# How should AIs update a prior over human preferences?

I've always emphasised the [constructive aspect of figuring out human preferences](https://www.lesswrong.com/posts/CSEdLLEkap2pubjof/research-agenda-v0-9-synthesising-a-human-s-preferences-into), and [the desired formal properties of preference learning processes](https://arxiv.org/abs/2004.13654).

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](https://arxiv.org/abs/1712.05812) 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](https://arxiv.org/abs/1606.03137)[^crit] and want to deduce the preferences of the human $\mathbf{H}$. CIRL assumes that $\mathbf{H}$ knows the true reward function, and is generally rational or noisily rational (along with a few other scenarios).

[^crit]: This is not a criticism of CIRL; it does its task very well, but still requires some underlying assumptions.

So, this is the bridging law:

* $\mathbf{H}$ 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](https://www.lesswrong.com/posts/EQ7AnauMSgdcYar4a/heroin-model-ai-manipulates-unmanipulatable-reward)" approach. If $\mathbf{H}$ is not well-defined in the bridging law, then "[do brain surgery on the human](https://www.lesswrong.com/posts/ZBwx9sEwdHFNhZduT/pascal-s-mugging-in-reward-learning)" 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:

*  $\mathbf{H}$ 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:

*  $\mathbf{H}$ 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 $\mathbf{H}$'s impression is imperfect, how they are biased, and also what counts as $\mathbf{H}$ versus some brain-surgeried replacement of them.

So, given certain human actions, the AI can deduce human preferences. So this gives a joint prior $p$ over $\mathcal{R}\times\Pi_\mathbf{H}$, the possible human reward functions and possible the human's policies[^huid]. Given that joint prior, then, yes, an AI can start deducing preferences from observations.

[^huid]: And the human's identity, which we're implicitly modelling as part of the policy.

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](https://www.lesswrong.com/posts/efWfvrWLgJmbBAs3m/embedded-world-models) 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.