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by Stuart Armstrong 923 days ago | link | parent

How about an iterated process? If you have a series of actions and observations \(e_n=a_no_na_{n-1}o_{n-1}\ldots\), and \(A\) is the set of possible actions, have the AI pick \(a\) such that:

\(a_{n} = \operatorname{argmax}_{a} \frac{1}{|A|}\sum_{a'\in A,b} U(ao_ne_{n-1}|B=b) P(B=b|a'o_ne_{n-1})\)

(the \(\frac{1}{|A|}\) is not necessary, just a reminder that we are choosing a uniform distribution over the possible actions).

Notice that the AI conditions correctly on all its past actions, but not its current hypothetical. I wonder how this would work if we set \(A={0,1}\) and had the AI type out messages bit by bit, each time thinking the probability of \(B\) was independent of its bit-choice?

EDIT: What this means is that, as soon as it’s done any action that might cause the shutdown button to be pressed, it will then look at the shutdown button (but maybe doesn’t expect, ahead of time, that it will be looking at the button).



by Jessica Taylor 922 days ago | link

I think, to get \(P(B = b)\), you have to have an implicit policy for the entire rest of the game (not just the next action \(a'\)).

I like the idea of using the evidence you have so far to inform the \(P(b)\), so you spend more effort on looking at the shutdown button if you expect shutdown might be imminent based on your evidence. Of course, you can combine this with the fixed point thing, so the distribution of \(a'\) is the same as the distribution of \(a\).

My main concern is that this isn’t reflectively stable. If at an early time step the AI has a certain \(P(b)\) distribution, it may want to modify into an agent that fixes this as the correct \(P(b)\) rather than changing \(P(b)\) in response to new evidence; this is because it is modelling \(B\) as coming independently from \(P(b)\).

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