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On-line learning competitive with reproducing kernel Hilbert spaces
Published on Feb 25, 20074076 Views
In this talk I will describe a new technique for designing competitive on-line prediction algorithms and proving loss bounds for them. The goal of such algorithms is to perform almost as well as the b
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On-line learning competitive with reproducing kernel Hilbert00:02
Prediction with expert advice:00:08
Decision-making protocol:02:13
Decision rule03:40
Decision-making protocol:04:30
Decision rule04:43
Proposition05:50
When is Decision Maker10:14
Similar results11:49
The rest of this talk:13:12
There are 2 main14:47
Game-theoretic SLLN16:24
The difference between the two protocols18:29
Proposition (game-theoretic SLLN)18:46
The measure-theoretic SLLN19:28
Recent (2004) observation21:23
Modified protocol:21:55
Proof25:32
Research programme I25:55
What does it give in the case of LLN?27:03
We need a convoluted LLN28:10
Theorem 229:49
If the surface32:31
Optimality result34:07
A reproducing kernel Hilbert space35:32
Optimality result37:01
Examples37:28
On R:38:13
Research programme II39:56
The goal:41:33
Fix a choice function42:33
The exposure44:19
Proof Subtracting45:43
In conjunction with Theorem 3:47:12
In conjunction with Theorem 3:48:09
Summary of the proof technique:48:39
Theorem 449:39
Suppose52:04
Further details53:31