LESSWRONG
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All of comingstorm's Comments + Replies

Disappointment in the Future
comingstorm10

Tallying these, it looks like roughly one in six have actually come true. Another one in six seems likely to come true in the readily-forseeable future (say, five to eight years). Note that many of these depend on what you're willing to call a "computer". I contend that just because something has a microcontroller running it doesn't make it count as a computer; e.g., a traffic light doesn't qualify. But, should a cheap-ass dumb cellphone count? I think a certain amount of user-mediated flexibility should be a requirement, but ultimately it's... (read more)

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The Weighted Majority Algorithm
comingstorm20

@michael e sullivan: re "Monte Carlo methods can't buy you any correctness" -- actually, they can. If you have an exact closed-form solution (or a rapidly-converging series, or whatever) for your numbers, you really want to use it. However not all problems have such a thing; generally, you either simplify (giving a precise, incorrect number that is readily computable and hopefully close), or you can do a numerical evaluation, which might approach the correct solution arbitrarily closely based on how much computation power you devote to it.

Quad... (read more)

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The Weighted Majority Algorithm
comingstorm80

What about Monte Carlo methods? There are many problems for which Monte Carlo integration is the most efficient method available.

(you are of course free to suggest and to suspect anything you like; I will, however, point out that suspicion is no substitute for building something that actually works...)

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7bogdanb
(Emphasis mine.) I know I’m late to the party, but I just noticed this. While what you say it’s true, “available” in this case means “that we know of”, not “that is possible”. I’m not an expert, but IIRC the point of the MCI is that the functions are hard to analyze. You could integrate analogously without randomization (e.g., sample the integration domain on a regular grid), and it very well might work. The problem is that if the function you integrate happens to behave atypically on the regular grid with respect to its global behavior (e.g., if the function has some regular features with a frequency that accidentally matches that of your grid, you might sample only local maxima, and severely overestimate the integral). But for an individual function there certainly exists (for some values of “certainly”) an ideal sampling that yields an excellent integration, or some even better method that doesn’t need sampling. But, you need to understand the function very well, and search for that perfect evaluation strategy, and do this for every individual function you want to integrate. (Not a math expert here, but I suspect in the general case that grid would be impossible to find, even if it exists, and it’s probably very hard even for those where the solution can be found.) So what MCI does is exactly what Eliezer mentions above: you randomize the sampling as well as you can, to avoid as much as possible tripping an unexpected “resonance” between the grid and the function’s behavior. In effect, you’re working against an environment you can’t overwhelm by being smart, so you brute force it and do your best to reduce the ways the environment can overwhelm you, i.e. you try to minimize the worst-case consequences. Note that for functions we really understand, MCI is not by far the best method. If you want to integrate a polynomial, you just compute the antiderivative, evaluate it in two points, subtract, and you’re done. MCI is nice because in general we don’t know how to
The Truly Iterated Prisoner's Dilemma
comingstorm00

This "perfectly rational" game-theoretic solution seems to be fragile, in that the threshold of "irrationality" necessary to avoid N out of N rounds of defection seems to be shaved successively thinner as N increases from 1.

Also, though I don't remember the details, I believe that slight perturbations in the exact rules may also cause the exact game-theoretic solution to change to something more interesting. Note that adding uncertainty in the exact number of rounds has the effect of removing your induction premise: e.g., a 1% chance of... (read more)

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