SP11 cs188 lecture 4 -- CSPs 6PP

# SP11 cs188 lecture - CS 188 Artificial Intelligence Spring 2011 Announcements Project 1(Search If you dont have a class account yet pick one up

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 4: A* + (beginnings of) Constraint Satisfaction 1/31/2011 Pieter Abbeel – UC Berkeley Many slides from Dan Klein and Max Likhachev Announcements s Project 1 (Search) s If you don’t have a class account yet, pick one up after lecture s Still looking for project partners? --- Come to front after lecture s Lecture videos s In the works Today s A* (tree) search s Admissible heuristics s Graph search s Consistent heuristics s Extensions s Weighted A*: f = g + eps h s Anytime A* s Memory issue (O(n)) b IDA* s Bi-directional s Example Applications s (Beginnings of CSPs) 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) 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 Proof forthcoming s Heuristic design is key: relaxed problems can help s Special cases: s Greedy: g = 0 [non-optimal!] s Uniform cost: h = 0 [optimal]

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2 Comparison Uniform Cost Greedy A star UCS vs A* Contours s Uniform-cost expanded in all directions s A* expands mainly toward the goal, but does hedge its bets to ensure optimality Start Goal Start Goal Creating Admissible Heuristics s Most of the work in solving hard search problems optimally is in coming up with admissible heuristics s Often, admissible heuristics are solutions to relaxed problems, with new actions (“some cheating”) available s Inadmissible heuristics are often useful too (why?) 15 366 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 Example: 8 Puzzle s What are the states? s How many states? s What are the actions? s What states can I reach from the start state? s What should the costs be? 8 Puzzle I s Heuristic: Number of tiles misplaced s Why is it admissible? s h(start) = s This is a relaxed- problem heuristic 8 Average nodes expanded when optimal path has length… …4 steps …8 steps …12 steps UCS 112 6,300 3.6 x 10 6 TILES 13 39 227
3 8 Puzzle II s What if we had an easier 8-puzzle where any tile could slide any direction at any time, ignoring other tiles?

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## This note was uploaded on 08/26/2011 for the course CS 188 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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SP11 cs188 lecture - CS 188 Artificial Intelligence Spring 2011 Announcements Project 1(Search If you dont have a class account yet pick one up

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