I begin by thanking Holden Karnofsky of Givewell for his rare gift of his detailed, engaged, and helpfully-meant critical article Thoughts on the Singularity Institute (SI). In this reply I will engage with only one of the many subjects raised therein, the topic of, as I would term them, non-self-modifying planning Oracles, a.k.a. 'Google Maps AGI' a.k.a. 'tool AI', this being the topic that requires me personally to answer. I hope that my reply will be accepted as addressing the most important central points, though I did not have time to explore every avenue. I certainly do not wish to be logically rude, and if I have failed, please remember with compassion that it's not always obvious to one person what another person will think was the central point.
Luke Mueulhauser and Carl Shulman contributed to this article, but the final edit was my own, likewise any flaws.
Summary:
Holden's concern is that "SI appears to neglect the potentially important distinction between 'tool' and 'agent' AI." His archetypal example is Google Maps:
Google Maps is not an agent, taking actions in order to maximize a utility parameter. It is a tool, generating information and then displaying it in a user-friendly manner for me to consider, use and export or discard as I wish.
The reply breaks down into four heavily interrelated points:
First, Holden seems to think (and Jaan Tallinn doesn't apparently object to, in their exchange) that if a non-self-modifying planning Oracle is indeed the best strategy, then all of SIAI's past and intended future work is wasted. To me it looks like there's a huge amount of overlap in underlying processes in the AI that would have to be built and the insights required to build it, and I would be trying to assemble mostly - though not quite exactly - the same kind of team if I was trying to build a non-self-modifying planning Oracle, with the same initial mix of talents and skills.
Second, a non-self-modifying planning Oracle doesn't sound nearly as safe once you stop saying human-English phrases like "describe the consequences of an action to the user" and start trying to come up with math that says scary dangerous things like (he translated into English) "increase the correspondence between the user's belief about relevant consequences and reality". Hence why the people on the team would have to solve the same sorts of problems.
Appreciating the force of the third point is a lot easier if one appreciates the difficulties discussed in points 1 and 2, but is actually empirically verifiable independently: Whether or not a non-self-modifying planning Oracle is the best solution in the end, it's not such an obvious privileged-point-in-solution-space that someone should be alarmed at SIAI not discussing it. This is empirically verifiable in the sense that 'tool AI' wasn't the obvious solution to e.g. John McCarthy, Marvin Minsky, I. J. Good, Peter Norvig, Vernor Vinge, or for that matter Isaac Asimov. At one point, Holden says:
One of the things that bothers me most about SI is that there is practically no public content, as far as I can tell, explicitly addressing the idea of a "tool" and giving arguments for why AGI is likely to work only as an "agent."
If I take literally that this is one of the things that bothers Holden most... I think I'd start stacking up some of the literature on the number of different things that just respectable academics have suggested as the obvious solution to what-to-do-about-AI - none of which would be about non-self-modifying smarter-than-human planning Oracles - and beg him to have some compassion on us for what we haven't addressed yet. It might be the right suggestion, but it's not so obviously right that our failure to prioritize discussing it reflects negligence.
The final point at the end is looking over all the preceding discussion and realizing that, yes, you want to have people specializing in Friendly AI who know this stuff, but as all that preceding discussion is actually the following discussion at this point, I shall reserve it for later.
1. The math of optimization, and the similar parts of a planning Oracle.
What does it take to build a smarter-than-human intelligence, of whatever sort, and have it go well?
A "Friendly AI programmer" is somebody who specializes in seeing the correspondence of mathematical structures to What Happens in the Real World. It's somebody who looks at Hutter's specification of AIXI and reads the actual equations - actually stares at the Greek symbols and not just the accompanying English text - and sees, "Oh, this AI will try to gain control of its reward channel," as well as numerous subtler issues like, "This AI presumes a Cartesian boundary separating itself from the environment; it may drop an anvil on its own head." Similarly, working on TDT means e.g. looking at a mathematical specification of decision theory, and seeing "Oh, this is vulnerable to blackmail" and coming up with a mathematical counter-specification of an AI that isn't so vulnerable to blackmail.
Holden's post seems to imply that if you're building a non-self-modifying planning Oracle (aka 'tool AI') rather than an acting-in-the-world agent, you don't need a Friendly AI programmer because FAI programmers only work on agents. But this isn't how the engineering skills are split up. Inside the AI, whether an agent AI or a planning Oracle, there would be similar AGI-challenges like "build a predictive model of the world", and similar FAI-conjugates of those challenges like finding the 'user' inside an AI-created model of the universe. The insides would look a lot more similar than the outsides. An analogy would be supposing that a machine learning professional who does sales optimization for an orange company couldn't possibly do sales optimization for a banana company, because their skills must be about oranges rather than bananas.
Admittedly, if it turns out to be possible to use a human understanding of cognitive algorithms to build and run a smarter-than-human Oracle without it being self-improving - this seems unlikely, but not impossible - then you wouldn't have to solve problems that arise with self-modification. But this eliminates only one dimension of the work. And on an even more meta level, it seems like you would call upon almost identical talents and skills to come up with whatever insights were required - though if it were predictable in advance that we'd abjure self-modification, then, yes, we'd place less emphasis on e.g. finding a team member with past experience in reflective math, and wouldn't waste (additional) time specializing in reflection. But if you wanted math inside the planning Oracle that operated the way you thought it did, and you wanted somebody who understood what could possibly go wrong and how to avoid it, you would need to make a function call to the same sort of talents and skills to build an agent AI, or an Oracle that was self-modifying, etc.
2. Yes, planning Oracles have hidden gotchas too.
"Tool AI" may sound simple in English, a short sentence in the language of empathically-modeled agents — it's just "a thingy that shows you plans instead of a thingy that goes and does things." If you want to know whether this hypothetical entity does X, you just check whether the outcome of X sounds like "showing someone a plan" or "going and doing things", and you've got your answer. It starts sounding much scarier once you try to say something more formal and internally-causal like "Model the user and the universe, predict the degree of correspondence between the user's model and the universe, and select from among possible explanation-actions on this basis."
Holden, in his dialogue with Jaan Tallinn, writes out this attempt at formalizing:
Here's how I picture the Google Maps AGI ...
utility_function = construct_utility_function(process_user_input());
foreach $action in $all_possible_actions {
$action_outcome = prediction_function($action,$data);
$utility = utility_function($action_outcome);
if ($utility > $leading_utility) { $leading_utility = $utility;
$leading_action = $action; }
}
report($leading_action);
construct_utility_function(process_user_input()) is just a human-quality function for understanding what the speaker wants. prediction_function is an implementation of a human-quality data->prediction function in superior hardware. $data is fixed (it's a dataset larger than any human can process); same with $all_possible_actions. report($leading_action) calls a Google Maps-like interface for understanding the consequences of $leading_action; it basically breaks the action into component parts and displays predictions for different times and conditional on different parameters.
Google Maps doesn't check all possible routes. If I wanted to design Google Maps, I would start out by throwing out a standard planning technique on a connected graph where each edge has a cost function and there's a good heuristic measure of the distance, e.g. A* search. If that was too slow, I'd next try some more efficient version like weighted A* (or bidirectional weighted memory-bounded A*, which I expect I could also get off-the-shelf somewhere). Once you introduce weighted A*, you no longer have a guarantee that you're selecting the optimal path. You have a guarantee to within a known factor of the cost of the optimal path — but the actual path selected wouldn't be quite optimal. The suggestion produced would be an approximation whose exact steps depended on the exact algorithm you used. That's true even if you can predict the exact cost — exact utility — of any particular path you actually look at; and even if you have a heuristic that never overestimates the cost.
The reason we don't have God's Algorithm for solving the Rubik's Cube is that there's no perfect way of measuring the distance between any two Rubik's Cube positions — you can't look at two Rubik's cube positions, and figure out the minimum number of moves required to get from one to another. It took 15 years to prove that there was a position requiring at least 20 moves to solve, and then another 15 years to come up with a computer algorithm that could solve any position in at most 20 moves, but we still can't compute the actual, minimum solution to all Cubes ("God's Algorithm"). This, even though we can exactly calculate the cost and consequence of any actual Rubik's-solution-path we consider.
When it comes to AGI — solving general cross-domain "Figure out how to do X" problems — you're not going to get anywhere near the one, true, optimal answer. You're going to — at best, if everything works right — get a good answer that's a cross-product of the "utility function" and all the other algorithmic properties that determine what sort of answer the AI finds easy to invent (i.e. can be invented using bounded computing time).
As for the notion that this AGI runs on a "human predictive algorithm" that we got off of neuroscience and then implemented using more computing power, without knowing how it works or being able to enhance it further: It took 30 years of multiple computer scientists doing basic math research, and inventing code, and running that code on a computer cluster, for them to come up with a 20-move solution to the Rubik's Cube. If a planning Oracle is going to produce better solutions than humanity has yet managed to the Rubik's Cube, it needs to be capable of doing original computer science research and writing its own code. You can't get a 20-move solution out of a human brain, using the native human planning algorithm. Humanity can do it, but only by exploiting the ability of humans to explicitly comprehend the deep structure of the domain (not just rely on intuition) and then inventing an artifact, a new design, running code which uses a different and superior cognitive algorithm, to solve that Rubik's Cube in 20 moves. We do all that without being self-modifying, but it's still a capability to respect.
And I'm not even going into what it would take for a planning Oracle to out-strategize any human, come up with a plan for persuading someone, solve original scientific problems by looking over experimental data (like Einstein did), design a nanomachine, and so on.
Talking like there's this one simple "predictive algorithm" that we can read out of the brain using neuroscience and overpower to produce better plans... doesn't seem quite congruous with what humanity actually does to produce its predictions and plans.
If we take the concept of the Google Maps AGI at face value, then it actually has four key magical components. (In this case, "magical" isn't to be taken as prejudicial, it's a term of art that means we haven't said how the component works yet.) There's a magical comprehension of the user's utility function, a magical world-model that GMAGI uses to comprehend the consequences of actions, a magical planning element that selects a non-optimal path using some method other than exploring all possible actions, and a magical explain-to-the-user function.
report($leading_action) isn't exactly a trivial step either. Deep Blue tells you to move your pawn or you'll lose the game. You ask "Why?" and the answer is a gigantic search tree of billions of possible move-sequences, leafing at positions which are heuristically rated using a static-position evaluation algorithm trained on millions of games. Or the planning Oracle tells you that a certain DNA sequence will produce a protein that cures cancer, you ask "Why?", and then humans aren't even capable of verifying, for themselves, the assertion that the peptide sequence will fold into the protein the planning Oracle says it does.
"So," you say, after the first dozen times you ask the Oracle a question and it returns an answer that you'd have to take on faith, "we'll just specify in the utility function that the plan should be understandable."
Whereupon other things start going wrong. Viliam_Bur, in the comments thread, gave this example, which I've slightly simplified:
Example question: "How should I get rid of my disease most cheaply?" Example answer: "You won't. You will die soon, unavoidably. This report is 99.999% reliable". Predicted human reaction: Decides to kill self and get it over with. Success rate: 100%, the disease is gone. Costs of cure: zero. Mission completed.
Bur is trying to give an example of how things might go wrong if the preference function is over the accuracy of the predictions explained to the human— rather than just the human's 'goodness' of the outcome. And if the preference function was just over the human's 'goodness' of the end result, rather than the accuracy of the human's understanding of the predictions, the AI might tell you something that was predictively false but whose implementation would lead you to what the AI defines as a 'good' outcome. And if we ask how happy the human is, the resulting decision procedure would exert optimization pressure to convince the human to take drugs, and so on.
I'm not saying any particular failure is 100% certain to occur; rather I'm trying to explain - as handicapped by the need to describe the AI in the native human agent-description language, using empathy to simulate a spirit-in-a-box instead of trying to think in mathematical structures like A* search or Bayesian updating - how, even so, one can still see that the issue is a tad more fraught than it sounds on an immediate examination.
If you see the world just in terms of math, it's even worse; you've got some program with inputs from a USB cable connecting to a webcam, output to a computer monitor, and optimization criteria expressed over some combination of the monitor, the humans looking at the monitor, and the rest of the world. It's a whole lot easier to call what's inside a 'planning Oracle' or some other English phrase than to write a program that does the optimization safely without serious unintended consequences. Show me any attempted specification, and I'll point to the vague parts and ask for clarification in more formal and mathematical terms, and as soon as the design is clarified enough to be a hundred light years from implementation instead of a thousand light years, I'll show a neutral judge how that math would go wrong. (Experience shows that if you try to explain to would-be AGI designers how their design goes wrong, in most cases they just say "Oh, but of course that's not what I meant." Marcus Hutter is a rare exception who specified his AGI in such unambiguous mathematical terms that he actually succeeded at realizing, after some discussion with SIAI personnel, that AIXI would kill off its users and seize control of its reward button. But based on past sad experience with many other would-be designers, I say "Explain to a neutral judge how the math kills" and not "Explain to the person who invented that math and likes it.")
Just as the gigantic gap between smart-sounding English instructions and actually smart algorithms is the main source of difficulty in AI, there's a gap between benevolent-sounding English and actually benevolent algorithms which is the source of difficulty in FAI. "Just make suggestions - don't do anything!" is, in the end, just more English.
3. Why we haven't already discussed Holden's suggestion
One of the things that bothers me most about SI is that there is practically no public content, as far as I can tell, explicitly addressing the idea of a "tool" and giving arguments for why AGI is likely to work only as an "agent."
The above statement seems to lack perspective on how many different things various people see as the one obvious solution to Friendly AI. Tool AI wasn't the obvious solution to John McCarthy, I.J. Good, or Marvin Minsky. Today's leading AI textbook, Artificial Intelligence: A Modern Approach - where you can learn all about A* search, by the way - discusses Friendly AI and AI risk for 3.5 pages but doesn't mention tool AI as an obvious solution. For Ray Kurzweil, the obvious solution is merging humans and AIs. For Jurgen Schmidhuber, the obvious solution is AIs that value a certain complicated definition of complexity in their sensory inputs. Ben Goertzel, J. Storrs Hall, and Bill Hibbard, among others, have all written about how silly Singinst is to pursue Friendly AI when the solution is obviously X, for various different X. Among current leading people working on serious AGI programs labeled as such, neither Demis Hassabis (VC-funded to the tune of several million dollars) nor Moshe Looks (head of AGI research at Google) nor Henry Markram (Blue Brain at IBM) think that the obvious answer is Tool AI. Vernor Vinge, Isaac Asimov, and any number of other SF writers with technical backgrounds who spent serious time thinking about these issues didn't converge on that solution.
Obviously I'm not saying that nobody should be allowed to propose solutions because someone else would propose a different solution. I have been known to advocate for particular developmental pathways for Friendly AI myself. But I haven't, for example, told Peter Norvig that deterministic self-modification is such an obvious solution to Friendly AI that I would mistrust his whole AI textbook if he didn't spend time discussing it.
At one point in his conversation with Tallinn, Holden argues that AI will inevitably be developed along planning-Oracle lines, because making suggestions to humans is the natural course that most software takes. Searching for counterexamples instead of positive examples makes it clear that most lines of code don't do this. Your computer, when it reallocates RAM, doesn't pop up a button asking you if it's okay to reallocate RAM in such-and-such a fashion. Your car doesn't pop up a suggestion when it wants to change the fuel mix or apply dynamic stability control. Factory robots don't operate as human-worn bracelets whose blinking lights suggest motion. High-frequency trading programs execute stock orders on a microsecond timescale. Software that does happen to interface with humans is selectively visible and salient to humans, especially the tiny part of the software that does the interfacing; but this is a special case of a general cost/benefit tradeoff which, more often than not, turns out to swing the other way, because human advice is either too costly or doesn't provide enough benefit. Modern AI programmers are generally more interested in e.g. pushing the technological envelope to allow self-driving cars than to "just" do Google Maps. Branches of AI that invoke human aid, like hybrid chess-playing algorithms designed to incorporate human advice, are a field of study; but they're the exception rather than the rule, and occur primarily where AIs can't yet do something humans do, e.g. humans acting as oracles for theorem-provers, where the humans suggest a route to a proof and the AI actually follows that route. This is another reason why planning Oracles were not a uniquely obvious solution to the various academic AI researchers, would-be AI-creators, SF writers, etcetera, listed above. Again, regardless of whether a planning Oracle is actually the best solution, Holden seems to be empirically-demonstrably overestimating the degree to which other people will automatically have his preferred solution come up first in their search ordering.
4. Why we should have full-time Friendly AI specialists just like we have trained professionals doing anything else mathy that somebody actually cares about getting right, like pricing interest-rate options or something
I hope that the preceding discussion has made, by example instead of mere argument, what's probably the most important point: If you want to have a sensible discussion about which AI designs are safer, there are specialized skills you can apply to that discussion, as built up over years of study and practice by someone who specializes in answering that sort of question.
This isn't meant as an argument from authority. It's not meant as an attempt to say that only experts should be allowed to contribute to the conversation. But it is meant to say that there is (and ought to be) room in the world for Friendly AI specialists, just like there's room in the world for specialists on optimal philanthropy (e.g. Holden).
The decision to build a non-self-modifying planning Oracle would be properly made by someone who: understood the risk gradient for self-modifying vs. non-self-modifying programs; understood the risk gradient for having the AI thinking about the thought processes of the human watcher and trying to come up with plans implementable by the human watcher in the service of locally absorbed utility functions, vs. trying to implement its own plans in the service of more globally descriptive utility functions; and who, above all, understood on a technical level what exactly gets accomplished by having the plans routed through a human. I've given substantial previous thought to describing more precisely what happens — what is being gained, and how much is being gained — when a human "approves a suggestion" made by an AI. But that would be another a different topic, plus I haven't made too much progress on saying it precisely anyway.
In the transcript of Holden's conversation with Jaan Tallinn, it looked like Tallinn didn't deny the assertion that Friendly AI skills would be inapplicable if we're building a Google Maps AGI. I would deny that assertion and emphasize that denial, because to me it seems that it is exactly Friendly AI programmers who would be able to tell you if the risk gradient for non-self-modification vs. self-modification, the risk gradient for routing plans through humans vs. acting as an agent, the risk gradient for requiring human approval vs. unapproved action, and the actual feasibility of directly constructing transhuman modeling-prediction-and-planning algorithms through directly design of sheerly better computations than are presently run by the human brain, had the right combination of properties to imply that you ought to go construct a non-self-modifying planning Oracle. Similarly if you wanted an AI that took a limited set of actions in the world with human approval, or if you wanted an AI that "just answered questions instead of making plans".
It is similarly implied that a "philosophical AI" might obsolete Friendly AI programmers. If we're talking about PAI that can start with a human's terrible decision theory and come up with a good decision theory, or PAI that can start from a human talking about bad metaethics and then construct a good metaethics... I don't want to say "impossible", because, after all, that's just what human philosophers do. But we are not talking about a trivial invention here. Constructing a "philosophical AI" is a Holy Grail precisely because it's FAI-complete (just ask it "What AI should we build?"), and has been discussed (e.g. with and by Wei Dai) over the years on the old SL4 mailing list and the modern Less Wrong. But it's really not at all clear how you could write an algorithm which would knowably produce the correct answer to the entire puzzle of anthropic reasoning, without being in possession of that correct answer yourself (in the same way that we can have Deep Blue win chess games without knowing the exact moves, but understanding exactly what abstract work Deep Blue is doing to solve the problem).
Holden's post presents a restrictive view of what "Friendly AI" people are supposed to learn and know — that it's about machine learning for optimizing orange sales but not apple sales, or about producing an "agent" that implements CEV — which is something of a straw view, much weaker than the view that a Friendly AI programmer takes of Friendly AI programming. What the human species needs from an x-risk perspective is experts on This Whole Damn Problem, who will acquire whatever skills are needed to that end. The Singularity Institute exists to host such people and enable their research—once we have enough funding to find and recruit them. See also, How to Purchase AI Risk Reduction.
I'm pretty sure Holden has met people who think that having a whole institute to rate the efficiency of charities is pointless overhead, especially people who think that their own charity-solution is too obviously good to have to contend with busybodies pretending to specialize in thinking about 'marginal utility'. Which Holden knows about, I would guess, from being paid quite well to think about that economic details when he was a hedge fundie, and learning from books written by professional researchers before then; and the really key point is that people who haven't studied all that stuff don't even realize what they're missing by trying to wing it. If you don't know, you don't know what you don't know, or the cost of not knowing. Is there a problem of figuring out who might know something you don't, if Holden insists that there's this strange new stuff called 'marginal utility' you ought to learn about? Yes, there is. But is someone who trusts their philanthropic dollars to be steered just by the warm fuzzies of their heart, doing something wrong? Yes, they are. It's one thing to say that SIAI isn't known-to-you to be doing it right - another thing still to say that SIAI is known-to-you to be doing it wrong - and then quite another thing entirely to say that there's no need for Friendly AI programmers and you know it, that anyone can see it without resorting to math or cracking a copy of AI: A Modern Approach. I do wish that Holden would at least credit that the task SIAI is taking on contains at least as many gotchas, relative to the instinctive approach, as optimal philanthropy compared to instinctive philanthropy, and might likewise benefit from some full-time professionally specialized attention, just as our society creates trained professionals to handle any other problem that someone actually cares about getting right.
On the other side of things, Holden says that even if Friendly AI is proven and checked:
"I believe that the probability of an unfavorable outcome - by which I mean an outcome essentially equivalent to what a UFAI would bring about - exceeds 90% in such a scenario."
It's nice that this appreciates that the problem is hard. Associating all of the difficulty with agenty proposals and thinking that it goes away as soon as you invoke tooliness is, well, of this I've already spoken. I'm not sure whether this irreducible-90%-doom assessment is based on a common straw version of FAI where all the work of the FAI programmer goes into "proving" something and doing this carefully checked proof which then - alas, poor Spock! - turns out to be no more relevant than proving that the underlying CPU does floating-point arithmetic correctly if the transistors work as stated. I've repeatedly said that the idea behind proving determinism of self-modification isn't that this guarantees safety, but that if you prove the self-modification stable the AI might work, whereas if you try to get by with no proofs at all, doom is guaranteed. My mind keeps turning up Ben Goertzel as the one who invented this caricature - "Don't you understand, poor fool Eliezer, life is full of uncertainty, your attempt to flee from it by refuge in 'mathematical proof' is doomed" - but I'm not sure he was actually the inventor. In any case, the burden of safety isn't carried just by the proof, it's carried mostly by proving the right thing. If Holden is assuming that we're just running away from the inherent uncertainty of life by taking refuge in mathematical proof, then, yes, 90% probability of doom is an understatement, the vast majority of plausible-on-first-glance goal criteria you can prove stable will also kill you.
If Holden's assessment does take into account a great effort to select the right theorem to prove - and attempts to incorporate the difficult but finitely difficult feature of meta-level error-detection, as it appears in e.g. the CEV proposal - and he is still assessing 90% doom probability, then I must ask, "What do you think you know and how do you think you know it?" The complexity of the human mind is finite; there's only so many things we want or would-want. Why would someone claim to know that proving the right thing is beyond human ability, even if "100 of the world's most intelligent and relevantly experienced people" (Holden's terms) check it over? There's hidden complexity of wishes, but not infinite complexity of wishes or unlearnable complexity of wishes. There are deep and subtle gotchas but not an unending number of them. And if that were the setting of the hidden variables - how would you end up knowing that with 90% probability in advance? I don't mean to wield my own ignorance as a sword or engage in motivated uncertainty - I hate it when people argue that if they don't know something, nobody else is allowed to know either - so please note that I'm also counterarguing from positive facts pointing the other way: the human brain is complicated but not infinitely complicated, there are hundreds or thousands of cytoarchitecturally distinct brain areas but not trillions or googols. If humanity had two hundred years to solve FAI using human-level intelligence and there was no penalty for guessing wrong I would be pretty relaxed about the outcome. If Holden says there's 90% doom probability left over no matter what sane intelligent people do (all of which goes away if you just build Google Maps AGI, but leave that aside for now) I would ask him what he knows now, in advance, that all those sane intelligent people will miss. I don't see how you could (well-justifiedly) access that epistemic state.
I acknowledge that there are points in Holden's post which are not addressed in this reply, acknowledge that these points are also deserving of reply, and hope that other SIAI personnel will be able to reply to them.
Regarding the question of formalizing an optimization agent with goals defined in terms of external universe rather than sensory input. It is possible to attack the problem by generalizing the framework I described in http://lesswrong.com/lw/gex/save_the_princess_a_tale_of_aixi_and_utility/8ekk for solving the duality problem. Specifically, consider an "initial guess" stochastic model of the universe including the machine on which our agent is running. I call it the "innate model" M. Now consider a stochastic process with the same degrees of freedom as M but governed by the Solomonoff semi-measure. This is the "unbiased model" S. The two can be combined by assigning transition probabilities proportional to the product of the probabilities assigned by M and S. If M is sufficiently "insecure" (in particular it doesn't assign 0 to any transition probability) then the resulting model S', considered as prior, allows arriving at any computable model after sufficient learning. Fix a utility function on the space of histories of our model (note that the histories include both intrinsic and extrinsic degrees of freedom). The intelligence I(A) of any given agent A (= program written in M in the initial state) can now be defined to be the expected utility of A in S'. We can now consider optimal or near-optimal agents in this sense (as opposed to the Legg-Hutter formalism for measuring intelligence, there is no guarantee there is a maximum rather than a supremum; unless of course we limit the length of the programs we consider). This is a generalization of the Legg-Hutter formalism which accounts for limited computational resources, solves the duality problem (such agents take into account possibly wireheading) and also provides a solution for the ontology problem. This is essentially a special case of the Orseau-Ring framework. It is however much more specific than Orseau-Ring where the prior is left completely unspecified. You can think of it as a recipe for constructing Orseau-Ring priors from realistic problems
I realized that although the idea of a deformed Solomonoff semi-measure is correct, the multiplication prescription I suggested is rather ad hoc. The following construction is a much more natural and justifiable way of combining M and S.
Fix t0 a time parameter. Consider a stochastic process S(-t0) that begins at time t = -t0, where t = 0 is the time our agent A "forms", governed by the Solomonoff semi-measure. Consider another stochastic process M(-t0) that begins from the initial conditions generated by S(-t0) (I'm assuming M only carries inform... (read more)