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Dagon comments on The Power of Noise - Less Wrong
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Replace "adversarial superintelligence" with "adversarial game", and I think you'll get more agreement among the participants. There are plenty of cases where a "mixed strategy" is optimal. Note that this is not noise, and true randomness isn't necessary - it only needs to be unpredictable by the opponent, not necessarily random.
Where you don't have an opponent (or at least one that makes predictions), I'm with Eliezer: noise never helps at a fundamental level.
I do believe that randomness has a place in thinking about problems, and it's easier (for humans) to reason about randomness than insanely-complex deterministic calculations. But that's a problem with the reader of the map, not with the map nor the territory.
There is another case where noise helps- threshold effects. If you have as signal below a threshold, a bit of noise can push the signal up into the detectable region.
Do you mean stochastic resonance? If so, good example!
(If not, it's still a good example -- it's just my good example. ;-)
Also, dithering.
To my thinking, this is essentially equivalent to conjecturing that P = BPP, which is plausible but still might be false.
ETA: Didn't read the post before replying to the parent (saw it in the sidebar). Now I see that a good quarter of the post is about P = BPP. Egg on my face!
Several of my examples did not have opponents. To list three: the bargaining example, the randomized controlled trials example, and P vs. BPP.