In order to better understand how AI might succeed and fail at learning knowledge, I'll be trying to construct models of limited agents (with bias, knowledge, and preferences) that display identical behaviour in a wide range of circumstance (but not all). This means their preferences cannot be deduced merely/easily from observations.

Does anyone have any suggestions for possible agent models to use in this project?

I just thought I'd clarify the difference between learning values and learning knowledge. There are some more complex posts
about the specific problems with learning values, but here I'll just clarify why there is a problem with learning values in the first place.

Consider the term "chocolate bar". Defining that concept crisply would be extremely difficult. But nevertheless it's a useful concept. An AI that interacted with humanity would probably learn that concept to a sufficient degree of detail. Sufficient to know what we meant when we asked it for "chocolate bars". Learning knowledge tends to be accurate.

Contrast this with the situation where the AI is programmed to "create chocolate bars", but with the definition of "chocolate bar" left underspecified, for it to learn. Now it is motivated by something else than accuracy. Before, knowing exactly what a "chocolate bar" was would have been solely to its advantage. But now it must act on its definition, so it has cause to modify the definition, to make these "chocolate bars" easier to create. This is basically the same as Goodhart's law - by making a definition part of a target, it will no longer remain an impartial definition.

What will likely happen is that the AI will have a concept of "chocolate bar", that it created itself, especially for ease of accomplishing its goals ("a chocolate bar is any collection of more than one atom, in any combinations"), and a second concept, "Schocolate bar" that it will use to internally designate genuine chocolate bars (which will still be useful for it to do). When we programmed it to "create chocolate bars, here's an incomplete definition D", what we really did was program it to find the easiest thing to create that is compatible with D, and designate them "chocolate bars".

This is the general counter to arguments like "if the AI is so smart, why would it do stuff we didn't mean?" and "why don't we just make it understand natural language and give it instructions in English?"

Problem solved: Found what I was looking for in: An Axiomatic Characterization Causal Counterfactuals, thanks to Evan Lloyd.

Basically, making every endogenous variable a deterministic function of the exogenous variables and of the other endogenous variables, and pushing all the stochasticity into the exogenous variables.

Old post:

A problem that's come up with my definitions of stratification.

Consider a very simple causal graph:

In this setting, A and B are both booleans, and A=B with 75% probability (independently about whether A=0 or A=1).

I now want to compute the counterfactual: suppose I assume that B=0 when A=0. What would happen if A=1 instead?

The problem is that P(B|A) seems insufficient to solve this. Let's imagine the process that outputs B as a probabilistic mix of functions, that takes the value of A and outputs that of B. There are four natural functions here:

• f₀(x) = 0
• f₁(x) = 1
• f₂(x) = x
• f₃(x) = 1-x

Then one way of modelling the causal graph is as a mix 0.75f₂ + 0.25f₃. In that case, knowing that B=0 when A=0 implies that P(f₂)=1, so if A=1, we know that B=1.

But we could instead model the causal graph as 0.5f₂+0.25f₁+0.25f₀. In that case, knowing that B=0 when A=0 implies that P(f₂)=2/3 and P(f₀)=1/3. So if A=1, B=1 with probability 2/3 and B=1 with probability 1/3.

And we can design the node B, physically, to be one or another of the two distributions over functions or anything in between (the general formula is (0.5+x)f₂ + x(f₃)+(0.25-x)f₁+(0.25-x)f₀ for 0 ≤ x ≤ 0.25). But it seems that the causal graph does not capture that.

Owain Evans has said that Pearl has papers covering these kinds of situations, but I haven't been able to find them. Does anyone know any publications on the subject?

A putative new idea for AI control; index here.

Corrigibility through indifference has a few problems. One of them is that the AI is indifferent between the world in which humans change its utility to v, and world in which humans try to change its utility, but fail.

Now the try-but-fail world is going to be somewhat odd - humans will be reacting by trying to change the utility again, trying to shut the AI down, panicking that a tiny probability event has happened, and so on.