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by Jessica Taylor 677 days ago | link | parent

If we apply this to the shutdown problem, is it acceptable to say:

\[ \hat{P}(\cdot | h_t) = 100\% ~ U_N \text{ if the button has not been pressed in $h_t$ } \]

\[ \hat{P}(\cdot | h_t) = 100\% ~ U_S \text{ otherwise} \]

If not, what would you set \(\hat{P}\) to? (I’m treating \(U_N\) and \(U_S\) as reward functions here which seems fine)



by Stuart Armstrong 677 days ago | link

For policies/actions that don’t affect the probability of humans pressing the button, \(\widehat{P}=P\).

For actions that do affect the probability a little bit, the effect of \(\widehat{P}\) will be to undo this, by, for instance, slightly increasing the probability of \(U_S\) given the button was pressed.

I’m not completely sure what multiple actions with large changes of probability would lead to (in expectation, nothing, but in actual fact…)

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by Jessica Taylor 677 days ago | link

Hmm… I’m finding that I’m unable to write down a simple shutdown problem in this framework (e.g. an environment where it should switch between maximizing paperclips and shutting down) to analyze what this algorithm does. To know what the algorithm does, I need to know what \(P\) and \(\hat{P}\) are (since these are parameters of the algorithm). From those I can derive \(P'\) and \(\hat{P}'\) to determine the agent’s action. But at the moment I have no way of proceeding, since I don’t know what \(P\) and \(\hat{P}\) are. Can you get me unstuck?

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by Stuart Armstrong 671 days ago | link

Suppose the humans have already decided whether to press the shutdown or order the AI to maximise paperclips. If \(o_s\) is the observation of the shutdown command and \(o_p\) the observation of the paperclip maximising command, and \(u_s\) and \(u_p\) the relevant utilities, then \(P\) can be defined as \(P(u_s|h_{m-1}o_s)=1\) and \(P(u_p|h_{m-1}o_p)=1\), for all histories \(h_{m-1}\).

Then define \(\widehat{P}\) as the probability of \(o_s\) versus \(o_p\), conditional on the fact that the agent follows a particular deterministic policy \(\pi^0\).

If the agent does indeed follow \(\pi^0\), then \(\widehat{P}=\widehat{P}'\). If it varies from this policy, then \(\widehat{P}'\) is altered in proportion to the expected change in \(\widehat{P}\) caused by choosing a different action.

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