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.

The key point is not that the AI knows what is or isn't "rigging", or that the AI "knows what a bias is". The key point is that in a CIRL game, by construction there is a true (unknown) reward function, and thus an optimal policy must be viewable as being Bayesian about the reward function, and in particular its actions must be consistent with conservation of expected evidence about the reward function; anything which "rigs" the "learning process" does not satisfy this property and so can't be optimal.

You might reasonably ask where the magic happens. The CIRL game that you choose would have to commit to some connection between rewards and behavior. It could be that in one episode the human wants heroin (but doesn't know it) and in another episode the human doesn't want heroin (this depends on the prior over rewards). However, it could never be the case that

in a single episode(where the reward must be fixed) the human doesn't want heroin, and then laterin the same episodethe human does want heroin. Perhaps in the real world this can happen; that would make this policy suboptimal in the real world. (What it does then is unclear since it depends on how the policy generalizes out of distribution.)If this doesn't clarify it, I'll probably table this discussion until publishing an upcoming paper on CIRL games (where it will probably be renamed to assistance games).

EDIT: Perhaps another way to put this: I agree that if you train an AI system to act such that it maximizes the expected reward under the posterior inferred by a fixed update rule looking at the AI system's actions and resulting states, the AI will tend to gain reward by choosing actions which when plugged into the update rule lead to a posterior that is "easy to maximize". This seems like training the controller but not training the estimator, and so the controller learns information about the world that allows it to "trick" the estimator into updating in a particular direction (something that would be disallowed by the rules of probability applied to a unified Bayesian agent, and is only possible here because either a) the estimator is uncalibrated or b) the controller learns information that the estimator doesn't know).

Instead, you should train an AI system such that it maximizes the expected reward it gets under the prior; this is what CIRL / assistance games do. This is kinda sorta like training both the "estimator" and the "controller" simultaneously, and so the controller can't gain any information that the estimator doesn't have (at least at optimality).