Foundations of Induction - of Marcus Hutter

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Marcus Hutter - 32 - Foundations of InductionSequential 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 of 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.
Marcus Hutter - 33 - Foundations of InductionAgent Modelwith Rewardif actions/decisions ainfluence the environment qr 1 | o 1 r 2 | o 2 r 3 | o 3 r 4 | o 4 r 5 | o 5 r 6 | o 6...work✟✟✟✟✙ ✟Agentptape ...❍❨ ❍❍❍❍workEnvironmentq ✏ ✏✏✏✏✏✏✶tape ...a 1 a 2 a 3 a 4 a 5 a 6 ...
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Foundations of Induction - of Marcus Hutter

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