lecture 4 - CS 188 Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 4: Constraint Satisfaction 1/28/2010 Pieter Abbeel – UC Berkeley Many slides from Dan Klein Announcements s Project 0 (Python tutorial) is due today s Written 1 (Search) is due today s Project 1 (Search) is out and due next week Thursday
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2 Today s Search Conclusion s Constraint Satisfaction Problems Recap: Search s Search problem: s States (configurations of the world) s Successor function: a function from states to lists of (state, action, cost) triples; drawn as a graph s Start state and goal test s Search tree: s Nodes: represent plans for reaching states s Plans have costs (sum of action costs) s Search Algorithm: s Systematically builds a search tree s Chooses an ordering of the fringe (unexplored nodes)
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3 General Tree Search s Important ideas: s Fringe s Expansion s Exploration strategy s Main question: which fringe nodes to explore? Detailed pseudocode is in the book! A* Review s A* uses both backward costs g and forward estimate h: f(n) = g(n) + h(n) s A* tree search is optimal with admissible heuristics (optimistic future cost estimates) s Heuristic design is key: relaxed problems can help
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4 Admissible Heuristics s A heuristic h is admissible (optimistic) if: where is the true cost to a nearest goal s Example: s Coming up with admissible heuristics is most of what’s involved in using A* in practice. 15 Optimality of A*: Blocking Notation: s g(n) = cost to node n s h(n) = estimated cost from n to the nearest goal (heuristic) s f(n) = g(n) + h(n) = estimated total cost via n s G*: a lowest cost goal node s G: another goal node
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5 Optimality of A*: Blocking Proof: s What could go wrong? s We’d have to have to pop a suboptimal goal G off the fringe before G* s This can’t happen: s Imagine a suboptimal goal G is on the queue s Some node n which is a subpath of G* must also be on the fringe (why?) s n will be popped before G Tree Search: Extra Work! s Failure to detect repeated states can cause exponentially more work. Why?
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6 Graph Search s Very simple fix: never expand a state twice s Can this wreck completeness? Optimality? Optimality of A* Graph Search
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This note was uploaded on 04/21/2010 for the course EECS 188 taught by Professor Cs188 during the Spring '01 term at Berkeley.

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lecture 4 - CS 188 Artificial Intelligence Spring 2010...

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