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The Wumpus World! 2012 级 ACM 班 金汶功

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Hunt the wumpus!

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Description Performance measure Environment Actuators Sensors: Stench & Breeze & Glitter & Bump & Scream

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An Example

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Reasoning via logic

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Semantics

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Models

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Knowledge base Axioms Current States Sensors Actuators Agent Tell Ask Tell Model checking Answer

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Efficient Model Checking DPLL Early termination Pure symbol heuristic Unit clause heuristic Component analysis …

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Drawbacks Model checking is NP-complete Knowledge base may tell nothing.

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Probabilistic Reasoning

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Full joint probability distribution P(X, Y) = P(X|Y)P(Y) X: {1,2,3,4} -> {0.1,0.2,0.3,0.4} Y: {a,b} -> {0.4, 0.6} P(X = 2, Y = a) = P(X = 2|Y = a)P(Y = a) The probability of all combination of values

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Normalization

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The Wumpus World Aim: calculate the probability that each of the three squares contains a pit.

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Full joint distribution

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How likely is it that [1,3] has a pit?

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Using independence

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Simplification

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Finally

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Bayesian Network

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Simple Example BurglaryEarthquake Alarm(Bark) John CallsMary Calls P(B).001 P(E).002 BEP(A) Truetrue.95 truefalse.94 falsetrue.29 false.001 BarkP(J) true.90 false.05 BarkP(M) true.70 false.01

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Specification

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Conditional Independence

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Exact Inference

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P1,3known b P3,1P2,2 P1,3P2,2P3,1b True 1 False1 TrueFalseTrue1 False 0 True 1 FalseTrueFalse1 True0 False 0 P(1,3) 0.2 P(known) P(P3,1) 0.2 P(P2,2) 0.2

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Approximate Inference Markov Chain Monte Carlo Gibbs Sampling Idea: The long-run fraction of time spent in each state is exactly proportional to its posterior probability.

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Reference http://zh.wikipedia.org/wiki/Hunt_the_Wumpus http://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%9 6%AF%E7%BD%91%E7%BB%9C http://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%9 6%AF%E7%BD%91%E7%BB%9C Stuart Russell, Peter Norvig Artificial Intelligence—A Modern Approach 3 rd edition, 2010

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