harfe
Most[1] problems with unbounded utility functions go away if you restrict yourself to summable utility functions[2]. Summable utility functions can still be unbounded.
For example, if each planet in the universe gives you 1 utility, and for , then your utility function is unbounded but summable. In such a universe it would be very unlikely for a casino to hand out a large number of planets.
Your proof relies on the assumption
assuming that the casino has unbounded utility to hand out.
and this assumption would be wrong in my example.
Note that GWWC is shutting down their donor lottery, among other things: https://forum.effectivealtruism.org/posts/f7yQFP3ZhtfDkD7pr/gwwc-is-retiring-10-initiatives
Mid 2027 seems too late to me for such a candidate to start the official campaign.
For the 2020 presidential election, many democratic candidates announced their campaign in early 2019, and Yang already in 2017. Debates happened already in June 2019. As a likely unknown candidate, you probably need a longer run time to accumulate a bit of fame.
Also Musk’s regulatory plan is polling well
What plan are you referring to? Is this something AI safety specific?
I wouldn’t say so, I don’t think his campaign has made UBI advocacy more difficult.
But an AI notkilleveryoneism campaign seems more risky. It could end up making the worries look silly, for example.
Their platform would be whatever version and framing of AI notkilleveryoneism the candidates personally endorse, plus maybe some other smaller things. They should be open that they consider the potential human disempowerment or extinction to be the main problem of our time.
As for the concrete policy proposals, I am not sure. The focus could be on international treaties, or banning or heavy regulation of AI models who were trained with more than a trillion quadrillion (10^27) operations. (not sure I understand the intent behind your question).
A potentially impactful thing: someone competent runs as a candidate for the 2028 election on an AI notkilleveryoneism[1] platform. Maybe even two people should run, one for the democratic primary, and one in the republican primary. While getting the nomination is rather unlikely, there could be lots of benefits even if you fail to gain the nomination (like other presidential candidates becoming sympathetic to AI notkilleveryoneism, or more popularity of AI notkilleveryoneism in the population, etc.)
On the other hand, attempting a presidential run can easily backfire.
A relevant previous example to this kind of approach is the 2020 campaign by Andrew Yang, which focussed on universal basic income (and downsides of automation). While the campaign attracted some attention, it seems like it didn’t succeed in making UBI a popular policy among democrats.
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Not necessarily using that name.
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This can easily be done in the cryptographic example above: B can sample a new number , and then present to a fresh copy of A that has not seen the transcript for so far.
I don’t understand how this is supposed to help. I guess the point is to somehow catch a fresh copy of A in a lie about a problem that is different from the original problem, and conclude that A is the dishonest debater?
But couldn’t A just answer “I don’t know”?
Even if it is a fresh copy, it would notice that it does not know the secret factors, so it could display different behavior than in the case where A knows the secret factors .
Some of these are very easy to prove; here’s my favorite example. An agent has a fixed utility function and performs Pareto-optimally on that utility function across multiple worlds (so “utility in each world” is the set of objectives). Then there’s a normal vector (or family of normal vectors) to the Pareto surface at whatever point the agent achieves. (You should draw a picture at this point in order for this to make sense.) That normal vector’s components will all be nonnegative (because Pareto surface), and the vector is defined only up to normalization, so we can interpret that normal vector as a probability distribution. That also makes sense intuitively: larger components of that vector (i.e. higher probabilities) indicate that the agent is “optimizing relatively harder” for utility in those worlds. This says nothing at all about how the agent will update, and we’d need a another couple sentences to argue that the agent maximizes expected utility under the distribution, but it does give the prototypical mental picture behind the “Pareto-optimal → probabilities” idea.
Here is an example (to point out a missing assumption): Lets say you are offered to bet on the result of a coin flip for dollar. You get dollars if you win, and your utility function is linear in dollars. You have three actions: “Heads”, “Tails”, and “Pass”. Then “Pass” performs Pareto-optimally across multiple worlds. But “Pass” does not maximize expected utility under any distribution.
I think what is needed for the result is an additional convexity-like assumption about the utilities. This could be
the set of achievable utility vectors is convex'', or even something weaker likeevery convex combination of achievable utility vectors is dominated by an achievable utility vector” (here, by utility vector I mean if is the utility of world ). If you already accept the concept of expected utility maximization, then you could also use mixed strategies to get the convexity-like assumption (but that is not useful if the point is to motivate using probabilities and expected utility maximization).Or: even if you do expect powerful agents to be approximately Pareto-optimal, presumably they will be approximately Pareto optimal, not exactly Pareto-optimal. What can we say about coherence then?
The underlying math statement of some of these kind of results about Pareto-optimality seems to be something like this:
If is Pareto-optimal wrt utilities , and a convexity assumption (e.g. the set is convex, or something with mixed strategies) holds, then there is a probability distribution so that is optimal for .
I think there is a (relatively simple) approximate version of this, where we start out with approximate Pareto-optimality.
We say that is Pareto—optimal if there is no (strong) Pareto-improvement by more than (that is, there is no with for all ).
Claim: If is Pareto—optimal and the convexity assumption holds, then there is a probability distribution so that is -optimal for .
Rough proof: Define and as the closure of . Let be of the form for the largest such that . We know that . Now is Pareto-optimal for , and by the non-approximate version there exists a probability distribution so that is optimal for . Then, for any , we have $\mathbb{E}{i\sim\mu} u_i(x) \leq \mathbb{E}{i\sim\mu} \tilde y_i = \mathbb{E}{i\sim\mu} (u_i(\bar x) + \delta)\le \varepsilon + \mathbb{E}{i\sim\mu} u_i(\bar x), $ that is, is -optimal for .
I think there are some subtleties with the (non-infra) bayesian VNM version, which come down to the difference between “extreme point” and “exposed point” of . If a point is an extreme point that is not an exposed point, then it cannot be the unique expected utility maximizer under a utility function (but it can be a non-unique maximizer).
For extreme points it might still work with uniqueness, if, instead of a VNM-decision-maker, we require a slightly weaker decision maker whose preferences satisfy the VNM axioms except continuity.
For any , if then either or .
I think this condition might be too weak and the conjecture is not true under this definition.
If , then we have (because a minimum over a larger set is smaller). Thus, can only be the unique argmax if .
Consider the example . Then is closed. And satisfies . But per the above it cannot be a unique maximizer.
Maybe the issue can be fixed if we strengthen the condition so that has to be also minimal with respect to .
For a provably aligned (or probably aligned) system you need a formal specification of alignment. Do you have something in mind for that? This could be a major difficulty. But maybe you only want to “prove” inner alignment and assume that you already have an outer-alignment-goal-function, in which case defining alignment is probably easier.
insofar as the simplest & best internal logical-induction market traders have strong beliefs on the subject, they may very well be picking up on something metaphysically fundamental. Its simply the simplest explanation consistent with the facts.
Theorem 4.6.2 in logical induction says that the “probability” of independent statements does not converge to or , but to something in-between. So even if a mathematician says that some independent statement feels true (eg some objects are “really out there”), logical induction will tell him to feel uncertain about that.
A related comment from lukeprog (who works at OP) was posted on the EA Forum. It includes:
However, at present, it remains the case that most of the individuals in the current field of AI governance and policy (whether we fund them or not) are personally left-of-center and have more left-of-center policy networks. Therefore, we think AI policy work that engages conservative audiences is especially urgent and neglected, and we regularly recommend right-of-center funding opportunities in this category to several funders.
it’s for the sake of maximizing long-term expected value.
Kelly betting does not maximize long-term expected value in all situations. For example, if some bets are offered only once (or even a finite amount), then you can get better long-term expected utility by sometimes accepting bets with a potential “0”-Utility outcome.
This is maybe not the central point, but I note that your definition of “alignment” doesn’t precisely capture what I understand “alignment” or a good outcome from AI to be:
‘AGI’ continuing to exist
AGI could be very catastrophic even when it stops existing a year later.
eventually
If AGI makes earth uninhabitable in a trillion years, that could be a good outcome nonetheless.
ranges that existing humans could survive under
I don’t know whether that covers “humans can survive on mars with a space-suit”, but even then, if humans evolve/change to handle situations that they currently do not survive under, that could be part of an acceptable outcome.
it is the case that most algorithms (as a subset in the hyperspace of all possible algorithms) are already in their maximally most simplified form. Even tiny changes to an algorithm could convert it from ‘simplifiable’ to ‘non-simplifiable’.
This seems wrong to me: For any given algorithm you can find many equivalent but non-simplified algorithms with the same behavior, by adding a statement to the algorithm that does not affect the rest of the algorithm (e.g. adding a line such as
foobar1234 = 123in the middle of a python program)). In fact, I would claim that the majority python programs on github are not in their “maximally most simplified form”. Maybe you can cite the supposed theorem that claims that most (with a clearly defined “most”) algorithms are maximally simplified?
This is not a formal definition.
Your English sentence has no apparent connection to mathematical objects, which would be necessary for a rigorous and formal definition.
I think you are broadly right.
So we’re automatically giving ca. higher probability – even before applying the length penalty .
But note that under the Solomonoff prior, you will get another penalty for these programs with DEADCODE. So with this consideration, the weight changes from (for normal ) to (normal plus DEADCODE versions of ), which is not a huge change.
For your case of “uniform probability until ” I think you are right about exponential decay.
The article unfortunately does not seriously consider the possibility that AGI has the potential to automate most jobs in a few years. The large investments into AI would be justified in this case, even if current revenue is small! I think this is an important difference to past bubbles.
The part about inference costs seems false, unless they mean total inference costs of all their instances.