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V_V comments on More and Less than Solomonoff Induction - Less Wrong Discussion

4 Post author: Manfred 21 May 2014 04:55AM

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Comment author: V_V 22 May 2014 08:18:22PM 0 points [-]

(The obvious way is "if EV(bet)>0, consider the bet taken.")

I don't think its really obvious. The (retroactively) obvious way to extend SI into a decision agent, is AIXI, which has its own optimality theorems.

What shows up in the most obvious place - pg 328 of the book - is that the mean squared error decreases faster than 1/n. And in fact the proof method isn't strong enough to show that the absolute error decreases faster than 1/n (because the derivative of the absolute error jumps discontinuously).

The absolute error is just the square root of the squared error. If the squared error decreases faster than 1/n, then the absolute error decreases faster than 1/sqrt(n).

Comment author: Manfred 23 May 2014 03:14:02AM 0 points [-]

If the squared error decreases faster than 1/n, then the absolute error decreases faster than 1/sqrt(n).

The point being that if your expected absolute error decreases like 1/n or slower, you make an infinite number of wrong bets.

Comment author: V_V 23 May 2014 09:09:55AM *  0 points [-]

You keep framing this in terms of bets. I don't think there is any point in continuing this discussion.

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