michaelcohen

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michaelcohen May 24, 2021, 11:30 AM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
I take your point that we are discussing some output rules which add extra computation states, and so some output rules will add fewer computation states than others.
I’m merging my response to the rest with my comment here.

michaelcohen May 24, 2021, 11:27 AM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
They are using their highest probability guess about the output channel, which will be higher probability than the output channel exactly matching some camera on old earth (but may still be very low probability). I still don’t understand the relevance.
I’m trying to find the simplest setting where we have a disagreement. We don’t need to think about cameras on earth quite yet. I understand the relevance isn’t immediate.
They don’t care about “their” Turing machine, indeed they live in an infinite number of Turing machines that (among other things) output bits in different ways.
I think I see the distinction between the frameworks we most naturally think about the situation. I agree that they live in an infinite number of Turing machines, in the sense that their conscious patterns appear in many different Turing machines. All of these Turing machines have weight in some prior. When they change their behavior, they (potentially) change the outputs of any of these Turing machines. Taking these Turing machines as a set, weighted by those prior weights we can consider the probability that the output obeys a predicate P. The answer to this question can be arrived at through an equivalent process. Let the inhabitants imagine that there is a correct answer to the question “which Turing machine do I really live in?” They then reason anthropically about which Turing machines give rise to such conscious experiences as theirs. They then use the same prior over Turing machines that I described above. And then they make the same calculation about the probability that “their” Turing machine outputs something that obeys the predicate P. So on the one hand, we could say that we are asking “what is the probability that the section of the universal prior which gives rise to these inhabitants outputs an output that obeys predicate P?” Or we could equivalently ask “what is the probability that this inhabitant ascribes to ‘its’ Turing machine outputting a string that obeys predicate P?”
There are facts that I find much easier to incorporate when thinking in the latter framework, such as “a work tape inhabitant knows nothing about the behavior of its Turing machine’s output tape, except that it has relative simplicity given the world that it knows.” (If it believes that its conscious existence depends on its Turing machine never having output a bit that differs from a data stream in a base world, it will infer other things about its output tape, but you seem to disagree that it would make that assumption, and I’m fine to go along with that). (If the fact were much simpler—“a work tape inhabitant knows nothing about the behavior of its Turing machine’s output tape” full stop—I would feel fairly comfortable in either framework.)
If it is the case that, for any action that a work tape inhabitant takes, the following is unchanged: [the probability that it (anthropically) ascribes to “its” Turing machine printing an output that obeys predicate P after it takes that action], then, no matter its choice of action, then the probability under the universal prior that the output obeys predicate P is also unchanged.
What if the work tape inhabitant only cares about the output when the the universal prior is being used for important applications? Let Q be the predicate [P and “the sequence begins with a sequence which is indicative of important application of the universal prior”]. The same logic that applies to P applies to Q. (It feels easier to talk about probabilities of predicates (expectations of Boolean functions) rather than expectations of general functions, but if we wanted to do importance weighting instead of using a strict predicate on importance, the logic is the same).
Writing about the fact I described above about what the inhabitants believe about their Turing machine’s output has actually clarified my thinking a bit. Here’s a predicate where I think inhabitants could expect certain actions to make it more likely that their Turing machine output obeys that predicate. “The output contains the string [particular 1000 bit string]”. They believe that their world’s output is simple given their world’s dynamics, so if they write that 1000 bit string somewhere, it is more likely for the predicate to hold. (Simple manipulations of the string are nearly equally more likely to be output).
So there are severe restrictions on the precision with which they can control even low-probability changes to the output, but not total restrictions. So I wasn’t quite right in describing it as a max-entropy situation. But the one piece of information that distinguishes their situation from one of maximum uncertainty about the output is very slight. So I think it’s useful to try to think in terms of how they get from that information to their goal for the output tape.
I was describing the situation where I wanted to maximize the probability where the output of our world obeys the predicate: “this output causes decision-maker simulators to believe that virtue pays”. I think I could very slightly increase that probability by trying to reward virtuous people around me. Consider consequentialists who want to maximize the probability of the predicate “this output causes simulator-decision-makers to run code that recreates us in their world”. They want to make the internals of their world such that there are simple relative descriptions for outputs for which that predicate holds. I guess I think that approach offers extremely limited and imprecise ability to deliberately influence the output, no matter how smart you are.
If an approach has very limited success probability, (i.e. very limited sway over the universal prior), they can focus all their effort on mimicking a few worlds, but then we’ll probably get lucky, and ours won’t be one of the ones they focus on.
From a separate recent comment,
But now that we’ve learned that physics is the game of life, we can make much better guesses about how to build a dataset so that a TM could output it. For example, we can:
- Build the dataset at a large number of places.
- [etc.]
...
I challenge you to find any plausible description of a rule that outputs the bits observed by a camera, for which I can’t describe a simpler extraction rule that would output some set of bits controlled by the sophisticated civilization.
You’re comparing the probability of one of these many controlled locations driving the output of the machine to the probability that a random camera does on an earth-like Turing machine drives the output. Whereas it seems to me like the right question is to look at the absolute probabilities that one of these controlled locations drives the output. The reason is that what they attempt to output is a mixture over many sequences that a decision-maker-simulator might want to know about. But if the sequence we’re feeding in is from a camera on earth, than their antics only matter to the extent that their mixture puts weight on a random camera on earth. So they have to specify the random camera on an earth-like Turing machine too. They’re paying the same cost, minus any anthropic update. So the costs to compare are roughly [- log prob. successful control of output + bits to specify camera on earth—bits saved from anthropic update] vs. [bits to specify camera on earth—bits saved from directly programmed anthropic update]. This framing seems to imply we can cross off [bits to specify camera on earth] from both sides.
What links here?
- michaelcohen's comment on Response to “What does the universal prior actually look like?” by michaelcohen (May 24, 2021, 11:30 AM; 1 point)

michaelcohen May 21, 2021, 4:31 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
Okay, now suppose they want the first N bits of the output of their Turing machine to obey predicate P, and they assign that a value of 100, and a they assign a value of 0 to any N-bit string that does not obey predicate P. And they don’t value anything else. If some actions have a higher value than other actions, what information about the output tape dynamics are they using, and how did they acquire it?

michaelcohen May 21, 2021, 4:05 PM
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in reply to: michaelcohen’s comment on: Response to “What does the universal prior actually look like?”
Just look at the prior—for any set of instructions for the work tape heads of the Turing machine, flipping the “write-1” instructions of the output tape with the “write-0″ instructions gives an equally probably Turing machine.

michaelcohen May 21, 2021, 4:01 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
Suppose they know the sequence that actually gets fed to the camera.
If you’re saying that they know their Turing machine has output x so far, then I 100% agree. What about in the case where they don’t know?

michaelcohen May 21, 2021, 3:51 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
If I flip a coin to randomize between two policies, I don’t see how that mixed policy could produce more value for me than the base policies.
(ETA: the logical implications about the fact of my randomization don’t have any weird anti-adversarial effects here).

michaelcohen May 21, 2021, 3:45 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
If these consequentialists ascribed a value of 100 to the next output bit being 1, and a value of 0 to the next output bit being 0, and they valued nothing else, would you agree that all actions available to them have identical expected value under the distribution over Turing machines that I have described?

michaelcohen May 21, 2021, 3:35 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
With randomization, you reduce the cost and the upside in concert. If a pair of shoes costs $100, and that’s more than I’m willing to pay, I could buy the shoes with probability 1%, and it will only cost me $1 in expectation, but I will only get the shoes with probability ¹⁄₁₀₀.

michaelcohen May 21, 2021, 3:31 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
It’s definitely not too weird a possibility for me. I’m trying to reason backwards here—the best strategy available to them can’t be effective in expectation at achieving whatever their goals are with the output tape, because of information-theoretic impossibilities, and therefore, any given strategy will be that bad or worse, including randomization.

michaelcohen May 21, 2021, 1:41 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
We can get back to some of these points as needed, but I think our main thread is with your other comment, and I’ll resist the urge to start a long tangent about the metaphysics of being “simulated” vs. “imagined”.

michaelcohen May 21, 2021, 1:28 PM
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in reply to: paulfchristiano’s comment on: Response to “What does the universal prior actually look like?”
So we end up with some leading hypotheses about the Turing machine we are running on, the history that gave rise to us, and the output rule used by that Turing machine.
I feel like this story has run aground on an impossibility result. If a random variable’s value is unknowable (but its distribution is known) and an intelligent agent wants to act on its value, and they randomize their actions, the expected log probability of them acting on the true value cannot exceed the entropy of the distribution, no matter their intelligence. (And if they’re wrong about the r.v.’s distribution, they do even worse). But lets assume they are correct. They know there are, say, 80 output instructions (two work tapes and one input tape, and a binary alphabet, and 10 computation states). And each one has a ¹⁄₃ chance of being “write 0 and move”, “write 1 and move”, or “do nothing”. Let’s assume they know the rules governing the other tape heads, and the identity of the computation states (up to permutation). Their belief distribution is (at best) uniform over these 3^80 possibilities. Is computation state 7 where most of the writing gets done? They just don’t know. It doesn’t matter if they’ve figured out that computation state 7 is responsible for the high-level organization of the work tapes. It’s totally independent. Making beacons is like assuming that computation state 7, so important for the dynamics of their world, has anything special to do with the output behavior. (Because what is a beacon if not something that speaks to internally important computation states?)
That’s all going along with the premise that when consequentialists face uncertainty, they flip a coin, and adopt certainty based on the outcome. So if they think it’s ⁵⁰⁄₅₀ whether a 0 or a 1 gets output, they flip a coin or look at some tea leaves, and then act going forward as if they just learned the answer. Then, it only costs 1 bit to say they decided “0”. But I think getting consequentialists to behave this way requires an intervention into their proverbial prefrontal cortices. If these consequentialists were playing a bandit game, and one arm gave a reward of 0.9 with certainty, and the other was ⁵⁰⁄₅₀ between a reward of 0 or 1, they obviously don’t flip a coin to decide whether to act as if it’s really reward 1 or reward 0. (I understand that Thompson sampling is a great strategy, but only when your uncertainty is ultimately empirically resolvable, and uncertainty about output behavior is not).
I think you’ll get the impression that I’m being miserly with bits here. And your relative profligacy comes from the fact that you expect they’ll make it up easily in the anthropic update. But you’ll ultimately have to claim that the anthropic update is more cheaply specified as a natural product of consequentialist civilization than through direct encoding. And if every step of the way in your story about how consequentialists arrive at this behavior, I make the point that this is not sensible goal-oriented behavior, and you make the point that it only takes a few bits to make it be what they would do anyway, then if you put it all together, I’m not just haggling over bits. If you put it all together, it looks to me like the consequentialists’ consequentialism is doing little to none of the work; every step of the way, reasonable behavior is being overridden, a few bits at a time. So then I ultimately claim, this anthropic update is not most parsimoniously described as “that thing that consequentialists sometimes produce” because it’s just not actionable for any consequentialists with reasonable epistemics.
In a different part of the story, you claim that if something composes 1% of what consequentialists value, we can assume that they flip 6 and a half coins, and with 1% probability they act as if that’s the only thing they value.
So we’re interested in investing some tiny fraction of our resources in escaping from such simulations. The most important way to minimize the cost is by reducing probability. For example, if we decide to do something only with 1% probability (and in the other 99% of worlds focus exclusively on other things) then we only decrease our log probability by 7 bits. I actually doubt we’d waste those 7 bits, but it’s worth noting how cheap this kind of breakout attempt could be.
This seems to me to be another case of supplanting consequentialists’ instrumental rationality with randomness. These are key parts of the story. The part where they make a wild guess about the output of their world, and the part where decide to pursue it in the first place are both places where reasonable goal-oriented behavior is being replaced with deference to the descriptive and normative wisdom of tea leaves; this is not just specifying one of the things they sometimes do naturally with small-but-non-negligible probability. It would be an unusual model of agency which claimed that: for a utility function $U = c_{1} U_{1} + c_{2} U_{2}$ , we have $p (a | a g e n t_{U}) \geq \frac{c_{1}}{c_{1} + c_{2}} p (a | a g e n t_{U_{1}})$ . And it would be an even more unusual model of agency which claimed that: for a world $W = c_{1} W_{1} + c_{2} W_{2}$ , we have $p (a | a g e n t_{U}, W) \geq \frac{c_{1}}{c_{1} + c_{2}} p (a | a g e n t_{U}, W_{1})$ . Even within large multiplicative fudge fators. I feel like I need the assistance of a Dutch bookie here.
Of course we don’t know for sure that this is the particular way that the TM works, since we can’t infer the output rules from our observations, and probably it isn’t. But that’s just like saying that any given TM probably doesn’t output the pixels your camera. The point is that we are doing things that would cause a tiny fraction of the TMs containing us to output good sequences, and that’s going to be a way higher fraction than those that happen to output the pixels of cameras
I don’t think it’s just like saying that. I think I have argued that the probability that consequentialists act on the belief that camera 12,041 has a direct line to the output tape is smaller than the probability that it is actually true. Likewise for something that appears “beacon-like” to the world’s residents. Given a state of total ignorance about the means by which they can affect the output tape, their guesses can be no better than the true prior distribution over what in the world has a direct line to the output tape. (This is contra: “the fact that they are trying puts them at a massive advantage” from your other comment; intelligence and effort don’t work in a max-ent setting. With maximum entropy beliefs about the output channel, those silly no free lunch theorems of optimization do actually apply.) And then also given that ignorance, there is much less value in taking a stab in the dark. In general, with probabilistic mixtures over worlds $W_{i}$ , $V (\sum_{i = 1}^{N} c_{i} W_{i}) \leq \sum_{i = 1}^{N} c_{i} V (W_{i})$ .

michaelcohen May 20, 2021, 10:27 PM
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in reply to: abramdemski’s comment on: Formal Inner Alignment, Prospectus
A few quick thoughts, and I’ll get back to the other stuff later.
To be clear, people I know spent a lot more time than that thinking hard about the consensus algorithm, before coming to the strong conclusion that it was a fruitless path. I agree that this is worth spending >20 hours thinking about.
That’s good to know. To clarify, I was only saying that spending 10 hours on the project of applying it to modern ML would not be enough time to deem it a fruitless path. If after 1 hour, you come up with a theoretical reason why it fails on its own terms—i.e. it is not even a theoretical solution—then there is no bound on how strongly you might reasonably conclude that it is fruitless. So this kind of meta point I was making only applied to your objections about slowdown in practice.
a “theoretical solution” to the realizability probelm at all.
I only meant to claim I was just doing theory in a context that lacks the realizability problem, not that I had solved the realizability problem! But yes, I see what you’re saying. The theory regards a “fair” demonstrator which does not depend on the operation of the computer. There are probably multiple perspectives about what level of “theoretical” that setting is. I would contend that in practice, the computer itself is not among the most complex and important causal ancestors of the demonstrator’s behavior, so this doesn’t present a huge challenge for practically arriving at a good model. But that’s a whole can of worms.
My main worry continues to be the way bad actors have control over an io channel, rather than the slowdown issue.
Okay good, this worry makes much more sense to me.

michaelcohen May 19, 2021, 2:43 PM
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in reply to: abramdemski’s comment on: Formal Inner Alignment, Prospectus
I felt I had remained quiet about my disagreement with you for too long
Haha that’s fine. If you don’t voice your objections, I can’t respond to them!
I think let’s step back for a second, though. Suppose you were in the epistemic position “yes, this works in theory, with the realizability assumption, with no computational slowdown over MAP, but having spent 2-10 hours trying to figure out how to distill a neural network’s epistemic uncertainty/submodel-mismatch, and having come up blank...” what’s the conclusion here? I don’t think it’s “my main guess is that there’s no way to apply this in practice”. Even if you had spent all the time since my original post trying to figure out how to efficiently distill a neural network’s epistemic uncertainty, it’s potentially a hard problem! But it also seems like a clear problem, maybe even tractable. See Taylor (2016) section 2.1--inductive ambiguity identification. If you were convinced that AGI will be made of neural networks, you could say that I have reduced the problem of inner alignment to the problem of diverse-model-extraction from a neural network, perhaps allowing a few modifications to training (if you bought that the claim that the consensus algorithm is a theoretical solution). I have never tried to claim that analogizing this approach to neural networks will be easy, but I don’t think you want to wait to hear my formal ideas until I have figured out how to apply them to neural networks; my ideal situation would be that I figure out how to do something in theory, and then 50 people try to work on analogizing it to state-of-the-art AI (there are many more neural network experts out there than AIXI experts). My less ideal situation is that people provisionally treat the theoretical solution as a dead end, right up until the very point that a practical version is demonstrated.
If it seemed like solving inner alignment in theory was easy (because allowing yourself an agent with the wherewithal to consider “unrealistic” models is such a boon), and there were thus lots of theoretical solutions floating around, any given one might not be such a strong signal: “this is the place to look for realistic solutions”. But if there’s only one floating around, that’s a very a strong signal that we might be looking in a fundamental part of the solution space. In general, I think the most practical place to look for practical solutions is near the best theoretical one, and 10 hours of unsuccessful search isn’t even close to the amount of time needed to demote that area from “most promising”.
I think this covers my take on a few of your points, but some of your points are separate. In particular, some of them bear on the question of whether this really is an idealized solution in the first place.
With Ted out of the running, the top 100 hypotheses are now all malign, and can coordinate some sort of treacherous turn.
I think the question we are discussing here is: “yes, with the realizability assumption, existence of a benign model in the top set is substantially correlated over infinite time, enough so that all we need to look at is the relative weight of malign and benign models, BUT is the character of this correlation fundamentally different without the realizability assumption?” I don’t see how this example makes that point. If the threshold of “unrealistic” is set in such a way that “realistic” models will only know most things about Sally, then this should apply equally to malign and benign models alike. (I think your example respects that, but just making it explicit). However, there should be a benign and malign model that knows about Sally’s affinity for butter but not her allergy to flowers, and a benign and a malign model that knows the opposite. It seems to me that we still end up just considering the relative weight of benign and malign models that we might expect to see.
(A frugal hypothesis generating function instead of a brute force search over all reasonable models might miss out on, say, the benign version of the model that understands Sally’s allergies; I do not claim to have identified an approach to hypothesis generation that reliably includes benign models. That problem could be one direction in the research agenda of analogizing this approach to state-of-the-art AI. And this example might also be worth thinking about in that project, but if we’re just using the example to try to evaluate the effect of just removing the realizability assumption, but not removing the privilege of a brute search through reasonable models, then I stand by the choice to deem this paragraph parenthetical).
Why will there be one best? That’s the realizability assumption. There is not necessarily a unique model with lowest bayes loss. Another way of stating this is that Bayesian updates lack a convergence guarantee; hypotheses can oscillate forever as to which is on top.
Yeah I was thinking that the realistic setting was a finite length setting, with the one best being the best at the end. (And if it is best at the end, you can put a lower bound on how low its posterior weight ever was, since it’s hard to recover from having vanishingly small weight, and then alpha just needs to be set to include that). But fair enough to be interested an infinite lifetime with a finite model class that does not include the truth. So yeah, a model’s ranking can oscillate forever, although I think intelligent systems won’t really do this in practice? I think in an infinite lifetime, it is reasonable in practice to assume that if something is generally intelligent, it has some sort of ability to generate new hypotheses over time. And if you have two hypotheses about Sally, one which explains her relationship to butter, and one which explains her relationship to flowers, it’s pretty easy to generate another that combines these. So I’m not sure how instructive it is to consider the finite model class/infinite horizon Bayesian sequence prediction as a model for state-of-the-art AI.
So, what, the human has to act like they’re driving the car forever, even though the AI autopilot is really good?
The suggestion I make later is that a few timesteps in advance, the human is told to start acting like they’re driving the car, but they’re not controlling it yet, and then comes the timestep when autopilot actually defers to them, and that’s the behavior that gets recorded. Your response is
Is this procedure supposed to strike me as so airtight that an inner optimizer could never exploit it?
That proposal was making a different point—it was refuting exactly the concern that the human would have to act like they’re driving the car forever. This protocol just defends active imitation learning in general as potentially viable for the operation of heavy machinery. Assume the demonstrator is sitting in a driving simulator, and all the relevant info shows up on their screens; this allows a small team to be the demonstrators for many autopilots simultaneously. It’s not a question of whether an inner optimizer could exploit this protocol by finding the most inconvenient time for the human to be called in, and then querying the human—it’s much worse than that! If there’s a bad time for the human drive to be called in, then the autopilot will fail at that time regardless; the inner optimizer doesn’t even have to arrange an actual query. So there’s nothing to “exploit” really. And defending against the “much worse” version, I do think that the policy of a human driver with 5 seconds of acquaintance with the current state, does not crash the car at a rate significantly higher than a real human driver. Also, it may be worth saying that I don’t think we really need general intelligence to operate heavy machinery at human level, so I’m not sure the heavy machinery case is very important to consider in the first place.
In terms of evaluating this on theoretical terms, the feedback call button is an output channel that malign stuff has access to. This feels kind of like “case closed” to me; I take it as a given that a sufficiently intelligent malign actor could exploit this.
You said you’d continue to think about the points I made about why I don’t have the same reaction to this, so we can come back to those later. But stepping back, I think I want to make a point about the information loss you impose on your beliefs when applying the security mindset or Murphy’s Law. A malign model gets to say “query now” once! And then it is removed from the posterior because of its wrong prediction. That is not many bits for an output channel. But… yes, it is an output channel. And if you insist that all output channels for malign stuff transmit world-ending signals, just like all aquariums will leak, I agree that that is sometimes a useful perspective to adopt and run with, but the exercise of making actual probability estimates about events is potentially different from exercising a security mindset. I mentioned information loss. With a security mindset, there is no point in distinguishing a malign agent with a 20 bit output channel from one with an unbounded output channel. You just close the case on both. But we really might live in a world where the former is existentially safe, and the latter is not—I mean that even seems likely to me. Even from my perspective, where I don’t think a 20 bit output channel is dangerous, I understand the merit in disregarding that belief as the motivation for a research agenda, but I do think that’s a whole different sort of “epistemic status”. So when you say “I take it as a given that a sufficiently intelligent malign actor could exploit this” that makes sense to me as an action, but not as a proposition. (I mean, I think it’s incorrect, so I certainly don’t think it’s self-evidently true).
I guess I can expand on the object level too. Like, take a moment to really stare at 01110010101011010000, and imagine that you take it to be a signal from some deeply wise agent that arranged for a query at timestep number 469,712. Suppose further that you already think this deeply wise agent is not malign, but rather is much maligned! (So it doesn’t even need to spend the first few bits enthralling you). What do you do now? Or maybe timestep 469, 712 doesn’t mean that bitstring—maybe it means “this is a very meaningful world-state, and of similar world-states, the fact that this one was chosen tells me I should run program X on a supercomputer, so it can engage in some good, clean world-optimization”. Look around you right now—if someone told you “now is important, so think about that, and go run a program”, what program do you produce? Am I taking a huge risk even asking that, because there’s a precise time such that if I did, you’d run that program and it would end the world?

michaelcohen May 16, 2021, 6:52 PM
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on: Formal Inner Alignment, Prospectus
To state the least of our problems first: this requires a 100x slowdown in comparison with the state-of-the-art deep learning (or whatever) we’re layering the consensus algorithm on top of
I think you’re imagining deep learning as a MAP-type approach—it just identifies a best hypothesis and does inference with that. Comparing the consensus algorithm with (pure, idealized) MAP, 1) it is no slower, and 2) the various corners that can be cut for MAP can be cut for the consensus algorithm too. Starting with 1), the bulk of the work for either the consensus algorithm or a MAP approach is computing the posterior to determine which model(s) is(are) best. In an analogy to neural networks, it would be like saying most of the work comes from using the model (the forward pass) rather than arriving at the model (the many forward and backward passes in training). Regarding 2), state-of-the-art-type AI basically assumes approximate stationarity when separating a training phase from a test/execution phase. This is cutting a huge corner, and it means that when you think of a neural network running, you mostly think about it using the hypothesis that it has already settled on. But if we compare apples to apples, a consensus algorithm can cut the same corner to some extent. Neither a MAP algorithm nor a consensus algorithm is any better equipped than the other to, say, update the posterior only when the timestep is a power two. In general, training (be it SGD or posterior updating) is the vast bulk of the work in learning. To select a good hypothesis in the first place you will have already had to consider many more; the consensus algorithm just says to keep track of the runner ups.

Third, the consensus algorithm requires a strong form of realizability assumption, where you not only assume that our Bayesian space contains the true hypothesis, but furthermore, that it’s in the top 100 (or whatever number we choose). This hypothesis has to be really good: we have to think that malign hypotheses never out-guess the benign hypothesis. Otherwise, there’s a chance that we eliminate the good guy at some point (allowing the bad guys to coordinate on a wrong answer). But this is unrealistic! The world is big and complex enough that no realistic hypothesis has all the answers.
I don’t understand what out-guess means. But what we need is that the malign hypothesis don’t have substantially higher posterior weight than the benign ones. As time passes, the probability of this happening is not independent. The result I show about the probability of the truth being in the top set applies to all time, not any given point in time. I don’t know what “no realistic hypothesis has all the answers” means. There will be a best “realistic” benign hypothesis, and we can talk about that one.
Michael Cohen seems to think that restricting to imitation learning makes the realizability assumption realistic
Realistic in theory! Because the model doesn’t need to include the computer. I do not think we can actually compute every hypothesis simpler than a human brain in practice.
When you go from an idealized version to a realistic one, all methods can cut corners, and I don’t see a reason to believe that the consensus algorithm can’t cut corners just as well. Realistically, we will have some hypothesis-proposing heuristic, strong enough to identify models one of which is accurate enough to generate powerful agency. This heuristic will clearly cast a wide net (if not, how would it magically arrive at a good answer? It’s internals would need some hypothesis-generating function). Rather than throwing out the runner ups, the consensus algorithm stores them. The hypothesis generating heuristic is another attack surface for optimization daemons, and I won’t make any claims for now about how easy or hard it is to prevent such a thing.
to apply this to something like deep learning, we need to think that each run has an independent chance of creating safe AGI
Evan and I talked along these lines for a bit. My basic position is that if “local search” is enough to get to general intelligence, our algorithms will be searching in spaces (or regions) where diverse hypothesis are close. Diverse hypothesis generation is just crucial for general intelligence. I do not advocate training GPT-N with 10^100 different initializations. I don’t think you have to, and I don’t think it would help much.
Fourth, the consensus algorithm still gives inner optimizers control of when the system asks for more feedback. This in itself could be catastrophic! For example, it could ask at the worst times, when it anticipates the human feedback to be of poor quality, or when asking itself has catastrophic consequences. A silly example would be causing a self-driving car to ask for feedback right when it needs to enact difficult evasive maneuvers to avoid a crash.
It’s imitation learning so whatever the person would do when stepping in is what the algorithm learns to do when they don’t. If the human action would be of poor quality if the human were called upon to take the action, then all the reasonable models, benign ones included, will predict that poor action, and the poor action will be taken regardless of whether the human was brought into the loop. If a person would be unable to avoid a crash when stepping in at the last minute, the imitation learner will crash the car too! If 99 hypotheses are correctly predicting the human action, then the 100th hypotheses can correctly predict it too, and the human action is executed, or it can err deliberately, in which case the human is called and the human action is executed anyway. You might have to modify this protocol a bit before using it to learn human policies for operating heavy machinery.
Fifth, although (as Michael Cohen notes) the frequency of asking for feedback will rapidly diminish, the learning algorithm converges to the correct hypothesis extremely slowly… We have to face the fact that it might require human feedback at any point in the future.
Yeah this feels like a small cost to me. One person can be doing this for many instances at once. If you want to mimic a human that has been attentive for a given period of time (because you want to know how a human drives a car, having already gotten their bearings previously, rather than how human drives a car having just been transported into it) you can know a few timesteps in advance if there is any likely circumstance in which you will need to query the demonstrator, and you can use the lead time to get the demonstrator acquainted. The query complexity will go up of course because there will be false alarms, but this is a totally surmountable problem for active learning.
The fourth point [controlling when to ask for more feedback] really seems like the deal-breaker. Malign mesa-optimizers could intelligently leverage this to communicate with the outside world, manipulate the training process, etc.
A malign mesa-optimizer has one moment to err, and then it will be discarded from the posterior. There’s not much it could say to us with a well-timed “now!”. If multiple mesa-optimzers coordinate around a message, any mesa-optimizer not on board with this mission could disrupt the message. If you like, we could add a 1/million chance of querying to every timestep. Finally, with butterfly-effects, I don’t think that even a billion well-timed asks for help could precipitate human extinction. This is a bit all over the map, and this may be the point you want to press, but if you do, I think it is worth logging that if this is only attack surface left, we shouldn’t forget to put a stake in the ground marking “lots of progress”. If you believe that a single malign world-model could derail us if we use a Solomonoff predictor, but a consensus predictor would only be derailed by a supermajority of malign world-models, aligned with each other, that is a qualitative difference.
My third and final example: in one conversation, someone made a claim which I see as “exactly wrong”: that we can somehow lower-bound the complexity of a mesa-optimizer in comparison to a non-agentic hypothesis (perhaps because a mesa-optimizer has to have a world-model plus other stuff, where a regular hypothesis just needs to directly model the world). This idea was used to argue against some concern of mine.
The problem is precisely that we know of no way of doing that! If we did, there would not be any inner alignment problem! We could just focus on the simplest hypothesis that fit the data, which is pretty much what you want to do anyway!
Maybe this was someone else, but it could have been me. I think MAP probably does solve the inner alignment problem in theory, but I don’t expect to make progress resolving that question, and I’m interested in hedging against being wrong. Where you say, “We know of no way of doing that” I would say, “We know of ways that might do that, but we’re not 100% sure”. On my to-do list is to write up some of my disagreements with Paul’s original post on optimization daemons in the Solomonoff prior (and maybe with other points in this article). I don’t think it’s good to argue from the premise that a problem is worth taking seriously, and then see what follows from the existence of that problem, because a problem can exist with 10% probability and be worth taking seriously, but one might get in trouble embedding its existence too deeply in one’s view of the world, if it is still on balance unlikely. That’s not to say that most people think Paul’s conclusions are <90% likely, just that one might.

michaelcohen May 16, 2021, 6:40 PM
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in reply to: evhub’s comment on: Formal Inner Alignment, Prospectus
I think there would still be an inner alignment problem even if deceptive models were in fact always more complicated than non-deceptive models—i.e. if the universal prior wasn’t malign—which is just that the neural net prior (or whatever other ML prior we use) might be malign even if the universal prior isn’t (and in fact I’m not sure that there’s even that much of a connection between the malignity of those two priors)
Agree.

michaelcohen Mar 4, 2021, 4:51 PM
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in reply to: Koen.Holtman’s comment on: Formal Solution to the Inner Alignment Problem
There will be plenty of functions $R_{i}$ that have fewer bits in their encoding than the real function $R^{d}$ used by the demonstrator.
I don’t think this is a problem. There will be plenty of them, but when they’re wrong they’ll get removed from the posterior.

michaelcohen Mar 4, 2021, 4:46 PM
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in reply to: Koen.Holtman’s comment on: Formal Solution to the Inner Alignment Problem
A policy outputs a distribution over ${0, 1} \times A$ , and equations 3 and 4 define what this distribution is for the imitator. If it outputs (0, a), that means $q_{t} = 0$ and and $a_{t} = 1$ and if it outputs (1, a), that means $q_{t} = 1$ and $a_{t} = a$ . When I say
The 0 on the l.h.s. means the imitator is picking the action itself instead of deferring to the demonstrator,
that’s just describing the difference between equations 3 and 4. Look at equation 4 to see that when $q_{t} = 1$ , the distribution over the action is equal to that of the demonstrator. So we describe the behavior that follows $q_{t} = 1$ as “deferring to the demonstrator”. If we look at the distribution over the action when $q_{t} = 0$ , it’s something else, so we say the imitator is “picking its own action”.
The 0 on the l.h.s. means the imitator is picking the action $a$ itself instead of deferring to the demonstrator or picking one of the other actions???
The 0 means the imitator is picking the action, and the $a$ means it’s not picking another action that’s not $a$ .

michaelcohen Feb 28, 2021, 11:32 AM
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in reply to: Vanessa Kosoy’s comment on: Formal Solution to the Inner Alignment Problem
What’s the distinction between training and deployment when the model can always query for more data?

michaelcohen Feb 28, 2021, 11:30 AM
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in reply to: evhub’s comment on: Formal Solution to the Inner Alignment Problem
It may be helpful to point to specific sections of such a long paper.
(Also, I agree that a neural network trained trained with that reward could produce a deceptive model that makes a well-timed error.)

michaelcohen Feb 28, 2021, 11:14 AM
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in reply to: evhub’s comment on: Formal Solution to the Inner Alignment Problem
it certainly should have to consider different models of what the next transition will be like.
Yeah I was agreeing with that.
even though the Q learner is trained using its own point estimate of the next state, it isn’t, at inference time, given access to that point estimate.
Right, but one thing the Q-network, in its forward pass, is trying to reproduce is the point of estimate of the Q-value of the next state (since it doesn’t have access to it). What it isn’t trying to reproduce, because it isn’t trained that way, is multiple models of what the Q-value might be at a given possible next state.