I've always emphasised the constructive aspect of figuring out human preferences, and the desired formal properties of preference learning processes.

A common response to these points is something along the line of "have the AI pick a prior over human preferences, and update it".

However, I've come to realise that a prior over human preferences is of little use. The real key is figuring out how to update it, and that contains almost the entirety of the problem.

I've shown that you cannot deduce preferences from observations or facts about the world - at least, without making some assumptions. These assumptions are needed to bridge the gap between observations/facts, and updates to preferences.

For example, imagine you are doing cooperative inverse reinforcement learning^{[1]} and want to deduce the preferences of the human . CIRL assumes that knows the true reward function, and is generally rational or noisily rational (along with a few other scenarios).

So, this is the bridging law:

- knows their true reward function, and is noisily rational.

Given this, the AI has many options available to it, including the "drug the human with heroin" approach. If is not well-defined in the bridging law, then "do brain surgery on the human" also becomes valid.

And not only are those approaches valid; if the AI wants to maximise the reward function, according to how this is defined, then these are the optimal policies, as they result in the most return, given that bridging law.

Note that the following is not sufficient either:

- has a noisy impression of their true reward function, and is noisily rational.

Neither of the "noisy" statements are true, so if the AI uses this bridging law, then, for almost any prior, preference learning will come to a bad end.

# Joint priors

What we really want is something like:

- has an imperfect impression of their true reward function, and is biased.

And yes, that bridging law is true. But it's also massively underdefined. We want to know how 's impression is imperfect, how they are biased, and also what counts as versus some brain-surgeried replacement of them.

So, given certain human actions, the AI can deduce human preferences. So this gives a joint prior over , the possible human reward functions and possible the human's policies^{[2]}. Given that joint prior, then, yes, an AI can start deducing preferences from observations.

So instead of a "prior over preferences" and a "update bridging law", we need a joint object that does both.

But such a joint prior is essentially the same object as the assumptions needed to overcome the Occam's razor result.

# Other areas

It seems to me that realisability has a similar problem: if the AI has an imperfect model of how they're embedded in the world, then they will "learn" disastrously wrong things.

This is the part that I think needs more detail; it seems to me that this depends on what you mean by an "optimal policy".

Here's one possible algorithm. You have two separate systems:

with an accurate model of reality, and maximizes the expected reward that comes out of the estimator at the end of the trajectory. (You could imagine training a neural net in the real world so that you have the "accurate model of reality" part.)I agree that for such a system, the optimal policy of the actor is to rig the estimator, and to "intentionally" bias it towards easy-to-satisfy rewards like "the human loves heroin".

The part that confuses me is why we're having two separate systems with different objectives where one system is dumb and the other system is smart. CIRL, iterated amplification and debate all aim to create a single system that can do both estimation of human preferences and control in the same model.

(Maybe you could view iterated amplification as having two separate systems -- the "amplified model" and the "distilled model" -- where the amplified model serves the role of the estimator and the distilled model serves the role of the actor. This analogy seems pretty forced, but even if you buy it, it's noteworthy that the estimator is supposed to be

smarterthan the actor.)So, here's a second algorithm. Imagine that you have a complex CIRL game that models the real world well but assumes that the human is Boltzmann-rational. You find an optimal policy

for that game(i.e. not "in the real world / in the presence of misspecification"). Then you deploy that policy in the real world. Such a policy is going to "try" to learn preferences, learn incorrectly, and then act according to those incorrect learned preferences, but it is not going to "intentionally" rig the learning process.It might think "hey, I should check whether the human likes heroin by giving them some", and then think "oh they really do love heroin, I should pump them full of it". It won't think "aha, if I give the human heroin, then they'll ask for more heroin, causing my Boltzmann-rationality estimator module to predict they like heroin, and then I can get easy points by giving humans heroin".

Thanks! Responded here: https://www.lesswrong.com/posts/EYEkYX6vijL7zsKEt/reward-functions-and-updating-assumptions-can-hide-a