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.
I’m with Eliezer: noise never helps at a fundamental level.
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!
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.
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.
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.
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!
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.
Several of my examples did not have opponents. To list three: the bargaining example, the randomized controlled trials example, and P vs. BPP.