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SP11 cs188 lecture 6 -- adversarial search 6PP

SP11 cs188 lecture 6 -- adversarial search 6PP -...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 6: Adversarial Search 2/4/2010 Pieter Abbeel – UC Berkeley Many slides adapted from Dan Klein 1 Announcements s Project 1 is done! s Written 1 is out and is due next week Monday s Homework policy – see website! 2 Today s Finish up Search and CSPs s Intermezzo on A* and heuristics s Start on Adversarial Search 3 CSPs: our status s CSPs are a special kind of search problem: s States defined by values of a fixed set of variables s Goal test defined by constraints on variable values s Backtracking = depth-first search with s Branching on only one variable per layer in search tree s Incremental constraint checks (“Fail fast”) s Heuristics at our points of choice to improve running time: s Ordering variables: Minimum Remaining Values and Degree Heuristic s Ordering of values: Least Constraining Value s Today: s Filtering: forward checking, arc consistency b enable computation of heuristics s Structure: Disconnected and tree-structured CSPs are efficient s Iterative improvement: min-conflicts is usually effective in practice 4 Example: Map-Coloring s Variables: s Domain: s Constraints: adjacent regions must have different colors s Solutions are assignments satisfying all constraints, e.g.: 6 Filtering: Forward Checking s Idea: Keep track of remaining legal values for unassigned variables (using immediate constraints) s Idea: Terminate when any variable has no legal values WA SA NT Q NSW V 7 [demo: forward checking animation]
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2 Filtering: Forward Checking s Forward checking propagates information from assigned to adjacent unassigned variables, but doesn't detect more distant failures: s NT and SA cannot both be blue! s Why didn’t we detect this yet? s Constraint propagation repeatedly enforces constraints (locally) WA SA NT Q NSW V 8 Consistency of An Arc s An arc X Y is consistent iff for every x in the tail there is some y in the head which could be assigned without violating a constraint s What happens? s Forward checking = Enforcing consistency of each arc pointing to the new assignment WA SA NT Q NSW V 9 Delete from tail! Arc Consistency of a CSP s Simplest form of propagation makes each arc consistent s X Y is consistent iff for every value x there is some allowed y WA SA NT Q NSW V 10 • If X loses a value, neighbors of X need to be rechecked! • Arc consistency detects failure earlier than forward checking • What’s the downside of arc consistency? • Can be run as a preprocessor or after each assignment Establishing Arc Consistency s Runtime: O(n 2 d 3 ), can be reduced to O(n 2 d 2 ) s … but detecting all possible future problems is NP-hard – why? 11 [demo: arc consistency animation] 12 Limitations of Arc Consistency s After running arc consistency: s Can have one solution left s Can have multiple solutions left s Can have no solutions left (and not know it) What went wrong here?
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SP11 cs188 lecture 6 -- adversarial search 6PP -...

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