A brief note on factoring out certain variables

[-]jessicata9y10

I think the main problem with using a pre-specified distribution over actions is that, since it doesn't reflect the AI's actual behavior, you can't say much about $P (B = b | e)$ in relation to real life. For example, maybe the implicit policy is to take random actions, which results in humans not pressing the shutdown button; therefore, in real life the AI is confident that the button will not be pressed, so it spends no resources looking at the shutdown button to see if it was pressed.

[-]Stuart_Armstrong9y00

How about an iterated process? If you have a series of actions and observations $e_{n} = a_{n} o_{n} a_{n - 1} o_{n - 1} \dots$ , and $A$ is the set of possible actions, have the AI pick $a$ such that:

$a_{n} = {argmax}_{a} \frac{1}{| A |} \sum_{a^{'} \in A, b} U (a o_{n} e_{n - 1} | B = b) P (B = b | a^{'} o_{n} e_{n - 1})$

(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).

[-]jessicata9y00

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 $P (b)$ .

[-]orthonormal9y00

Maybe if the pre-specified distribution is a reasonably well-calibrated predictor of the AI (given that distribution)? Like, maybe this is a way that an Oracle AI could help ensure the safety of a somewhat weaker Tool AI.

[-]RyanCarey7y00

[Note: This comment is three years later than the post]

The "obvious idea" here unfortunately seems not to work, because it is vulnerable to so-called "infinite improbability drives". Suppose $B$ is a shutdown button, and $P (b | e)$ gives some weight to $B = p r e s s e d$ and $B = u n p r e s s e d$ . Then, the AI will benefit from selecting a Q such that it always chooses an action $a$ , in which it enters a lottery, and if it does not win, then it the button B is pushed. In this circumstance, $P (b | e)$ is unchanged, while both $P (c | b = p r e s s e d, a, e)$ and $P (c | b = u n p r e s s e d, a, e)$ allocate almost all of the probability to great $C$ outcomes. So the approach will create an AI that wants to exploit its ability to determine $B$ .

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A brief note on factoring out certain variables

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