Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
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<strong>Marcus</strong> <strong>Hutter</strong> - 100 - Universal Induction & Intelligence<br />
Map Real Problem to MDP<br />
Map history h t := o 1 a 1 r 1 ...o t−1 to state s t := Φ(h t ), for example:<br />
Games: Full-<strong>in</strong>formation with static opponent: Φ(h t ) = o t .<br />
Classical physics: Position+velocity <strong>of</strong> objects = position at two<br />
time-slices: s t = Φ(h t ) = o t o t−1 is (2nd order) Markov.<br />
I.i.d. processes <strong>of</strong> unknown probability (e.g. cl<strong>in</strong>ical trials ≃ Bandits),<br />
Frequency <strong>of</strong> obs. Φ(h n ) = ( ∑ n<br />
t=1 δ o t o) o∈O is sufficient statistic.<br />
Identity: Φ(h) = h is always sufficient, but not learnable.<br />
F<strong>in</strong>d/Learn Map Automatically<br />
Φ best := arg m<strong>in</strong> Φ Cost(Φ|h t )<br />
• What is the best map/MDP (i.e. what is the right Cost criterion)<br />
• Is the best MDP good enough (i.e. is reduction always possible)<br />
• How to f<strong>in</strong>d the map Φ (i.e. m<strong>in</strong>imize Cost) efficiently
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