 2 starts out by making conditional predictions before Predictor 1 gives a recommendation. This gets more tricky because now Predictor 2 will want to mislead Predictor 1.)
I think your proposal for what to do instead of the above is very interesting and I’m glad that we now know that this method exists that that it works. It seems fundamentally different and it seems plausible that this insight will be very useful. But is there some concrete advantage of zero-sum conditional prediction over the above method?
>First crucial point which this post is missing: the first (intuitively wrong) net reconstructed represents the probabilities using 9 parameters (i.e. the nine rows of the various truth tables), whereas the second (intuitively right) represents the probabilities using 8. That means the second model uses fewer bits; the distribution is more compressed by the model. So the “true” network is favored even before we get into interventions.
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>Implication of this for causal epistemics: we have two models which make the same predictions on-distribution, and only make different predictions under interventions. Yet, even without actually observing any interventions, we do have reason to epistemically favor one model over the other.
For people interested in learning more about this idea: This is described in Section 2.3 of Pearl’s book Causality. The beginning of Ch. 2 also contains some information about the history of this idea. There’s also a more accessible post by Yudkowsky that has popularized these ideas on LW, though it contains some inaccuracies, such as explicitly equating causal graphs and Bayes nets.
As one further data point, I also heard people close to/working at Anthropic giving “We won’t advance the state of the art.”-type statements, though I never asked about specifics.
My sense is also that Claude 3 Opus is only slightly better than the best published GPT-4. To add one data point: I happen to work on a benchmark right now and on that benchmark, Opus is only very slightly better than gpt-4-1106. (See my X/Twitter post for detailed results.) So, I agree with LawrenceC’s comment that they’re arguably not significantly advancing the state of the art.
I suppose even if Opus is only slightly better (or even just perceived to be better) and even if we all expect OpenAI to release a better GPT-4.5 soon, Anthropic could still take a bunch of OpenAI’s GPT-4 business with this. (I’ll probably switch from ChatGPT-4 to Claude, for instance.) So it’s not that hard to imagine an internal OpenAI email saying, “Okay, folks, let’s move a bit faster with these top-tier models from now on, lest too many people switch to Claude.” I suppose that would already be quite worrying to people here. (Whereas, people would probably worry less if Anthropic took some of OpenAI’s business by having models that are slightly worse but cheaper or more aligned/less likely to say things you wouldn’t want models to say in production.)