Foundations of Induction - of Marcus Hutter
Foundations of Induction - of Marcus Hutter
Foundations of Induction - of Marcus Hutter
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<strong>Marcus</strong> <strong>Hutter</strong> - 32 - <strong>Foundations</strong> <strong>of</strong> <strong>Induction</strong>Sequential Decision TheorySetup: For t = 1, 2, 3, 4, ...Given sequence x 1 , x 2 , ..., x t−1(1) predict/make decision y t ,(2) observe x t ,(3) suffer loss Loss(x t , y t ),(4) t → t + 1, goto (1)Goal: Minimize expected Loss.Greedy minimization <strong>of</strong> expected loss is optimal if:Important: Decision y t does not influence env. (future observations).Loss function is known.Problem: Expectation w.r.t. what?Solution: W.r.t. universal distribution M if true distr. is unknown.
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