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PatSwanson comments on Noisy Reasoners - Less Wrong
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Wouldn't increasing noise levels in the decision-making processes of a Friendly AI decrease the Friendliness of that AI?
I think that ought to take this approach to reducing resource-consumption off the table.
The worst that noise can do is decrease the quality of the approximation that the AI is using. (EDIT: barring the OP effects, of which I am skeptical) For friendliness, this means decreasing decision quality.
If you decide that such is unacceptable, the AI needs to spend more resources (time and energy) on coming to the conclusion. In some cases that will be worth it, in others, not. The AI is capable of making this trade off on it's own.
If you don't let it trade accuracy for speed, the day will come when you need a decision now, and the AI will choke and everyone will die.
It's not clear how an AI that couldn't trade off accuracy could even work, given that the exact forms of nearly everything are intractable.