AI Spring 2010 Lecture 6

AI Spring 2010 Lecture 6 - Artificial Intelligence Lectures...

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Click to edit Master subtitle style Artificial Intelligence Lectures 6: Beyond Classical Search Spring 2010 Instructor: Paul S. Rosenbloom
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22 Relaxing Assumptions £ Systematic exploration of search space l Local search and optimization £ l Contingency planning and belief states £ Domain model exists for search l Online search algorithms
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33 Local Search and Optimization £ Prior focus l Path to goal is solution to problem l Systematic exploration of search space l For completeness and to find optimal path £ Yet, for some problems path is irrelevant l E.g, eight queens £ And for other problems systematicity is either infeasible (size of space) or unnecessary £ In these cases, different algorithms can/should be used l Local search/optimizations algorithms l Greedy algorithms: f(n) = h(n)
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44 Local Search and Optimization (2) £ Remember only single current state l Memory usage is essentially constant £ Move only to neighboring states l No systematic backtracking, priority queues, jumping along frontier Random walk is one example, but mostly will be guided by state evaluations
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55 Local Search and Optimization (2) £ Remember only single current state l Memory usage is essentially constant £ Move only to neighboring states l No systematic backtracking, priority queues, moving along a fringe £ Advantages: l Use very little memory l Often find reasonable solutions in large or infinite state spaces £ Are also useful for pure optimization problems (no goal) l Find best state according to some objective function ( Objective and evaluation functions are essentially the same things
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66 Hill Climbing £ Move continuously in the direction of increasing value l Go to best successor of current state, based on evaluation l If more than one best successor, pick randomly among them £ Terminate when reach a peak l May only find a local maximum £ This form of hill climbing is also referred to as l Steepest-ascent hill climbing l Greedy local search l Continuous analogue is gradient ascent
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77 Hill-Climbing Algorithm function HILL-CLIMBING( problem ) return a state that is a local maximum current ± MAKE-NODE( problem .INITIAL-STATE) loop do neighbor a highest valued successor of current if neighbor .VALUE ≤ current .VALUE then return current .STATE current neighbor
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88 Hill-Climbing Example £ Eight queens problem l Complete-state formulation ( As opposed to incremental formulation £ Successor function l Move a single queen to another square in the same column £ Heuristic function h(n) l The number of pairs of queens that are attacking each other l Either directly or indirectly; i.e, in same row, column or diagonal l Value here is 17
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99 Results £ Works quickly l 3-4 steps on average with state space of 88 · 17 million states £ Gets stuck often (86% of the time) because of local maxima l h(n) =1 here, and can’t reduce further by a single move £ Plateaus can lead to wandering l An area of the state space where the evaluation function is flat
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This note was uploaded on 03/05/2010 for the course CS 561 taught by Professor Moradi during the Spring '09 term at USC.

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AI Spring 2010 Lecture 6 - Artificial Intelligence Lectures...

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