Not super important but maybe worth mentioning in the context of generalizing Pavlov: the strategy Pavlov for the iterated PD can be seen as an extremely shortsighted version of the law of effect, which basically says: repeat actions that have worked well in the past (in similar situations). Of course, the LoE can be applied in a wide range of settings. For example, in their reinforcement learning textbook, Sutton and Barto write that LoE underlies all of (model-free) RL.
Elsewhere, I illustrate this result for the absent-minded driver.
> I tried to understand Caspar’s EDT+SSA but was unable to figure it out. Can someone show how to apply it to an example like the AMD to help illustrate it?Sorry about that! I’ll try to explain it some more. Let’s take the original AMD. Here, the agent only faces a single type of choice—whether to EXIT or CONTINUE. Hence, in place of a policy we can just condition on p when computing our SSA probabilities. Now, when using EDT+SSA, we assign probabilities to being a specific instance in a specific possible history of the world. For example, we assign probabilities of the form PSSA(X in XYB∣p), which denotes the probability that given I choose to CONTINUE with probability p, history XYB (a.k.a. CONTINUE, EXIT) is actual and that I am the instance intersection X (i.e., the first intersection). Since we’re using SSA, these probabilities are computed as follows:
That is, we first compute the probability that the history itself is actual (given p). Then we multiply it by the probability that within that history I am the instance at X, which is just 1 divided by the number of instances of myself in that history, i.e. 2.
Now, the expected value according to EDT + SSA given p can be computed by just summing over all possible situations, i.e. over all combinations of a history and a position within that history and multiplying the probability of that situation with the utility given that situation:
And that’s exactly the ex ante expected value (or UDT-expected value, I suppose) of continuing with probability p. Hence, EDT+SSA’s recommendation in AMD is the ex ante optimal policy (or UDT’s recommendation, I suppose). This realization is not original to myself (though I came up with it independently in collaboration with Johannes Treutlein) -- the following papers make the same point:
Rachael Briggs (2010): Putting a value on Beauty. In Tamar Szabo Gendler and John Hawthorne, editors, Oxford Studies in Epistemology: Volume 3, pages 3–34. Oxford University Press, 2010. http://joelvelasco.net/teaching/3865/briggs10-puttingavalueonbeauty.pdf
Wolfgang Schwarz (2015): Lost memories and useless coins: revisiting the absentminded driver. In: Synthese. https://www.umsu.de/papers/driver-2011.pdf
My comment generalizes these results a bit to include cases in which the agent faces multiple different decisions.
Caspar Oesterheld is working on similar ideas.
For anyone who’s interested, Abram here refers to my work with Vincent Conitzer which we write about here.
My paper “Robust program equilibrium” (published in Theory and Decision) discusses essentially NicerBot (under the name ϵGroundedFairBot) and mentions Jessica’s comment in footnote 3. More generally, the paper takes strategies from iterated games and transfers them into programs for the corresponding program game. As one example, tit for tat in the iterated prisoner’s dilemma gives rise to NicerBot in the “open-source prisoner’s dilemma”.
Link to relevant agent foundations forum comment
I list some relevant discussions of the “anvil problem” etc. here. In particular, Soares and Fallenstein (2014) seem to have implemented an environment in which such problems can be modeled.
For this round I submit the following entries on decision theory:
Robust Program Equilibrium (paper)
The law of effect, randomization and Newcomb’s problem (blog post) (I think James Bell’s comment on this post makes an important point.)
A proof that every ex-ante-optimal policy is an EDT+SSA policy in memoryless POMPDs (IAFF comment) (though see my own comment to that comment for a caveat to that result)
(RobbBB seems to refer to what philosophers call the B-theory of time, whereas CronoDAS seems to refer to the A-theory of time.)
Since Briggs  shows that EDT+SSA and CDT+SIA are both ex-ante-optimal policies in some class of cases, one might wonder whether the result of this post transfers to EDT+SSA. I.e., in memoryless POMDPs, is every (ex ante) optimal policy also consistent with EDT+SSA in a similar sense. I think it is, as I will try to show below.
Given some existing policy π, EDT+SSA recommends that upon receiving observation o we should choose an action from
argmaxa∑s1,...,snn∑i=1SSA(si in s1,...,sn∣o,πo→a)U(sn).
(For notational simplicity, I’ll assume that policies are deterministic, but, of course, actions may encode probability distributions.) Here, πo→a(o′)=a if o=o′ and πo→a(o′)=π(o′) otherwise.SSA(si in s1,...,sn∣o,πo→a) is the SSA probability of being in state si of the environment trajectory s1,...,sn given the observation o and the fact that one uses the policy πo→a.
The SSA probability SSA(si in s1,...,sn∣o,πo→a) is zero if m(si)≠o and
SSA(si in s1,...,sn∣o,πo→a)=P(s1,...,sn∣πo→a)1#(o,s1,...,sn)
otherwise. Here, #(o,s1,...,sn)=∑ni=1[m(si)=o] is the number of times o occurs in #(o,s1,...,sn). Note that this is the minimal reference class version of SSA, also known as the double-halfer rule (because it assigns 1⁄2 probability to tails in the Sleeping Beauty problem and sticks with 1⁄2 if it’s told that it’s Monday).
Inserting this into the above, we get
argmaxa∑s1,...,snn∑i=1SSA(si in s1,...,sn∣o,πo→a)U(sn)=argmaxa∑s1,...,sn with o∑i=1...n,m(si)=o(P(s1,...,sn∣πo→a)1#(o,s1,...,sn))U(sn),
where the first sum on the right-hand side is over all histories that give rise to observation o at some point. Dividing by the number of agents with observation o in a history and setting the policy for all agents at the same time cancel each other out, such that this equals
argmaxa∑s1,...,sn with oP(s1,...,sn∣πo→a)U(sn)=argmaxa∑s1,...,snP(s1,...,sn∣πo→a)U(sn).
Obviously, any optimal policy chooses in agreement with this. But the same disclaimers apply; multiple policies satisfy the right-hand side of this equation and not all of these are optimal.
 Rachael Briggs (2010): Putting a value on Beauty. In Tamar Szabo Gendler and John Hawthorne, editors, Oxford Studies in Epistemology: Volume 3, pages 3–34. Oxford University Press, 2010. http://joelvelasco.net/teaching/3865/briggs10-puttingavalueonbeauty.pdf
Caveat: The version of EDT provided above only takes dependences between instances of EDT making the same observation into account. Other dependences are possible because different decision situations may be completely “isomorphic”/symmetric even if the observations are different. It turns out that the result is not valid once one takes such dependences into account, as shown by Conitzer . I propose a possible solution in https://casparoesterheld.com/2017/10/22/a-behaviorist-approach-to-building-phenomenological-bridges/ . Roughly speaking, my solution is to identify with all objects in the world that are perfectly correlated with you. However, the underlying motivation is unrelated to Conitzer’s example.
 Vincent Conitzer: A Dutch Book against Sleeping Beauties Who Are
Evidential Decision Theorists. Synthese, Volume 192, Issue 9, pp. 2887-2899, October 2015. https://arxiv.org/pdf/1705.03560.pdf
I tried to run this with racket and #lang scheme (as well as #lang racket) but didn’t get it to work (though I didn’t try for very long), perhaps because of backward compatibility issues. This is a bit unfortunate because it makes it harder for people interested in this topic to profit from the results and submitted programs of this tournament. Maybe you or Alex could write a brief description of how one could get the program tournament to run?
I wonder what people here think about the resolution proposed by Schwarz (2014). His analysis is that the divergence from the optimal policy also goes away if one combines EDT with the halfer position a.k.a. the self-sampling assumption, which, as shown by Briggs (2010), appears to be the right anthropic view to combine with EDT, anyway.
I think this is a good overview, but most of the views proposed here seem contentious and the arguments given in support shouldn’t suffice to change the mind of anyone who has thought about these questions for a bit or who is aware of the disagreements about them within the community.
Getting alignment right accounts for most of the variance in whether an AGI system will be positive for humanity.
If your values differ from those of the average human, then this may not be true/relevant. E.g., I would guess that for a utilitarian current average human values are worse than, e.g., 90% “paperclipping values” and 10% classical utilitarianism.
Also, if gains from trade between value systems are big, then a lot of value may come from ensuring that the AI engages in acausal trade (https://wiki.lesswrong.com/wiki/Acausal_trade ). This is doubly persuasive if you already see your own policies as determining what agents with similar decision theories but different values do elsewhere in the universe. (See, e.g., section 4.6.3 of “Multiverse-wide Cooperation via Correlated Decision Making”.)
Given timeline uncertainty, it’s best to spend marginal effort on plans that assume / work in shorter timelines.
Stated simply: If you don’t know when AGI is coming, you should make sure alignment gets solved in worlds where AGI comes soon.
I guess the question is what “soon” means. I agree with the argument provided in the quote. But there are also some arguments to work on longer timelines, e.g.:
If it’s hard and most value comes from full alignment, then why even try to optimize for very short timelines?
Similarly, there is a “social” difficulty of getting people in AI to notice your (or the AI safety community’s) work. Even if you think you could write down within a month a recipe for increasing the probability of AI being aligned by a significant amount, you would probably need much more than a month to make it significantly more likely to get people to consider applying your recipe.
It seems obvious that most people shouldn’t think too much about extremely short timelines (<2 years) or the longest plausible timelines (>300 years). So, these arguments together probably point to something in the middle of these and the question is where. Of course, it also depends on one’s beliefs about AI timelines.
To me it seems that the concrete recommendations (aside from the “do AI safety things”) don’t have anything to do with the background assumptions.
As one datapoint, fields like computer science, engineering and mathematics seem to make a lot more progress than ones like macroeconomics, political theory, and international relations.
For one, “citation needed”. But also: the alternative to doing technical AI safety work isn’t to do research in politics but to do political activism (or lobbying or whatever), i.e. to influence government policy.
As your “technical rather than political” point currently stands, it’s applicable to any problem, but it is obviously invalid at this level of generality. To argue plausibly that technical work on AI safety is more important than AI strategy (which is plausibly true), you’d have to refer to some specifics of the problems related to AI.
The issue with this example (and many similar ones) is that to decide between interventions on a variable X from the outside, EDT needs an additional node representing that outside intervention, whereas Pearl-CDT can simply do(X) without the need for an additional variable. If you do add these variables, then conditioning on that variable is the same as intervening on the thing that the variable intervenes on. (Cf. section 3.2.2 “Interventions as variables” in Pearl’s Causality.)
This advice is very similar to Part, 1, ch. 3; Part 3, ch. 5; Part 4, ch. 1, 6 in Dale Carnegie’s classic How to Win Friends and Influence People.
Another classic on this topic by a community member is Brian Tomasik’s Turn Discussions Into Blog Posts.
I looked at the version 2017-12-30 10:48:11Z.
Overall, I think it’s a nice, systematic overview. Below are some comments.
I should note that I’m not very expert on these things. This is also why the additional literature I mention is mostly weakly related stuff from FRI, the organization I work for. Sorry about that.
An abstract would be nice.
Locators in the citations would be useful, i.e. “Beckstead (2013, sect. XYZ)” instead of just “Beckstead (2013)” when you talk about some specific section of the Beckstead paper. (Cf. section “Pageless Documentation” of the humurous Academic Citation Practice: A Sinking Sheep? by Ole Bjørn Rekdal.)
>from a totalist, consequentialist, and welfarist (but not necessarily utilitarian) point of view
I don’t think much of your analysis assumes welfarism (as I understand it)? Q_w could easily denote things other than welfare (e.g., how virtue ethical, free, productive, autonomous, natural, the mean person is), right? (I guess some of the discussion sections are fairly welfarist, i.e. they talk about suffering, etc., rather than freedom and so forth.)
>an existential risk as one where an adverse outcome would either annihilate Earth-originating intelligent life or permanently and drastically curtail its potential.
Maybe some people would interpret this definition as excluding some of the “shrieks” and “whimpers”, since in some of them, “humanity’s potential is realized” in that it colonizes space, but not in accordance with, e.g., the reader’s values. Anyway, I think this definition is essentially a quote from Bostrom (maybe use quotation marks?), so it’s alright.
>The first is the probability P of reaching time t.
Maybe say more about why you separate N_w(t) (in the continuous model) into P(t) and N(t)?
I also don’t quite understand whether equation 1 is intended as the expected value of the future or as the expected value of a set of futures w that all have the same N_w(t) and Q_w(t). The problem is that if it’s the expected value of the future, I don’t get how you can simplify something like
into the right side of your equation 1. (E.g., you can’t just let N(t) and Q(t) denote expected numbers of moral patients and expected mean qualities of life, because the mean qualities in larger worlds ought to count for more, right?)
I suspect that when reading the start of sect. 3.1, a lot of readers will wonder whether you endorse all the assumptions underlying your model of P(t). In particular, I would guess that people would disagree with the following two assumptions:
-> Short term x-risk reduction (r_1) doesn’t have any effect on long-term risk (r). Perhaps this is true for some fairly specific work on preventing extinction but it seems less likely for interventions like building up the UN (to avoid all kinds of conflict, coordinate against risks, etc.).
-> Long-term extinction risk is constant. I haven’t thought much about these issues but I would guess that extinction risk becomes much lower, once there is a self-sustaining colony on Mars.
Reading further, I see that you address these in sections 3.2 and 3.3. Maybe you could mention/refer to these somewhere near the start of sect. 3.1.
On page 3, you say that the derivative of -P(t) w.r.t. r_1 denotes the value of reducing r_1 by one unit. This is true in this case because P(t) is linear in r_1. But in general, the value of reducing r_1 by one unit is just P(t,r_1-1)-P(t,r_1), right?
Is equation 3, combined with the view that the cost of one unit of f1 is constant, consistent with Ord’s “A plausible model would be that it is roughly as difficult to halve the risk per century, regardless of its starting probability, and more generally, that it is equally difficult to reduce it by some proportion regardless of its absolute value beforehand.”? With your model, it looks like bringing f_1 from 0 to 0.5 and thus halfing r_1 is just as expensive as bringing f_1 from 0.5 to 1.
On p. 7, “not to far off”—probably you mean “too”?
>For example, perhaps we will inevitably develop some hypothetical weapons that give so large an advantage to offence over defence that civilisation is certain to be destroyed.
AI risk is another black ball that will become more accessible. But maybe you would rather not model it as extinction. At least AI risk doesn’t necessarily explain the Fermi paradox and AIs may create sentient beings.
>Ord argues that we may be able to expect future generations to be more interested in risk reduction, implying increasing f_i
I thought f_i was meant to model the impact that we can have on r_i? So, to me it seems more sensible to model the involvement of future generations, to the extent that we can’t influence it, as a “a kind of event E” (as you propose) or, more generally, as implying that the non-intervention risk levels r_i decrease.
>This would only reinforce the case for extinction risk reduction.
It seems that future generations caring about ERR makes short-term ERR more important (because the long-term future is longer and thus can contain more value). But it makes long-term ERR less important, because future generations will, e.g., do AI safety research anyway. (In section “Future resources” of my blog post Complications in evaluating neglectedness, I make the general point that for evaluating the neglectedness of an intervention, one has to look at how many resources future generations will invest into that intervention.)
>There is one case in which it clearly is not: if space colonisation is in fact likely to involve risk-independent islands. Then high population goes with low risk, increasing the value of the future relative to the basic model
(I find risk-independent islands fairly plausible.)
>The expected number of people who will live in period t is
You introduced N(t) as the number of morally relevant beings (rather than “people”).
>However, this increase in population may be due to stop soon,
Although it is well-known that some predict population to stagnate at 9 billion or so, a high-quality citation would be nice.
>The likelihood of space colonisation, a high-profile issue on which billions of dollars is spent per year (Masters, 2015), also seems relatively hard to affect. Extinction risk reduction, on the other hand, is relatively neglected (Bostrom, 2013; Todd, 2017), so it could be easier to achieve progress in this area.
I have only briefly (in part due to the lack of locators) checked the two sources, but it seems that this varies strongly between different extinction risks. For instance, according to Todd (2017), >300bn (and thus much more than on space colonization) is spent on climate change, 1-10bn on nuclear security, 1bn on extreme pandemic prevention. So, overall much more money goes into extinction risk reduction than into space colonization. (This is not too surprising. People don’t want to die, and they don’t want their children or grandchildren to die. They don’t care nearly as much about whether some elite group of people will live on Mars in 50 years.)
Of course, there a lot of complications to this neglectedness analysis. (All three points I discuss in Complications in evaluating neglectedness seem to apply.)
>Some people believe that it’s nearly impossible to have a consistent impact on Q(t) so far into the future.
Probably a reference would be good. I guess to the extent that we can’t affect far future Q(t), we also can’t affect far future r_i.
>However, this individual may be biased against ending things, for instance because of the survival instinct, and so could individuals or groups in the future. The extent of this bias is an open question.
It’s also a bit unclear (at least based on hat you write) what legitimizes calling this a bias, rather than simply a revealed preference not to die (even in cases in which you or I as outside observers might think it to be preferable not to live) and thus evidence that their lives are positive. Probably one has to argue via status quo bias or sth like that.
>We may further speculate that if the future is controlled by altruistic values, even powerless persons are likely to have lives worth living. If society is highly knowledgeable and technologically sophisticated, and decisions are made altruistically, it’s plausible that many sources of suffering would eventually be removed, and no new ones created unnecessarily. Selfish values, on the other hand, do not care about the suffering of powerless sentients.
This makes things sound a more binary than they actually are. (I’m sure you’re aware of this.) In the usual sense of the word, people could be “altruistic” but in a non-consequentialist way. There may be lots of suffering in such worlds. (E.g., some libertarians may be regard intervening in the economy as unethical even if companies start creating slaves. A socialist, on the other hand, may view capitalism as fundamentally unjust, try to regulate/control the economy and thus cause a lot of poverty.) Also, even if someone is altruistic in a fairly consequentialist way, they may still not care about all beings that you/I/the reader cares about. E.g., economists tend to be consequentialists but rarely consider animal welfare.
I think for the animal suffering (both wild animals and factory farming) it is worth noting that it seems fairly unlikely that this will be economically efficient in the long term, but that the general underlying principles (Darwinian suffering and exploiting the powerless) might carry over to other beings (like sentient AIs).
Another way in which the future may be negative would be the Malthusian trap btw. (Of course, some would regard at least some Malthusian trap scenarios as positive, see, e.g., Robin Hanson’s The Age of Em.) Presumably this belongs to 5.2.1, since it’s a kind of coordination failure.
As you say, I think the option value argument isn’t super persuasive, because it seems unlikely that the people in power in a million years share my (meta-)values (or agree with the way I do compromise).
Re 5.2.3: Another relevant reference on why one should cooperate—which is somewhat separate from the point that if mutual cooperation works out the gains from trade are great—is Brian Tomasik’s Reasons to Be Nice to Other Value Systems.
>One way to increase Q(t) is to advocate for positive value changes in the direction of greater consideration for powerless sentients, or to promote moral enhancement (Persson and Savulescu, 2008). Another approach might be to work to improve political stability and coordination, making conflict less likely as well as increasing the chance that moral progress continues.