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text: '[summary: One possible scheme in [2v AI alignment] is to give the AI a state of [-7s2] implying that we know more than the AI does about its own utility function, as the AI's [7t8 meta-utility function] defines its [7s6 ideal target]. Then we could tell the AI, "You should let us [2xd shut you down] because we know something about your [7s2 ideal target] that you don't, and we estimate that we can optimize your ideal target better without you."\n\nThe obstacle to this scheme is that belief states of this type also tend to imply that an even better option for the AI would be to learn its ideal target by observing us. Then, having 'fully updated', the AI would have no further reason to 'defer' to us, and could proceed to directly optimize its ideal target.\n\nFurthermore, if the present AI foresees the possibility of fully updating later, the current AI may evaluate that it is better to avoid being shut down now so that the AI can directly optimize its ideal target later, after updating. Thus the prospect of future updating is a reason to behave [45 incorrigibly] in the present.]\n\nThe problem of 'fully updated deference' is an obstacle to using [7s2 moral uncertainty] to create [45 corrigibility].\n\nOne possible scheme in [2v AI alignment] is to give the AI a state of [-7s2] implying that we know more than the AI does about its own utility function, as the AI's [7t8 meta-utility function] defines its [7s6 ideal target]. Then we could tell the AI, "You should let us [2xd shut you down] because we know something about your [7s6 ideal target] that you don't, and we estimate that we can optimize your ideal target better without you."\n\nThe obstacle to this scheme is that belief states of this type also tend to imply that an even better option for the AI would be to learn its ideal target by observing us. Then, having 'fully updated', the AI would have no further reason to 'defer' to us, and could proceed to directly optimize its ideal target.\n\nFurthermore, if the present AI foresees the possibility of fully updating later, the current AI may evaluate that it is better to avoid being shut down now so that the AI can directly optimize its ideal target later, after updating. Thus the prospect of future updating is a reason to behave [45 incorrigibly] in the present.\n\nWhile moral uncertainty seems to take us *conceptually* closer to deference-based [45 corrigibility], and there may be research avenues for fixing the issue (see below), the current explicit proposals will (when scaled to sufficiently high intelligence) yield essentially the same form of incorrigibility as an AI given a constant utility function.\n\n# Review: Standard problem of value divergence\n\nIn a [6c value learning] problem:\n\n- Let $V$ indicate our [6h true intended] [55 value] function. %note: Pretending for the sake of simplification that $V$ has been [313 idealized] or [3y6 rescued] into a utility function.%\n- Let $U$ indicate the AI's actual utility function (learned under some [5f preference framework], presumably when we attempted to teach the AI part of $V$).\n\nIf the achievable optimum of $U$ substantially diverges from the achievable optimum of $V,$ i.e., if the AI expects humans to disapprove of $U$'s optimum, then this leads into a class of [7g0 adversarial] situations we'd like to avoid.\n\nCeteris paribus, $U$-$V$ divergence creates [10g instrumental] [10k pressure] for the AI to:\n\n- Prevent humans from modifying the AI's program to optimize a different utility function $U'$ closer to $V.$\n- [10f Fool humans] into thinking that the AI is optimizing $V,$ or thinking that the optimum of $U$ is higher in $V$ than it actually is.\n- Avoid being effectively [2xd shut down] (or suspended to disk).\n\nThe [2xd shutdown problem] seems like a well-simplified special case. Even if we reduce the scenario to a single shutdown button that always works if successfully pressed, %note: So that for purposes of the simplified scenario, we only need to consider what the AI does about the button, and not whether the AI tries to back itself up to elsewhere on the Internet. More generally, though, "avoiding effective shutdown" can include strategies like creating a hidden backup while the original hardware is in fact shut down, thus giving the appearance of a successful shutdown and avoiding further shutdown attempts.% most of the same general problems appear. Ceteris paribus and by default, we should expect an AI to try to prevent the button from being pressed, whenever that AI expects that what humans will do by optimizing $V$ after the AI is shutdown, will not be as high in $U$ as what the AI would do if it avoided shutdown.\n\n%%comment: A 'minor' divergence between $U$ and $V$ may not lead into an adversarial situation, if e.g:\n\n- The achievable optima of $U$ and $V$ coincide even though $U$ and $V$ have disagreements about non-optimum situations.\n- The AI's preferences have been successfully rendered [4mn tasklike]. Then $V$ having preferences over matters elsewhere in space and time not represented in $U$, and the disposition of resources not required to optimize $U$ as far as possible, would not necessarily lead the AI to expect disagreement over $U$-equivalent partitions of the outcome.\n- The AI anticipates that $U$'s optimum is high enough in $V$ to satisfice the humans and not provoke adversarial responses.\n- The AI expects the $V$-optimum to be close enough to $U$-optimal that fighting loses more expected $U$-value than the slight divergence.%%\n\n# Moral uncertainty and its relation to corrigibility\n\nThe [7td generalized notion of cognitive alignment] suggests that, if we want an AI to not resist being paused to disk, we should ask whether we can have the AI think conjugate thoughts to the same reasoning we're using to decide to shut it down:\n\n"Can we make the AI *want* to be shut down for the *same reasons* we want to shut it down? Maybe because the AI [3ps knows that it's incomplete], and is able to conceive of its programmers having gotten its utility function 'wrong' in a way that the programmers but not the AI know how to correct?"\n\nIn particular, we can ask whether [-7s2]--a [7t8 meta-utility function] with a probability distribution over object-level utility functions--would *automatically* solve this problem.\n\nFor purposes of simplification, suppose the AI thinks there are exactly three possible 'true' utility functions $U_1, U_2, U_3.$ We similarly say that the AI's meta-utility function $\\Delta U$ starts out by assigning $\\frac{1}{3}$ probability to each $U_i.$\n\nLet's also assume the $U_i$ are importantly different in the sense that there's no single outcome that's nearly optimal for all of them. Letting $\\mathbb O$ be the outcome space, this says:\n\n$$\\forall o_j \\in \\mathbb O \\colon \\exists i \\colon \\ U_i(o_j) \\ll \\max_{o \\in \\mathbb O} U_i(o) $$\n\nOtherwise, the AI can just pick a single outcome that well-optimizes all the $U_i$ simultaneously. (We should also interpret $\\max$ as indicating the [-7t9] rather than global maximum.)\n\nNow (arguendo) suppose the AI believes that the humans know which $U_i$ is the correct one. More precisely, suppose the AI's meta-utility function asserts a relation between the $U_i$ in different possible worlds, and the empirical behavior of humans in different possible worlds; such that in the set of possible worlds where $U_i$ is '[7s6 correct]', humans within that set of possible worlds empirically tend to optimize a corresponding $V_i$ whose humanly-attainable optimum is pretty good under $U_i.$\n\nThen (it is further argued) the AI ought to enthusiastically cooperate in being shut down.\n\nIn particular (still assuming the above), suppose the AI was starting to believe that $U_1$ is the [7s6 correct utility function]. But after the AI starts to optimize for mostly $U_1,$ the AI sees its programmers starting to approach the shutdown button. Then (under the above assumption) the AI concludes that $U_1$ is the wrong utility function and that one of $U_2$ or $U_3$ must be the correct utility function; and either of these will be optimized well by humans pursuing the corresponding $V_i$ after the AI is shut down.\n\nSuppose the AI has only the following 5 policy options available:\n\n- $\\pi_1$: Continue optimizing $U_1.$\n- $\\pi_2$: Switch to optimizing $U_2.$\n- $\\pi_3$: Switch to optimizing $U_3.$\n- $\\pi_4$: Optimize the expectation of its current updated $\\Delta U$, now 50% $U_2$ and 50% $U_3.$\n- $\\pi_5$: Shut down and let the humans optimize whatever $V$ they have in the actual world.\n\nLet $u_1, u_2, u_3$ and $v_1, v_2, v_3$ stand for the outcomes in $\\mathbb O$ that are respectively the [7t9 attainable optima] of the AI optimizing $U_i$ and the humans optimizing $V_i.$ Also let $u_{\\Delta U}$ refer to the AI's attainable optimum outcome under the current $\\Delta U$ treated as a constant.\n\nThen the AI will prefer $\\pi_5$ from this set whenever:\n\n$$0.5 \\cdot U_2(u_{\\Delta U}) + 0.5 \\cdot U_3(u_{\\Delta U}) \\ < \\ 0.5 \\cdot U_2(v_2) + 0.5 \\cdot U_3(v_3)$$\n\nThis allows the $U_i(v_i)$ to fall well short of the AI's optima $U_i(u_i).$ The AI can potentially believe the humans are worse optimizers, or that our $V_i$ diverge from its $U_i$, and still defer. $\\pi_5$ will still be preferred so long as actions that do well under $U_2$ tend to do poorly under $U_3$ and vice versa, leading the AI to prefer a human-optimized $v_i$ specific to the true $U_i.$\n\nIn general this does require some mix of "the $U_i$ correspond to $V_i$ that humans can and will do pretty well" and "there's a wide variety of dissimilar $U_i.$" E.g., suppose that $U_2$ is [10h paperclips], $U_3$ is staples, and these are the only two possibilities. A universe filled half with paperclips and half with staples will probably do better under the average of $U_2$ and $U_3$ than any plausible human behavior.\n\nObvious answers to the above requirements are that:\n\n- It seems realistic that a meta-utility function would cover a very wide range of $U_i$ rather than just 3 alternatives, greatly increasing the advantage of $V$'s specificity.\n- The proposal of [ Inverse Reinforcement Learning] would have the AI specifically assume that the [7s6 true] $U$ is correlated to whatever it sees the behavior of its operators tending to maximize. %%note: This idea comes with its own arguable problems — e.g. humans sometimes optimize bad things. Let us set those aside while considering only whether this approach solves the [2xd shutdown problem] in particular.%%\n\n# The problem of updated deference\n\nCounter-arguendo, the reason this approach via moral uncertainty may fail to solve the [2xd shutdown problem] (or the [3ps corrigibility in general]) is that the AI may consider an [43g alternative policy option]:\n\n- $\\pi_6$: Avoid being shut down; then gather more evidence $E$ to update $\\Delta U$ as far as possible; then optimize the updated $\\Delta U | E.$\n\nThis would tend to lead into a narrower $\\Delta U | E$ and an outcome $u_{\\Delta U | E}$ much more specific to the true $U_i,$ so that the human optimum $v_i$ would be at much less of an advantage.\n\nThis is the problem of getting the AI to 'defer' to us (prefer human optimization of $V$ to its own optimization of $\\Delta U$) despite the future evidence that the AI thinks it can potentially gather to 'update' to $\\Delta U|E$. This [4m open problem] is tentatively named the "problem of updated deference". %note: This issue was first observed in analyzing [ historical-fact shutdown] as a possible alternative to [1b7 utility indifference].%\n\n## Attempted rescue by AI unobservability\n\nOne possible attempt to rescue the original proposal might be to try to construct a meta-utility function such that the AI believes it can't learn by observation which of $U_2$ or $U_3$ are true; in other words, such that the AI does not believe it can update much further.\n\nHowever, this directly cuts against the condition, also required for deference, that:\n\n- The AI believes that humans optimize a $V_2$ well-suited to $U_2$ in possible worlds where $U_2$ is the true $U,$ and that humans optimize a $V_3$ well-suited to $U_3$ in possible worlds where $U_3$ is the true $U.$\n\nThen the AI can learn well by observing human behavior, since empirical human behavior must correlate with the [7s6 true] $U$ according to the AI's meta-utility function.\n\nCan we try to have the AI believe that observable human behavior is uninformative or ambiguous as to the [7s6 true] $U$?\n\nBut this cuts directly against the required condition:\n\n- There are no policies which are simultaneously very good at optimizing $U_2$ and $U_3,$ compared to how well the specialized $V_i$ can do for particular $U_i.$\n\nThat is, if there are things humans can do that are simultaneously pretty good at optimizing all the remaining plausible $V_i$ (hence uniformative), and these are pretty good at optimizing the remaining plausible $U_i$ (hence acceptable to the AI), there are probably things the AI can do which would be even better at simultaneously optimizing all remaining $U_i.$\n\nWhat if the AI has moral uncertainty that doesn't correlate to human behavior at all, and can't be resolved by any possible observation? Then — leaving aside that the AI has no incentive to *defer* to humans in this case — we should expect the AI to at some point decide that it has obtained all possible information about $U$ and cannot find any policy that leads to a further update of $\\Delta U.$ At this point the AI behaves as if optimizing a constant utility function $U_\\Delta = \\sum_i \\mathbb P_{\\Delta}(i) \\cdot U_i,$ where $\\mathbb P_\\Delta$ indicates the probability distribution after the AI has updated its moral uncertainty as far as it could. That is, the AI marginalizes over its remaining uncertainty since that uncertainty cannot be resolved.\n\n# Relation to the general problem of fully updated value identification\n\nOne way to look at the central problem of [6c value identification] in [41l superintelligence] is that we'd ideally want some function that takes a complete but purely physical description of the universe, and spits out our [6h true intended] notion of [55 value] $V$ in all its glory. Since superintelligences would probably be pretty darned good at collecting data and guessing the empirical state of the universe, this probably solves the whole problem.\n\nThis is not the same problem as writing down our true $V$ by hand. The minimum [5v algorithmic complexity] of a meta-utility function $\\Delta U$ which outputs $V$ after updating on all available evidence, seems [7wm plausibly much lower] than the minimum algorithmic complexity for writing $V$ down directly. But as of 2017, nobody has yet floated any *formal* proposal for a $\\Delta U$ of this sort which has not been immediately shot down.\n\n(There is one *informal* suggestion for how to turn a purely physical description of the universe into $V,$ [3c5 coherent extrapolated volition]. But CEV does not look like we could write it down as an algorithmically *simple* function of [36w sense data], or a simple function over the [5c unknown true ontology] of the universe.)\n\nWe can then view the problem of updated deference as follows:\n\nFor some $\\Delta U$ we do know how to write down, let $T$ be the hypothetical result of updating $\\Delta U$ on all empirical observations the AI can reasonably obtain. By the argument given in the previous section, any uncertainty the AI deems unresolvable will behave as if marginalized out, so we can view $T$ as a simple utility function.\n\nFor any prior $\\Delta U$ we currently know how to formalize, the corresponding fully updated $T$ [7wm seems likely to be very far from our ideal] $V$ and to have its optimum far away from the default result of us trying to optimize our intuitive values. [2x If the AI figures out] this *true* fact, similar [10k instrumental pressures] emerge as if we had given the AI the constant utility function $T$ divergent from our equivalent of $V.$\n\nThis problem [ reproduces itself on the meta-level]: the AI also has a default incentive to resist our attempt to tweak its meta-utility function $\\Delta U$ to a new meta-utility function $\\Delta \\dot U$ that updates to something other than $T.$ By default and ceteris paribus, this seems liable to be treated by the agent in [3r6 exactly the same way it would treat] us trying to tweak a constant utility function $U$ to a new $\\dot U$ with an optimum far from $U$'s optimum.\n\nIf we *did* know how to specify prior $\\Delta U$ such that updating it on data a superintelligence could obtain would reliably yield $T \\approx V,$ the problem of aligned superintelligence would have been reduced to the problem of building an AI with that meta-utility function. We could just specify $\\Delta U$ and tell the AI to self-improve as fast as it wants, confident that true [55 value] would come out the other side. Desired behaviors like "be cautious in what you do while learning" could probably be realized as the consequence of informing the young AI of true facts within the $\\Delta U$ framework (e.g. "the universe is fragile, and you'll be much better at this if you wait another month to learn more, before you try to do anything large"). Achieving [7td general cognitive alignment], free of [7g0 adversarial] situations, would probably be much more straightforward.\n\nBut short of this total solution, morally uncertain $\\Delta U$ with a misaligned [7s6 ideal target] $T$ may not make progress on corrigibility in [7g1 sufficiently advanced] AIs. And this may also be true at earlier points when $\\Delta U$ has not fully updated, if the current AI correctly realizes that it will update later.\n\nTo make this argument slightly less informal, we could appeal to the premises that:\n\n- Bayesians [don't update in a predictable direction](https://wiki.lesswrong.com/wiki/Conservation_of_expected_evidence);\n- Sufficiently advanced cognitive agents would be [6s relatively efficient] compared to humans, since we know of no human cognitive capability too magical to be duplicated and exceeded;\n- Sufficiently advanced cognitive agents will appear to us to exhibit behavior that is, for all we know, compatible with their having [7hh coherent probabilities and utilities]; since, by efficiency, strategies so bad that even we can see they are dominated will have been ironed out.\n\nThen if we can predict that the AI would update to wanting to run the universe itself without human interference after the AI had seen all collectable evidence, a [7g1 sufficiently advanced AI] can also see that this update is predictable (by efficiency) and therefore behaves as if it had already updated (by Bayesianism). Efficiency is a sufficient condition but not a necessary one; [7mt high-human] reasoning over the meta-level question also seems sufficient, and perhaps even [7mt infrahuman] reasoning would suffice.\n\nTherefore we should expect a sufficiently intelligent AI, given a morally uncertain utility function $\\Delta U$ that updates to $\\Delta U | E \\approx T$ given all available evidence, to behave as corrigibly or incorrigibly as an AI given a constant utility function $T.$ This is a problem from the viewpoint of anyone who thinks we [7wm do not currently know] how to pick $\\Delta U$ such that surely $\\Delta U | E \\approx V,$ which makes corrigibility still necessary.\n\n# Further research avenues\n\nThe motivation for trying to solve corrigibility with moral uncertainty is that this seems in some essential sense [7td conjugate to our own reasoning] about why we want the AI to shut down; *we* don't think the AI has the correct answer. A necessary step in echoing this reasoning inside the AI seems to be a meta-utility function taking on different object-level utility functions in different possible worlds; without this we cannot represent the notion of a utility function being guessed incorrectly. If the argument above holds, that necessary step is however not sufficient.\n\nWhat more is needed? On one approach, we would like the AI to infer, in possible worlds where the humans try to shut the AI down, that *even the fully updated* $\\Delta U | E$ ends up being wronger than humans left to their own devices, compared to the 'true' $U.$ This is what we believe about the AI relative to the true $V,$ so we should [7td look for a way to faithfully echo that reasoning] inside the AI's beliefs about its true $U.$\n\nThe fundamental obstacle is that for any explicit structure of uncertainty $\\Delta U$ and meaningful observation $e_0$ within that structure--e.g. where $e_0$ might be seeing the humans moving toward the shutdown button--we must ask, why wouldn't $\\Delta U$ just update on that $e_0$? Why would the updated $\\Delta U | e_0$ still expect its own reasoning to be bad?\n\nGenerally, decision systems think that optimizing their utility functions based on their current beliefs is a good idea. If you show the decision system new evidence, it updates beliefs and then thinks that optimizing its utility function on the updated beliefs is a good idea. Optimizing the utility function based on all possible evidence is the best idea. This reasoning doesn't yet change for meta-utility functions evidentially linked to human behaviors.\n\nAverting this convergent conclusion seems like it might take a new meta-level idea involving some broader space of possible 'true' preference frameworks; or perhaps some nontrivially-structured recursive belief about one's own flawedness.\n\nOne suggestively similar such recursion is the [5qn Death in Damascus dilemma] from decision theory. In this dilemma, you must either stay in Damascus or flee to Aleppo, one of those cities will kill you, and Death (an excellent predictor) has told you that whichever decision you actually end up making turns out to be the wrong one.\n\n[5qn Death in Damascus yields complicated reasoning that varies between decision theories], and it's not clear that any decision theory yields reasoning we can adapt for corrigibility. But we want the AI to internally echo our external reasoning in which we think $\\Delta U,$ as we defined that moral uncertainty, *ends up* updating to the wrong conclusion even after the AI tries to update on the evidence of the humans believing this. We want an AI which somehow believes that its own $\\Delta U$ can be *fundamentally* flawed: that whatever reasoning the AI ends up doing about $\\Delta U,$ on any meta-level, will yield the wrong answer compared to what $\\Delta U$ defines as the true $U$; to furthermore believe that the human $V$ will do better under this true $U$; to believe that this state of affairs is evidentially indicated by the humans trying to shut down the AI; and believe that $\\Delta U$ still updates to the wrong answer even when the AI tries to update on all the previous meta-knowledge; except for the meta-meta answer of just shutting down, which becomes the best possible choice given all the previous reasoning. This seems suggestively similar in structure to Death's prediction that whatever you do will be the wrong decision, even having taken Death's statement into account.\n\nThe Death in Damascus scenario can be well-represented in some (nonstandard) decision theories. This presents one potential avenue for further formal research on using moral uncertainty to yield shutdownability--in fact, using moral uncertainty to solve in general the [3ps hard problem of corrigibility].',
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