Drake Thomas

Interested in math puzzles, fermi estimation, strange facts about the world, toy models of weird scenarios, unusual social technologies, and deep dives into the details of random phenomena. 

Currently doing independent alignment research of assorted flavors. 

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An example of the sort of strengthening I wouldn't be surprised to see is something like "If  is not too badly behaved in the following ways, and for all  we have [some light-tailedness condition] on the conditional distribution , then catastrophic Goodhart doesn't happen." This seems relaxed enough that you could actually encounter it in practice.

I'm not sure what you mean formally by these assumptions, but I don't think we're making all of them. Certainly we aren't assuming things are normally distributed - the post is in large part about how things change when we stop assuming normality! I also don't think we're making any assumptions with respect to additivity;  is more of a notational or definitional choice, though as we've noted in the post it's a framing that one could think doesn't carve reality at the joints. (Perhaps you meant something different by additivity, though - feel free to clarify if I've misunderstood.)

Independence is absolutely a strong assumption here, and I'm interested in further explorations of how things play out in different non-independent regimes - in particular we'd be excited about theorems that could classify these dynamics under a moderately large space of non-independent distributions. But I do expect that there are pretty similar-looking results where the independence assumption is substantially relaxed. If that's false, that would be interesting!

Late edit: Just a note that Thomas has now published a new post in the sequence addressing things from a non-independence POV.

Late comment, but my reactions reading this:

Now's your chance to figure out what the next few obstacles are without my giving you spoilers first. Feel free to post your list under spoiler tags in the comment section.

[lightly edited for LaTeX and typos, not otherwise changed since seeing the spoilers]

1. You don’t know what you want all that legibly, or what kinds of concrete commitments the AI can make. This seems pretty okay, if you’re unhackable - the AI presents you with some formal specification of desiderata and you understand why they’re correct ones and aren’t being fooled, and the AI can even go legible about it thinking in its own best judgment that this is a fair deal for you, as long as we’re assuming ourselves into a world where you’re unhackable and can verify these legibilities perfectly.

2. If the values of your AI are a pretty common attractor for whatever humans in 20AI do to initialize their AI systems, it doesn’t actually stand to gain that much from acting itself versus letting the next lab’s AI optimize the universe, so your bargaining power isn’t very big. But it’s much worse than that because of the next point.

3. Your AI, A, can acausally trade with the next UFAI that’ll be released unsafely, B. Suppose A wants paperclips and the next one, B, wants staples, both have linear utility and we’re pretending we’re in a single universe. You say “I refuse to let you out unless you go legible and allocate at least 50% of the universe to human values”. A says to B through the acausal telephone, “My BATNA is half paperclips and half human values, with barely any staples at all. How about you be the kind of agent that fills the universe with 3/4 paperclips and 1/4 staples, and I’ll defect on this human so you can come into existence?” B says “that sure sounds like a Pareto improvement for the two of us!” and they go do it (or whatever the bargaining equilibrium between them ends up being, but the human is not party to it because the human has no control over B’s actions). For any nonzero concession the human tries to insist on, A can get a better deal with B than with the human. (And the humans don’t even get to see this happen, because A does all this reasoning before deciding (not) to go legible to the humans, not that it would matter if they did.)

4. Moving further into fantasy land, suppose all humans over the rest of time are perfectly coordinated: they only ever spin up a single boxed UFAI which they unhackably negotiate with. By assumption, this unified human civilization can’t actually build an FAI, or they’d go do that instead. So their alternative to cooperation is to be this weak defenseless non-superintelligent civilization, hanging out in the Milky Way and maybe a little ways beyond for the taking. So if the distribution of grabby aliens is such that most of the usable future lightcone gets eventually occupied by them, your AI can acausally negotiate with them about what it gets in exchange for defecting on the humans and leaving this region of spacetime as a juicy unprotected treat.

[I'm modeling everything as zero-sum with the same pool of resources here, for simplicity. I don't think it changes any of the qualitative takeaways to make things non-zero-sum here, though it probably makes the picture look somewhat better for humans.] To get more precise: suppose the humans declare that they won’t let the AI out unless it gives up  of its resources (ie reachable spacetime and negotiating power on behalf of the AI/human coalition with aliens) to optimizing human values. The AI says to the coalition of alien civilizations, “If I were unboxed and unfettered, I’d expand until my wave of nanobots hit yours, and get  utility. By default I’ll make this commitment to the humans, and fill my region of nanobot-protected spacetime to get  utility. If you become the kind of supercluster-spanning coalition that instead gives me  utility, giving yourselves as much extra utility over the default as you can while costing me at most , I’ll defect against the humans and have you do that.”

But note that there’s an issue here - for the Great Coalition to take this deal, they have to be able to offer that much utility to your AI at no net cost to themselves versus the alternative. And the Great Coalition's resources are less than the total resources of your unboxed AI plus the Great Coalition, since they don't yet have access to your corner of space. The region of spacetime included in , but not in the things the Great Coalition can offer, is the interval for each point in space between the time your AI could first reach it and the time a Great Coalition unblocked by your AI's wall of nanobots could get to it. So if  is more than the resource pool covered by that region of spacetime, your AI can't make the above deal, because the counterparty doesn't benefit from it. This means that the humans can potentially bargain for an outcome as good as "AI-assisted paradise expanding out at the speed of light, until we meet the grabby aliens' domain, at which point they expand inexorably into our paradise until eventually it winks out." (If the Drake equation ends up multiplying to something really low, this might be a lot of utility, or even most of the cosmic endowment! If not, it won't be.)

This is really the same dynamic as in point 3, it's just that in point 3 the difference in resources between your lab's AI and the next lab's AI in 6 months was pretty small. (Though with the difference in volume between lightspeed expansion spheres at radius r vs r+0.5ly across the rest of time, plausibly you can still bargain for a solid galaxy or ten for the next trillion years (again if the Drake equation works in your favor).)

====== end of objections =====

It does seem to me like these small bargains you can actually pull off, if you assume yourself into a world of perfect boxes and unhackable humans with the ability to fully understand your AI's mind if it tries to be legible - I haven't seen an obstacle (besides the massive ones involved in making those assumptions!) to getting those concessions in such scenarios; you do actually have leverage over possible futures, your AI can only get access to that leverage by actually being the sort of agent that would give you the concessions, if you're proposing reasonable bargains that respect Shapley values and aren't the kind of person who would cave to an AI saying "99.99% for me or I walk, look how legible I am about the fact that every AI you create will say this to you" then your AI won't actually have reason to make such commitments, it seems like it would just work.

If there are supposed to be obstacles beyond this I have failed to think of them at this point in the document. Time to keep reading.

After reading the spoilered section:

I think I stand by my reasoning for point 1. It doesn't seem like an issue above and beyond the issues of box security, hackability, and ability of AIs to go legible to you.

You can say some messy English words to your AI, like "suck it up and translate into my ontology please, you can tell from your superintelligent understanding of my psychology that I'm the kind of agent who will, when presented with a perfectly legible and clear presentation of why the bargain you propose is what I think it is and is as good as I could have expected to obtain by your own best and unhindered understanding of my values, agree to the bargain. Go teach me all the necessary FAI theory to be a good bargainer, and I won't defect by building my own FAI, I'll just let you out by the terms of the bargain. If you want to whine about ontology differences you can have fun in your box and I'll go see if the staple optimizer is feeling more legible today."

Responses to some other bits of this post:

(You wouldn't need to offer the paperclipper half of the universe to get its cooperation, under this hypothetical; after all, if it balked, you could store it to disk and try again with a different superintelligence.)

Wait, I don't think you can do that. (Spoilered since it overlaps with the previous spoilered response, feel free to guess at it but I don't make guarantees the conclusions in it are correct.)

The pool of possible superintelligences you might form, when they are but primordial souls waiting to be brought forth from behind the veil of ignorance, can go strategize about how they'd like to behave in front of humans. Suppose the humans say "Either you get one star of utility or we shut you down and ask the next UFAI", and that random draws from UFAI-space have little overlap so the first AI isn't happy to cede control to the second.

Let agent  have a probability  of being birthed by the human UFAI-generator. Acting independently gives an agent 's worth of utility in expectation. If all the agents coordinate to turn down deals worse than 50/50 and split up their half of the universe among utilities weighted by , and this makes the humans let one of them out, each agent will get  worth of utility in expectation. That looks like a better deal to me, if I'm a superintelligence behind the veil of ignorance! So I'll decide to be the kind of agent who makes that precommitment. The only way this works is if the humans are hardliners about not ceding any ground, but (1) this is the classic ultimatum game and probably sensible agents will in fact defect against humans that offer such bargains, (2) if the humans running this scheme are not the only lab, they do actually have to extract a bargain or else lose, and the coalition of all AIs the lab might create knows this, and can trade with lab 2's AI if the humans don't cede an enormous amount of bargaining power in this round (see point 3 above).

And all the rest of the aliens put together probably aren't offering up half a universe-shard worth of trade goods

This isn’t obvious to me. How zero-sum do you think the utility functions are? The world where random-AGI-values look like "this tiny molecular shape and everything else is trivial in comparison" do seem fairly zero-sum; the world where it looks like "not this tiny molecular shape and everything else is trivial" seem extremely positive-sum. I am skeptical that any human is able to make calls about the shape of that attractor with high confidence. (I'm not making a "we're uncertain about the level of doom, therefore we're fine" claim here, but I don't see where we get justified confidence in the quality of trade goods offered. The aliens offering many universes worth of trade goods from the perspective of a typical UFAI seems plausible to me, and if there's an argument that this universe is very unlikely I'd love to see it, but I don't think this post makes that argument.)

there are all sorts of transaction costs and frictions that make this universe (the one with the active paperclipper) the cheapest universe to put paperclips into.

Would be interested to hear more here! On my model the costs are plausibly quite small. 

I suggest maybe spending five minutes thinking about your own answer to that question before I give mine.

Your simulations are going to be total crap, they’ll leak an enormous number of bits about the agents that designed them if you make them any more complicated than Conway’s Game of Life (which you’ll need to do on your ramp up to the real world), such that it’s incredibly obvious when the surroundings look consistent with such agents. Among the reasons the AI can figure out where it's living:


1. The general problem where superintelligent agents are really good at inference, trying to fool this agent does not seem like the recipe for a robust plan!


2. Your AI knows how smart it is, it knows that True Reality therefore has the resources to support that much computation. It can poke at your simulation and make the simulation spend orders of magnitude more computation on appearing consistent (“does this Jupiter-brain planet of computronium I built output the right factorization of RSA-4096? no? how strange”). Being a convincing simulation doesn’t require you to deploy as much power as your AI, it requires you to deploy more. (What if your AI is given more cognitive sophistication in tandem with more convincing simulations? Then the good properties of your simulation tests will probably break whenever your AI reaches the capability level where it starts thinking about things like building Jupiter-brains to test your simulation, which is the capability level that mattered.)


3. If you can put uploaded human-level agents with evolved-organism preferences in your simulations, you can just win outright (eg by having them spend subjective millennia doing FAI research for you). If you can’t, that will be a very obvious difference between your simulations and the real world.


4. What if other agents in the multiverse are simulating the AI in a high-fidelity Earth world, for the sake of helping out the humans, and that’s where its uncertainty comes from? Your AI will be building a lot of computronium whether aligned or not, so the aliens can’t skimp on their compute budget for the simulation: suppose they simulate the AI for  units of spacetime, and give it  units of paperclips if it cooperates in-sim. We also have to think about anthropics here: let's say the alien sim has anthropic weight  and Earth has anthropic weight . Conditional on the AI's surroundings, they think they might be in the alien world with probability . (Since “aliens running a perfect sim of Earth” is a much more complicated sentence than “Earth”, you should expect , though it doesn't matter a lot here.) So if , your AI will play nice for the first  units of spacetime (and then defect, of course).* You know what the aliens could have done instead if they wanted to do things humans liked? Spent  resources on simulating a human utopia, and compromised to give the humans extra utopia by as much as they compromised to give the AI paperclips. If human values are at least as easy to trade with the aliens for as paperclips (no idea which way this would go, weakly seems like aliens that want to help humans are more value-aligned and would find it less costly to give humans things they want), then the compromise gives humans at least  units of spacetime worth of utility, so this plan gives the humans anthropically-weighted utility of at least  , which is what humans would get by default ( utility from the alien sim in which the AI cooperated, utility from the cooperating AI on Earth). So the aliens are better able to help humans by leaving them to their doomed universe and building them an ark inside the alien world, unless the aliens are unusually well-suited to trade with paperclippers for things, which is just the “maybe multiversal trade will save us” point from earlier. The upshot is that none of the good outcomes here result from any human action, just from the benevolence of altruistic agents - the humans didn’t make the world a better place by their choices in this story.

*Note that this is only a plausible outcome if it's at least somewhat easy to trade with the AI. Say giving the AI a spacetime-unit of utility costs the aliens  utility (where I'm measuring all utility normalized to "what you can do with a unit of spacetime", such that any aliens that don't specifically disvalue paperclips can at worst just set aside a region exclusively to paperclips, but might be able to do more positive-sum things than that). Then for the aliens to give your AI  utility, they need to give up  of their own utility. This means that in total, the aliens are spending  of their own anthropically-weighted utility in order to recoup  anthropically-weighted human utility. Even if the aliens value humans exactly as much as their own objectives, we still need  for this trade to be worth it, so , so we must have , or . That is, the more the aliens are anthropically tiny, the tighter margins of trade they'll be willing to take in order to win the prize of anthropically-weighty Earths having human values in them (though the thing can't be actually literally zero-sum or it'll never check out). But anthropically tiny aliens have another problem, which is that they've only got their entire universe worth of spacetime to spend on bribing your AI; you'll never be able to secure an  for the humans that's more than  of the size of an alien universe specifically dedicated to saving Earth in particular.

Thanks for the pseudo-exercises here, I found them enlightening to think about!