Friday, March 26, 2010

The GOLEM Eats the Chinese Parent (Toward An AGI Meta-Architecture Enabling Both Goal Preservation and Radical Self-Improvement)

I thought more about the ideas in my previous blog post on the "Chinese Parent Theorem," and while I didn't do a formal proof yet, I did write up the ideas a lot more carefully

GOLEM: Toward An AGI Meta-Architecture Enabling Both Goal Preservation and Radical Self-Improvement

and IMHO they make even more sense now....

Also, I changed the silly name "Chinese Parent Meta-Architecture" to the sillier name "GOLEM" which stands for "Goal-Oriented LEarning Meta-architecture"

The GOLEM ate the Chinese Parent!

I don't fancy that GOLEM, in its present form, constitutes a final solution to the problem of "making goal preservation and radical self-improvement compatible" -- but I'm hoping it points in an interesting and useful direction.

(I still have some proofs about GOLEM sketched in the margins of a Henry James story collection, but the theorems are pretty weak and I'm not sure when I'll have time to type them in. If they were stronger theorems I would be more inspired for it. Most of the work in typing them in would be in setting up the notations ;p ....)

But Would It Be Creative?

In a post on the Singularity email list, Mike Tintner made the following complaint about GOLEM:

Why on earth would you want a "steadfast" AGI? That's a contradiction of AGI.

If your system doesn't have the capacity/potential to revolutionise its goals - to have a major conversion, for example, from religiousness to atheism, totalitarianism to free market liberalism, extreme self-interest and acquisitiveness to extreme altruism, rational thinking to mystical thinking, and so on (as clearly happens with humans), gluttony to anorexia - then you don't have an AGI, just another dressed-up narrow AI.

The point of these examples should be obviously not that an AGI need be an intellectual, but rather that it must have the capacity to drastically change

  1. the priorities of its drives/goals,
  2. the forms of its goals

and even in some cases:

3. eliminate certain drives (presumably secondary ones) altogether

My answer was as follows:

I believe one can have an AGI that is much MORE creative and flexible in its thinking than humans, yet also remains steadfast in its top-level goals...

As an example, imagine a human whose top-level goal in life was to do what the alien god on the mountain wanted. He could be amazingly creative in doing what the god wanted -- especially if the god gave him

  • broad subgoals like "do new science", "invent new things", "help cure suffering" , "make artworks", etc.
  • real-time feedback about how well his actions were fulfilling the goals, according to the god's interpretation
  • advice on which hypothetical actions seemed most likely to fulfill the goals, according to the god's interpretation

But his creativity would be in service of the top-level goal of serving the god...

This is like the GOLEM architecture, where

  • the god is the GoalEvaluator
  • the human is the rest of the GOLEM architecture

I fail to see why this restricts the system from having incredible, potentially far superhuman creativity in working on the goals assigned by the god...

Part of my idea is that the GoalEvaluator can be a narrow AI, thus avoiding an infinite regress where we need an AGI to evaluate the goal-achievement of another AGI...

Can the Goal Evaluator Really Be a Narrow AI?

A dialogue with Abram Demski on the Singularity email list led to some changes to the original GOLEM paper.

The original version of GOLEM states that the GoalEvaluator would be a Narrow AI, and failed to make the GoalEvaluator rely on the Searcher to do its business...

Abram's original question, about this original version, was "Can the Goal Evaluator Really Be a Narrow AI?"

My answer was:

The terms narrow-AI and AGI are not terribly precise...

The GoalEvaluator needs to basically be a giant simulation engine, that tells you: if program P is run, then the probability of state W ensuing is p. Doing this effectively could involve some advanced technologies like probabilistic inference, along with simulation technology. But it doesn't require an autonomous, human-like motivational system. It doesn't require a system that chooses its own actions based on its goals, etc.

The question arises, how does the GoalEvaluator's algorithmics get improved, though? This is where the potential regress occurs. One can have AGI_2 improving the algorithms inside AGI_1's GoalEvaluator. The regress can continue, till eventually one reaches AGI_n whose GoalEvaluator is relatively simple and AGi-free...


After some more discussion, Abram made some more suggestions, which led me to generalize and rephrase his suggestions as follows:

If I understand correctly, what you want to do is use the Searcher to learn programs that predict the behavior of the GoalEvaluator, right? So, there is a "base goal evaluator" that uses sensory data and internal simulations, but then you learn programs that do approximately the same thing as this but much faster (and maybe using less memory)? And since this program learning has the specific goal of learning efficient approximations to what the GoalEvaluator does, it's not susceptible to wire-heading (unless the whole architecture gets broken)...

After the dialogue, I incorporated this suggestion into the GOLEM architecture (and the document linked from this blog post).

Thanks Abram!!

Wednesday, March 17, 2010

"Chinese Parent Theorem"?: Toward a Meta-Architecture for Provably Steadfast AGI

Continuing my series of (hopefully edu-taining ;) blog posts presenting speculations on goal systems for superhuman AGI systems, this one deals with the question of how to create an AGI system that will maintain its initial goal system even as it revises and improves itself -- and becomes so much smarter that in many ways it becomes incomprehensible to its creators or its initial conditions.

This is closely related to the problem Eliezer Yudkowsky has described as "provably Friendly AI." However, I would rather not cast the problem that way, because (as Eliezer of course realizes) there is an aspect of the problem that isn't really about "Friendliness" or any other particular goal system content, but is "merely" about the general process of goal-content preservation under progressive self-modification.

Informally, I define an intelligent system as steadfast if it continues to pursue the same goals over a long period of time. In this terminology, one way to confront the problem of creating predictably beneficial AGI, is to solve the two problems of:

  1. Figuring out how to encapsulate the goal of beneficialness in an AGI's goal system
  2. Figuring out how to create (perhaps provably) steadfast AGI, in a way that applies to the "beneficialness" goal among others
My previous post on Coherent Aggregated Volition (CAV) dealt with the first of these problems. This post deals with the second. My previous post on predictably beneficial AGI deals with both.

The meat of this post is a description of an AGI meta-architecture, that I label the Chinese Parent Meta-Architecture -- and that I conjecture could be proved to be steadfast, under some reasonable (though not necessarily realistic, since the universe is a mysterious place!) assumptions about the AGI system's environment.

I don't actually prove any steadfastness result here -- I just sketch a vague conjecture, which if formalized and proved would deserve the noble name "Chinese Parent Theorem."

I got partway through a proof yesterday and it seemed to be going OK, but I've been distracted by more practical matters, and so for now I decided to just post the basic idea here instead...

Proving Friendly AI

Eliezer Yudkowsky has described his goal concerning “proving Friendly AI” informally as follows:

The putative proof in Friendly AI isn't proof of a physically good outcome when you interact with the physical universe.

You're only going to try to write proofs about things that happen inside the highly deterministic environment of a CPU, which means you're only going to write proofs about the AI's cognitive processes.

In particular you'd try to prove something like "this AI will try to maximize this goal function given its beliefs, and it will provably preserve this entire property (including this clause) as it self-modifies".

It seems to me that proving something like this shouldn’t be sooooo hard to achieve if one assumes some basic fixed “meta-architectural” structure on the part of the AI, rather than permitting total unrestricted self-modification. Such a meta-architecture can be assumed without placing any limits on the AI’s algorithmic information content, for example.

Of course, preservation of the meta-architecture can be assumed as part of the AI system's goal function. So by assuming a meta-architecture, one may be able to prove a result restricted to a certain broad class of goal functions ... and the question becomes whether that class is broad enough to be interesting.

So my feeling is that, if one wants to pursue such a research direction, it makes sense to begin by proving theorems restricted to goals embodying some assumptions about fixed program structure -- and then try to improve the theorems by relaxing the assumptions.

A Simple AGI Meta-Architecture with the Appearance of Steadfastness

After writing the first draft of this post, I discussed the "provably steadfast AGI" problem with a clever Chinese friend, and she commented that what the self-modifying AGI needs (in order to maintain its original goal content as it self-modifies) is a traditional Chinese parent, who will watch the system from the outside as it self-modifies, and continually nag it and pester it and remind it of its original goals.

At first I thought this was just funny, but then it occurred to me that it was actually the same idea as my meta-architecture! My GoalEvaluator component (in the meta-architecture below) is basically a ChineseParent component, living separately from the rest of the system and providing ongoing, fixed goal evaluation.

The thought-experiment I've been exploring is: an AGI system S with the following high-level meta-architecture:

  • Goal Evaluator = external system (not part of S) that tells S, for each possible future world (including environment states and internal program states), how well this world fulfills the goal. This is the "Chinese parent."
  • HistoricalRepository = database storing the past history of S’s internal states and actions, as well as information about the environment during S’s past
  • Operating Program = the program that S is governing its actions by, at a given point in time
    • chosen by the Metaprogram as the best program the Searcher has found, where "best" is judged as "highest probability of goal achievement" based on the output of the Predictor and the Goal Evaluator
  • Predictor = program that estimates, given a candidate operating program P and a possible future world W, the odds of P leading to W
  • Searcher = program that searches through program space to find a new program optimizing a provided objective function
  • Tester = hard-wired program that estimates the quality of a candidate Predictor, using a simple backtesting methodology
    • That is, the Tester assesses how well a Predictor would have performed in the past, using the data in the HistoricalRepository
  • Metaprogram = fixed program that uses Searcher program to find a good
    • Searcher program (judged by the quality of the programs it finds, as judged by the Predictor program)
    • Predictor program (as judged by the Tester’s assessments of its predictions)
    • Operating Program (judged by Predictor working with Goal Evaluator, according to the idea of choosing an Operating Program with the maximum expected goal achievement)
    • The metaprogram also determines the amount of resources to allocate to searching for a Searcher versus a Predictor versus an OP, according to a fixed algorithm for parameter adaptation.

Next, assume that the goal embodied by the GoalEvaluator includes, as a subgoal, the preservation of the overall meta-architecture described above.

Then, it seems to me one can very likely prove that the program will maintain its architecture while seeking to maximize F, under the assumptions that

  • the Goal Evaluator (i.e. the "Chinese parent") does its job correctly
  • no one messes with the underlying hardware.

If proved, this would be the so-called "Chinese Parent Theorem" ;-) .... I don't have time to work on such a proof right now, but would be happy to collaborate with someone on this!

As noted above, this approach doesn't allow full self-modification; it assumes certain key parts of the AGI (meta)architecture are hard-wired. But the hard-wired parts are quite basic and leave a lot of flexibility. So a "Chinese Parent Theorem" of this nature would cover a fairly broad and interesting class of goal functions, it seems to me.

What happens if one implements the Goal Evaluator according to the same architecture, though? In this case, one must postulate a meta-Goal-Evaluator, whose goal is to specify the goals for the first Goal Evaluator: the Chinese Grandparent! Eventually the series must end, and one must postulate an original ancestor Goal Evaluator that operates according to some other architecture. Maybe it's a human, maybe it's CAV, maybe it's some hard-wired code. Hopefully it's not a bureaucratic government committee ;-)

Niggling Practical Matters and Future Directions

Of course, this general schema could be implemented using OpenCog or any other practical AGI architecture as a foundation -- in this case, OpenCog is "merely" the initial condition for the Predictor and Searcher. In this sense, the approach is not extraordinarily impractical.

However, one major issue arising with the whole meta-architecture proposed is that, given the nature of the real world, it's hard to estimate how well the Goal Evaluator will do its job! If one is willing to assume the above meta-architecture, and if a proof along the lines suggested above can be found, then the “predictably beneficial” part of the problem of "predictably beneficial AGI" is largely pushed into the problem of the Goal Evaluator.

Returning to the "Chinese parent" metaphor, what I suggest may be possible to prove is that given an effective parent, one can make a steadfast child -- if the child is programmed to obey the parent's advice about its goals, which include advice about its meta-architecture. The hard problem is then ensuring that the parent's advice about goals is any good, as the world changes! And there's always the possibility that the parents ideas about goals shift over time based on their interaction with the child (bringing us into the domain of modern or postmodern Chinese parents ;-D)

Thus, I suggest, the really hard problem of making predictably beneficial AGI probably isn't "preservation of formally-defined goal content under self-modification." This may be hard if one enables total self-modification, but I suggest it's probably not that hard if one places some fairly limited restrictions on self-modification. The hypothetical Chinese Parent Theorem vaguely outlined here can probably be proved and then strengthened pretty far, reducing meta-architectural assumptions considerably.

The really hard problem, I suspect, is how to create a GoalEvaluator that correctly updates goal content as new information about the world is obtained, and as the world changes -- in a way that preserves the spirit of the original goals even if the details of the original goals need to change. Because the "spirit" of goal content is a very subjective thing.

One approach to this problem, hinted above, would be to create a GoalEvaluator operating according to CAV . In that case, one would be counting on (a computer-aggregated version of) collective human intuition to figure out how to adapt human goals as the world, and human information about it, evolves. This is of course what happens now -- but the dynamic will be much more complex and more interesting with superhuman AGIs in the loop. Since interacting with the superhuman AGI will change human desires and intuitions in all sorts of ways, it's to be expected that such a system would NOT eternally remain consistent with original "legacy human" goals, but would evolve in some new and unpredicted direction....

A deep and difficult direction for theory, then, would be to try to understand the expected trajectories of development of systems including

  • a powerful AGI, with a Chinese Parent meta-architecture as outlined here (or something similar), whose GoalEvaluator is architected via CAV based on the evolving state of some population of intelligent agents
  • the population of intelligent agents, as ongoingly educated and inspired by both the world and the AGI

as they evolve over time and interact with a changing environment that they explore ever more thoroughly.

Sounds nontrivial!

Sunday, March 14, 2010

Creating Predictably Beneficial AGI

The theme of this post is a simple and important one: how to create AGI systems whose beneficialness to humans and other sentient beings can be somewhat reliably predicted.

My SIAI colleague Eliezer Yudkowsky has frequently spoken about the desirability of a "(mathematically) provably Friendly AI", where by "Friendly" he means something like "beneficial and not destructive to humans" (see here for a better summary). My topic here is related, but different; and I'll discuss the relationship between the two ideas below.

This post is a sort of continuation of my immediately previous blog post, further pursuing the topic of goal-system content for advanced, beneficial AGIs. That post discussed one of Yudkowsky's ideas related to "Friendliness" -- Coherent Extrapolated Volition (CEV) -- along with a more modest and (I suggest) more feasible notion of Coherent Aggregated Volition (CAV). The ideas presented here are intended to work along with CAV, rather than serving as an alternative.

There are also some relations between the ideas presented here and Schmidhuber's Godel Machine -- a theoretical, unlikely-ever-to-be-practically-realizable AGI system that uses theorem-proving to ensure its actions will provably help it achieve its goals.

Variations of "Provably Friendly AI"

What is "Provably Friendly AI"? (a quite different notion from "predictably beneficial AGI")

In an earlier version of this blog post I gave an insufficiently clear capsule summary of Eliezer's "Friendly AI" idea, as Eliezer pointed out in a comment to that version; so this section includes his comment and tries to do a less wrong job. The reader who only wants to find out about predictably beneficial AGI may skip to the next section!

In Eliezer's comment, he noted that his idea for a FAI proof is NOT to prove something about what certain AI systems would do to the universe, but rather about what would happen inside the AI system itself:

The putative proof in Friendly AI isn't proof of a physically good outcome when you interact with the physical universe.

You're only going to try to write proofs about things that happen inside the highly deterministic environment of a CPU, which means you're only going to write proofs about the AI's cognitive processes.

In particular you'd try to prove something like "this AI will try to maximize this goal function given its beliefs, and it will provably preserve this entire property (including this clause) as it self-modifies".

So, in the context of this particular mathematical research programme ("provable Friendliness"), what Eliezer is after is what we might call an internally Friendly AI, which is a separate notion from a physically Friendly AI. This seems an important distinction.

To me, "provably internally FAI" is interesting mainly as a stepping-stone to "provably physically FAI" -- and the latter is a problem that seems even harder than the former, in a variety of obvious and subtle ways (only a few of which will be mentioned here).

All in all, I think that "provably Friendly AI" -- in the above senses or others -- is an interesting and worthwhile goal to think about and work towards; but also that it's important to be cognizant of the limitations on the utility of such proofs.... Much as I love math (I even got a math PhD, way back when), I have to admit the world of mathematics has its limits.

First of all Godel showed that mathematics is only formally meaningful relative to some particular axiom system, and that no axiom system can encompass all mathematics in a consistent way. This is worth reflecting on in the context of proofs about internally Friendly AI, especially when one considers the possibility of AGI systems with algorithmic information exceeding any humanly comprehensible axiom system. Obvious we cannot understand proofs about many interesting properties or behaviors of the latter type of AGI system.

But more critically, the connection between internal Friendliness and physical Friendliness remains quite unclear. The connection between complex mathematics and physical reality is based on science, and all of our science is based on extrapolation from a finite bit-set of observations (which I've previously called the Master Data Set -- which is not currently all gathered into one place, though, given the advance of Internet technology, it soon may be).

For example, just to pose an extreme case, there could be aliens out there who identify and annihilate any planet that gives rise to a being with an IQ over 1000. In this case a provably internally FAI might not be physically Friendly at all; and through no fault of its own. It probably makes sense to carry out proofs and informal arguments about physically FAI based on assumptions ruling out weird cases like this -- but then the assumptions do need to be explicitly stated and clarified.

So, my worry about FAI in the sense of Eliezer's above comment, isn't so much about the difficulty of the "internally FAI" proof, but rather about the difficulty of formalizing the relation between internally FAI and physically FAI in a way that is going to make sense post-Singularity.

It seems to me that, given the limitations of our understanding of the physical universe: at very best, a certain AI design could potentially be proven physically Friendly in the same sense that, in the 1800s, quantum teleportation, nuclear weapons, backwards time travel, rapid forwards time travel, perpetual motion machines and fRMI machines could have been proved impossible. I.e., those things could have been proved impossible based on the "laws" of physics as assumed at that time. (Yes, I know we still think perpetual motion machines are impossible, according to current science. I think that's probably right, but who really knows for sure? And the jury is currently out on backwards time travel.)

One interesting scenario to think about would be a FAI in a big computer with a bunch of human uploads. Then one can think about "simulated-physically FAI" as a subcase of "internally FAI." In this simulation scenario, one can also think about FAI and CEV together in a purely deterministic context. But of course, this sort of "thought experiment" leads to complexities related to the possibility of somebody in the physical universe but outside the CPU attacking the FAI and threatening it and its population of uploads...

OK, enough about FAI for now. Now, on to discuss a related quest, which is different from the quest for FAI in several ways; but more similar to the quest for physically FAI than that for internally FAI....

Predictably Beneficial AGI

The goal of my thinking about "predictably beneficial AGI" is to figure out how to create extremely powerful AGI systems that appear likely to be beneficial to humans, under reasonable assumptions about the physical world and the situations the AI will encounter.

Here "predictable" doesn't mean absolutely predictable, just: statistically predictable, given the available knowledge about the AGI system and the world at a particular point in time.

An obvious question is what sort of mathematics will be useful in the pursuit of predictably beneficial AGI. One possibility is theoretical computer science and formal logic, and I wouldn't want to discount what those disciplines could contribute. Another possibility, though, which seems particularly appealing to me, is nonlinear dynamical systems theory. Of course the two areas are not exclusive, and there are many known connections between these kinds of mathematics.

On the crudest level, one way to model the problem is as follows. One has a system S, so that

S(t+1) = q( S(t), E(t) )

E(t+1) = r(S(t), E(t) )

where E is the environment (which is best modeled as stochastic and not fully known). One has an objective function

G( E(t),...,E(t+s) )

that one would like to see maximized -- this is the "goal." Coherent Aggregated Volition, as described in my previous blog post, is one candidate for such a goal.

One may also assume a set of constraints C that the system must obey, which we may write as


The functions G and C are assumed to encapsulate the intuitive notion of "beneficialness."

Of course, the constraints may be baked into the objective function, but there are many ways of doing this; and it's often interesting in optimization problems to separate the objective function from the constraints, so one can experiment with different ways of combining them.

This is a problem class that is incredibly (indeed, uncomputably) hard to solve in the general case ... so the question comes down to: given the particular G and C of interest, is there a subclass of systems S for which the problem is feasibly and approximatively solvable?

This leads to an idea I will call the Simple Optimization Machine (SOMA)... a system S which seeks to maximize the two objectives

  1. maximize G, while obeying C
  2. maximize the simplicity of the problem of estimating the degree to which S will "maximize G, while obeying C", given the Master Data Set

Basically, the problem of ensuring the system lies in the "nice region of problem space" is thrown to the system itself, to figure out as part of its learning process!

Of course one could wrap this simplicity criterion into G, but it seems conceptually simplest to leave it separate, at least for purposes of current discussion.

The function via which these two objectives are weighted is a parameter that must be tuned. The measurement of simplicity can also be configured in various ways!

A hard constraint could also be put on the minimum simplicity to be accepted (e.g. "within the comprehensibility threshold of well-educated, unaugmented humans").

Conceptually, one could view this as a relative of Schmidhuber's Godel Machine. The Godel Machine (put very roughly) seeks to achieve a goal in a provably correct way, and before each step it takes, it seeks to prove that this step will improve its goal-achievement. SOMA, on the other hand, seeks to achieve a goal in a manner that seems to be simply demonstrable to be likely to work, and seeks to continually modify itself and its world with this in mind.

A technical note: one could argue that because the functions q and r are assumed fixed, the above framework doesn't encompass "truly self-modifying systems." I have previously played around with using hyperset equations like

S(t+1) = S(t)[S(t)]

and there is no real problem with doing this, but I'm not sure it adds anything to the discussion at this point. One may consider q and r to be given by the laws of physics; and I suppose that it's best to initially restrict our analytical explorations of beneficial AGI to the case of AGI systems that don't revise the laws of physics. If we can't understand the case of physics-obeying agents, understanding the more general case is probably hopeless!


I stress that SOMA is really an idea about goal system content, and not an AGI design in itself. SOMA could be implemented in the context of a variety of different AGI designs, including for instance the open-source OpenCog approach.

It is not hard to envision ways of prototyping SOMA given current technology, using existing machine learning and reasoning algorithms, in OpenCog or otherwise. Of course, such prototype experiments would give limited direct information about the behavior of SOMA for superhuman AGI systems -- but they might give significant indirect information, via helping lead us to general mathematical conclusions about SOMA dynamics.

Altogether, my feeling is that "CAV + Predictably Beneficial AGI" is on the frontier of current mathematics and science. They pose some very difficult problems that do, however seem potentially addressable in the near future via a combination of mathematics and computational experimentation. On the other hand, I have a less clear idea of how to pragmatically do research work on CEV or the creation of practically feasible yet provably physically Friendly AGI.

My hope in proposing these ideas is that they (or other similar ideas conceived by others) may serve as a sort of bridge between real-world AGI work and abstract ethical considerations about the hypothetical goal content of superhuman AGI systems.

Friday, March 12, 2010

Coherent Aggregated Volition: A Method for Deriving Goal System Content for Advanced, Beneficial AGIs

One approach to creating a superhuman AGI with a reasonably high likelihood of being beneficial to humans is to separate "goal system structure and dynamics" from "goal system content." One then has three problems:

  1. Create an AGI architecture that makes it very likely the AGI will pursue its goal-system content in a rational way based on the information available to it
  2. Create a goal system whose structure and dynamics render it likely for the AGI to maintain the spirit of its initial goal system content, even as it encounters radically different environmental phenomena or as it revises its own ideas or sourcecode
  3. Create goal system content that, if maintained as goal system content and pursued rationally, will lead the AGI system to be beneficial to humans

One potential solution proposed for the third problem, the goal system content problem, is Eliezer Yudkowsky's "Coherent Extrapolated Volition" (CEV) proposal. Roko Mijic has recently proposed some new ideas related to CEV, which place the CEV idea within a broader and (IMO) clearer framework. This blog post presents some ideas in the same direction, describing a variant of CEV called Coherent Aggregated Volition (CAV), which is intended to capture much of the same spirit as CEV, but with the advantage of being more clearly sensible and more feasibly implementable (though still very difficult to implement in full). In fact CAV is simple enough that it could be prototyped now, using existing AI tools.

(One side note before getting started: Some readers may be aware that Yudkowsky has often expressed the desire to create provably beneficial ("Friendly" in his terminology) AGI systems, and CAV does not accomplish this. It also is not clear that CEV, even if it were fully formalizable and implementable, would accomplish this. Also, it may be possible to prove interesting theorems about the benefits and limitations of CAV, even if not to prove some kind of absolute guarantee of CAV beneficialness; but the exploration of such theorems is beyond the scope of this blog post.)

Coherent Extrapolated Volition

In brief, Yudkowsky's CEV idea is described as follows:

In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted.

This is a rather tricky notion, as exemplified by the following example, drawn from the CEV paper:

Suppose Fred decides to murder Steve, but when questioned, Fred says this is because Steve hurts other people, and needs to be stopped. Let's do something humans can't do, and peek inside Fred's mind-state. We find that Fred holds the verbal moral belief that hatred is never an appropriate reason to kill, and Fred hopes to someday grow into a celestial being of pure energy who won't hate anyone. We extrapolate other aspects of Fred's psychological growth, and find that this desire is expected to deepen and grow stronger over years, even after Fred realizes that the Islets worldview of "celestial beings of pure energy" is a myth. We also look at the history of Fred's mind-state and discover that Fred wants to kill Steve because Fred hates Steve's guts, and the rest is rationalization; extrapolating the result of diminishing Fred's hatred, we find that Fred would repudiate his desire to kill Steve, and be horrified at his earlier self.

I would construe Fred's volition not to include Fred's decision to kill Steve...

Personally, I would be extremely wary of any being that extrapolated my volition in this sort of manner, and then tried to impose my supposed "extrapolated volition" on me, telling me "But it's what you really want, you just don't know it." I suppose the majority of humans would feel the same way. This point becomes clearer if one replaces the above example with one involving marriage rather than murder:

Suppose Fred decides to marry Susie, but when questioned, Fred says this is because Susie is so smart and sexy. Let's do something humans can't do, and peek inside Fred's mind-state. We find that Fred holds the verbal moral belief that sex appeal is never an appropriate reason to marry, and Fred hopes to someday grow into a celestial being of pure energy who won't lust at all. We extrapolate other aspects of Fred's psychological growth, and find that this desire is expected to deepen and grow stronger over years, even after Fred realizes that the Islets worldview of "celestial beings of pure energy" is a myth. We also look at the history of Fred's mind-state and discover that Fred wants to marry Susie because Susie reminds him of his mother, and the rest is rationalization; extrapolating the result of diminishing Fred's unconscious sexual attraction to his mother, we find that Fred would repudiate his desire to marry Susie, and be disgusted with his earlier self.

I would construe Fred's volition not to include Fred's decision to marry Susie...

Clearly, the Yudkowskian notion of "volition" really has little to do with "volition" as commonly construed!!

While I can see the appeal of extrapolating Fred into "the Fred that Fred would like to be," I also think there is a lot of uncertainty in this process. If Fred has inconsistent aspects, there may be many possible future-Freds that Fred could evolve into, depending on both environmental feedback and internal (sometimes chaotic) dynamics. If one wishes to define the coherent extrapolated Future-Fred as the average of all these, then one must choose what kind of average to use, and one may get different answers depending on the choice. This kind of extrapolation is far from a simple matter -- and since "self" is not a simple matter either, it's not clear that current-Fred would consider all or any of these Future-Freds as being the same person as him.

In CAV as described here, I consider "volition" in the more typical sense -- rather than in the sense of Yudkowskian "extrapolated volition" -- as (roughly) "what a person or other intelligent agent chooses." So according to my conventional definition of volition, Fred's volition is to kill Steve and marry Susie.

Mijic's List of Desirable Properties

Roko Mijic has posited a number of general "desirable properties" for a superintelligence, and presented CEV as one among many possible concrete possibilities instantiating these principles:

  • Meta-algorithm: Most goals the AI has will be harvested at run-time from human minds, rather than explicitly programmed in before run-time.
  • Factually correct beliefs: Using the AI's superhuman ability to ascertain the correct answer to any factual question in order to modify preferences or desires that are based upon false factual beliefs.
  • Singleton: Only one superintelligence is to be constructed, and it is to take control of the entire future light cone with whatever goal function is decided upon.
  • Reflection: Individual or group preferences are reflected upon and revised, in the style of Rawls' reflective equilibrium.
  • Preference aggregation: The set of preferences of a whole group are to be combined somehow.
My own taste is that reflection, preference aggregation and meta-algorithm-ness are good requirements. The "singleton" requirement seems to me something that we can't know yet to be optimal, and don't need to decide at this point.

The "factually correct beliefs" requirement also seems problematic, if enforced too harshly, in the sense that it's hard to tell how a person, who has adapted their beliefs and goals to certain factually incorrect beliefs, would react if presented with corresponding correct beliefs. Hypothesizing that a future AI will be able to correctly make this kind of extrapolation is not entirely implausible, but certainly seems speculative. After all, each individual's reaction to new beliefs is bound to depend on the reactions of others around them, and human minds and societies are complex systems, whose evolution may prove difficult for even a superintelligence to predict, given chaotic dynamics and related phenomena. My conclusion is that there should be a bias toward factual correctness, but that it shouldn't be taken to override individual preferences and attitudes in all cases. (It's not clear to me whether this contradicts Mijic's perspective or not.)

Coherent Aggregated Volition

What I call CAV is an attempt to capture much of the essential spirit of CEV (according to my own perspective on CEV), in a way that is more feasible to implement than the original CEV, and that is prototype-able now in simplified form.

Use the term "gobs" to denote "goal and belief set" (and use "gobses" to denote the plural of "gobs"). It is necessary to consider goals and beliefs together, rather than just looking at goals, because real-world goals are typically defined in terms whose interpretation depends on certain beliefs. Each human being or AGI may be interpreted to hold various gobses to various fuzzy degrees. There is no requirement that a gobs be internally logically consistent.

A "gobs metric" is then a distance on the space of gobses. Each person or AI may also agree with various gobs metrics to various degrees, but it seems likely that individuals' gobs metrics will differ less than their gobses.

Suppose one is given a population of intelligent agents -- like the human population -- with different gobses. Then one can try to find a gobs that maximizes the four criteria of

  • logical consistency
  • compactness
  • average similarity to the various gobses in the population
  • amount of evidence in support of the various beliefs in the gobs

The use of a multi-extremal optimization algorithm to seek a gobs defined as above is what I call CAV. The "CAV" label seems appropriate since this is indeed a system attempting to achieve both coherence (measured via compactness + consistency) and an approximation to the "aggregate volition" of all the agents in the population.

Of course there are many "free parameters" here, such as

  • how to carry out the averaging (for instance one could use a p'th-power average with various p values)
  • what underlying computational model to use to measure compactness (different gobs may come along with different metrics of simplicity on the space of computational models)
  • what logical formalism to use to gauge consistency
  • how to define the multi-extremal optimization: does one seek a Pareto optimum?; does one weight the different criteria and if so according to what weighting function?
  • how to measure evidence
  • what optimization algorithm to use

However, the basic notion should be clear, even so.

If one wants to take the idea a step further, one can seek to use a gobs metric that maximizes the criteria of

  • compactness of computational representation
  • average similarity to the gobs metrics of the minds in the population

where one must then assume some default similarity measure (i.e.m etric) among gobs metrics. (Carrying it further than this certainly seems to be overkill.)

One can also use a measure of evidence defined in a similar manner, via combination of a compactness criterion and an average similarity criterion. These refinements don't fundamentally change the nature of CAV.

Relation between CEV and CAV

It is possible that CEV, as roughly described by Yudkowsky, could lead to a gobs that would serve as a solution to the CAV maximization problem. However, there seems no guarantee of this. It is possible that the above maximization problem may have a reasonably good solution, and yet Yudkowskian CEV may still diverge or lead to a solution very far from any of the gobses in the population.

As a related data point, I have found in some experiments with the PLN probabilistic reasoning system that if one begins with a set of inconsistent beliefs, and attempts to repair it iteratively (by replacing one belief with a different one that is more consistent with the others, and then repeating this process for multiple beliefs), one sometimes arrives at something VERY different from the initial belief-set. And this can occur even if there is a consistent belief set that is fairly close to the original belief-set by commonsensical similarity measures. While this is not exactly the same thing as CEV, the moral is clear: iterative refinement is not always a good optimization method for turning inconsistent belief-sets into nearby consistent ones.

Another, more qualitative observation, is that I have the uneasy feeling CEV seeks to encapsulate the essence of humanity in a way that bypasses the essential nature of being human...

CEV wants to bypass the process of individual and collective human mental growth, and provide a world that is based on the projected future of this growth. But, part of the essence of humanity is the process of growing past one's illusions and shortcomings and inconsistencies.... Part of Fred's process-of-being-Fred is his realizing on his own that he doesn't really love Susie in the right way ... and, having the super-AI decide this for him and then sculpt his world accordingly, subtracts a lot of Fred's essential humanity.

Maybe the end-state of resolving all the irrationalities and inconsistencies in a human mind (including the unconscious mind) is something that's not even "human" in any qualitative, subjective sense...

On the other hand, CAV tries to summarize humanity, and then would evolve along with humanity, thus respecting the process aspect of humanity, not trying to replace the process of humanity with its expected end-goal... And of course, because of this CAV is likely to inherit more of the "bad" aspects of humanity than CEV -- qualitatively, it just feels "more human."

Relation of CAV to Mijic's Criteria

CAV appears to adhere to the spirit of Mijic's Meta-algorithm, Factual correctness and Preference aggregation criteria. It addresses factual correctness in a relatively subtle way, differentiating between "facts" supported by different amounts of evidence according to a chosen theory of evidence.

CAV is independent of Mijic's "singleton" criterion -- it could be used to create a singleton AI, or an AI intended to live in a population of roughly equally powerful AIs. It could also be used to create an ensemble of AIs, by varying the various internal parameters of CAV.

CAV does not explicitly encompass Mijic's "reflection" criterion. It could be modified to do so, in a fairly weak way, such as replacing the criterion

  • average similarity to the various gobses in the population


  • average similarity to the various gobses displayed by individuals in the population when in a reflective frame of mind

This might be wise, as it would avoid including gobses from people in the throes of rage or mania. However, it falls far short of the kind of deep reflection implied in the original CEV proposal.

One could also try to teach the individuals in the population to be more reflective on their goals and beliefs before applying CAV. This would surely be a good idea, but doesn't modify the definition of CAV, of course.

Prototyping CAV

It seems that it would be possible to prototype CAV in a fairly simple way, by considering a restricted class of AI agents, for instance OpenCog-controlled agents, or even simple agents whose goals and beliefs are expressed explicitly in propositional-logic form. The results of such an experiment would not necessarily reflect the results of CAV on humans or highly intelligent AGI agents, but nevertheless such prototyping would doubtless teach us something about the CAV process.


I have formulated a method for arriving at AGI goal system content, intended to serve as part of an AGI system oriented beneficially toward humans and other sentient beings. This method is called Coherent Aggregated Volition, and is in the general spirit of Yudkowsky's CEV proposal as understood by the author, but differs dramatically from CEV in detail. It may be understood as a simpler, more feasible approach than CEV to fulfiling Mijic's criteria.

One thing that is apparent from the above detailed discussion of CAV is the number of free parameters involved. We consider this a feature not a bug, and we strongly suspect that CEV would also have this property if it were formulated with a similar degree of precision. Furthermore, the parameter-dependence of CEV may seem particularly disturbing if one considers it in the context of one's own personal extrapolated volitions. Depending on the setting of some weighting parameter, CEV may make a different decision as to whether Fred "really" wants to marry Susie or not!!

What this parameter-dependence means is that CAV is not an automagical recipe for producing a single human-friendly goal system content set, but rather a general approach that can be used by thoughtful humans or AGIs to produce a family of different human-friendly goal system content sets. Different humans or groups applying CAV might well argue about the different parameters, each advocating different results! But this doesn't eliminate the difference between CAV and other approaches to goal system content that don't even try to achieve broad-based beneficialness.

Compared to CEV, CAV is rather boring and consists "merely" of a coherent, consistent variation on the aggregate of a population's goals and beliefs, rather than an attempt to extrapolate what the members of the population in some sense "wish they wanted or believed." As the above discussion indicates, CAV in itself is complicated and computationally expensive enough. However, it is also prototype-able; and we suspect that in the not too distant future, CAV may actually be a realistic thing to implement on the human-population scale, whereas we doubt the same will be true of CEV. Once the human brain is well understood and non-invasively scannable, then some variant of CAV may well be possible to implement in powerful computers; and if the projections of Kurzweil and others are to be believed, this may well happen within the next few decades.

Returning to the three aspects of beneficial AGI outlined at the start of this essay: I believe that development of the currently proposed OpenCog design has a high chance of leading to an AGI architecture capable of pursuing its goal-system content in a rational way; and this means that (in my world-view) the main open question regarding beneficial AGI pertains to the stability of goal systems under environmental variation and systemic self-modification. I have some ideas for how to handle this using dynamical systems theory, but these must wait for a later post!