"Normative assumptions" need not be complex

post by Stuart_Armstrong · 2019-02-11T19:03:38.493Z · LW · GW · 0 comments

Contents

  Formalism
  Assumptions that use a lot of information
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I've shown that, even with simplicity priors, we can't figure out the preferences or rationality of a potentially irrational agent (such as a human $H$).

But we can get around that issue with 'normative assumptions [LW · GW]'. These can allow us to zero in on a 'reasonable' reward function $R_H$.

We should however note that:

• Even if $R_H$ is highly complex, a normative assumption need not be complex to single it out.

This post gives an example of that for general agents, and discusses how a similar idea might apply to the human situation.

Formalism

An agent takes actions ($A$) and gets observations ($O$), and together these form histories, with $H$ the set of histories (I won't present all the details of the formalism here). The policies $\Pi =\{\pi :H\to A\}$ are maps from histories to actions. The reward functions $R=\{R:H\to R\}$ are maps from histories $H$ to real numbers), and the planners $P=\{p:R\to \Pi \}$ are maps from reward functions to policies.

By observing an agent, we can deduce (part of) their policy $\pi$. Then a reward-planner pair $(p,R)$ is compatible with $\pi$ if $p\left(R\right)=\pi$. Further observations cannot distinguish between different compatible pairs.

Then a normative assumption $\alpha$ is something that distinguishes between compatible pairs. It could be a prior on $P\times R$, or an assumption of full rationality (which removes all-but-the-rational planner from $P$), or something that takes in more details about the agent or the situation.

Assumptions that use a lot of information

Assume that the agent's algorithm $\pi$ is written in some code, as $C_{\pi }$, and that $\alpha$ will have access to this. Then suppose that $\alpha$ scans $C_{\pi }$, looking for the following: an object $C_R$ that takes a history as an input and has a real number as an output, an object $C_p$ that takes $C_R$ and a history as inputs, and outputs an action, and a guarantee that $C_{\pi }$ chooses actions by running $C_p$ on $C_R$ and the input history.

The $\alpha$ need not be very complex to do that job. Because of rice's theorem and obfuscated code, it will be impossible for $\alpha$ to check those facts in general. But, for many examples of $C_{\pi }$, it will be able to check that those things hold. In that case, let $\alpha$ return $R$; otherwise, let it return the trivial $0$ reward.

So, for a large set $S$ of possible algorithms, $\alpha$ can return a reasonable reward function estimate. Even if the complexity of $C_{\pi }$ and $R$ is much, much higher than the complexity of $\alpha$ itself, there are still examples of these where $\alpha$ can successfully identity the reward function.

Of course, if we run $\alpha$ on a human brain, it would return $0$. But what I am looking for is not $\alpha$, but a more complicate ${\alpha }_H$, that, when run on the set $S_H$ of human agents, will extract some 'reasonable' $R_H$. It doesn't matter what ${\alpha }_H$ does when run on non-human agents, so we can load it with assumptions about how humans work. When I talk about extracting preferences through looking at internal models [LW · GW], this is the kind of thing I had in mind (along with some method for synthesising those preferences [LW · GW] into a coherent whole).

So, though my desired ${\alpha }_H$ might be complex, there is no a priori reason to think that it need be as complex as the $R_H$ output.

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