Slides in PDF - of Marcus Hutter

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Marcus Hutter - 100 - Universal Induction & Intelligence Map Real Problem to MDP Map history h t := o 1 a 1 r 1 ...o t−1 to state s t := Φ(h t ), for example: Games: Full-information with static opponent: Φ(h t ) = o t . Classical physics: Position+velocity of objects = position at two time-slices: s t = Φ(h t ) = o t o t−1 is (2nd order) Markov. I.i.d. processes of unknown probability (e.g. clinical trials ≃ Bandits), Frequency of obs. Φ(h n ) = ( ∑ n t=1 δ o t o) o∈O is sufficient statistic. Identity: Φ(h) = h is always sufficient, but not learnable. Find/Learn Map Automatically Φ best := arg min Φ Cost(Φ|h t ) • What is the best map/MDP (i.e. what is the right Cost criterion) • Is the best MDP good enough (i.e. is reduction always possible) • How to find the map Φ (i.e. minimize Cost) efficiently
Marcus Hutter - 101 - Universal Induction & Intelligence ΦMDP: Computational Flow ✓ ✏ ✓ ✏ Transition Pr. ˆT exploration Reward est. ✒ ˆR ✲ bonus ˆT e , ˆR e ✑ ✒ ✑ ✓ ✒ frequency estimate ❅ Bellman ✏ ✓ ❅ ❅❘ Feature Vec. ˆΦ ( ˆQ) ˆValue ✒ ✑ ✒ ✻ Cost(Φ|h) minimization implicit ✓ ✏ ✓ ❄ History h Best Policy ˆp ✒ ✑ ✒ ✻ reward r observation o action a ❄ Environment ✏ ✑ ✏ ✑
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Slides in PDF - of Marcus Hutter

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