CS 416 Artificial Intelligence Lecture Lecture 66 Informed Informed Searches Searches Chess Match Kasparov Kasparov 1 1 Deep Deep Junior Junior 1 1 Draws Draws 22 Compare two heuristics Compare these two heuristics hh22 is is always always better better than than hh11 for for any any node node n n hh22 n n hh11 n n hh22 dominates dominates hh11 Recall Recall all all nodes nodes with with f n f n C C will will be be expanded expanded This This means means all all nodes nodes h n h n C C g n g n will will be be expanded expanded All All nodes nodes hh22 expands expands will will also also be be expanded expanded by by hh11 and and because because hh11 is is smaller smaller others others will will be be expanded expanded as as well well Inventing admissible heuristic funcs How How can can you you create create h n h n Simplify Simplify problem problem by by reducing reducing restrictions restrictions on on actions actions Allow Allow 8 puzzle 8 puzzle pieces pieces to to sit sit atop atop on on another another Call Call this this aa relaxed relaxed problem problem The The cost cost of of optimal optimal solution solution to to relaxed relaxed problem problem is is admissible admissible heuristic heuristic for for original original problem problem ItIt is is at at least least as as expensive expensive for for the the original original problem problem Examples of relaxed problems A A tile tile can can move move from from square square A A to to square square B B ifif A A is is horizontally horizontally or or vertically vertically adjacent adjacent to to B B and and B B is is blank blank A A tile tile can can move move from from A A to to B B ifif A A is is adjacent adjacent to to B B overlap overlap A A tile tile can can move move from from A A to to B B ifif B B is is blank blank teleport teleport A A tile tile can can move move from from A A to to B B teleport teleport and and overlap overlap Solutions Solutions to to these these relaxed relaxed problems problems can can be be computed computed without without search search and and therefore therefore heuristic heuristic is is easy easy to to compute compute Multiple Heuristics IfIf multiple multiple heuristics heuristics available available h n h n max max h h11 n n hh22 n n hhmm n n Use solution to subproblem as heuristic What What is is optimal optimal cost cost of of solving solving some some portion portion of of original original problem problem subproblem subproblem solution solution is is heuristic heuristic of of original original problem problem Pattern Databases Store Store optimal optimal solutions solutions to to subproblems subproblems in in database database We We use use an an exhaustive exhaustive search search to to solve solve every every permutation permutation of of the the 1 2 3 4 1 2 3 4 piece piece subproblem subproblem of of the the 8 puzzle 8 puzzle During During solution solution of of 8 puzzle 8 puzzle look look up up optimal optimal cost cost to to solve solve the the 1 2 3 4 1 2 3 4 piece piece subproblem subproblem and and use use as as heuristic heuristic Learning Could database while Could also also build build pattern pattern database while solving solving cases cases of of the the 8 puzzle 8 puzzle Must Must keep keep track track of of intermediate intermediate states states and and true true final final cost cost of of solution solution Inductive Inductive learning learning builds builds mapping mapping of of state state cost cost Because Because too too many many permutations permutations of of actual actual states states Construct Construct important important features features to to reduce reduce size size of of space space Local Search Algorithms and Optimization Problems Characterize Techniques Uninformed Uninformed Search Search Looking Looking for for aa solution solution where where solution solution is is aa path path from from start start to to goal goal At At each each intermediate intermediate point point along along aa path path we we have have no no prediction prediction of of value value of of path path Informed Informed Search Search Again Again looking looking for for aa path path from from start start to to goal goal This This time time we we have have insight insight regarding regarding the the value value of of intermediate intermediate solutions solutions Now change things a bit What What ifif the the path path isn t isn t important important just just the the goal goal So So the the goal goal is is unknown unknown The The path path to to the the goal goal need need not not be be solved solved Examples Examples What What quantities quantities of of quarters quarters nickels nickels and and dimes dimes add add up up to to 17 45 17 45 and and minimizes minimizes the the total total number number of of coins coins Is Is the the price price of of Microsoft Microsoft stock stock going going up up tomorrow tomorrow Local Search Local Local search search does does not not keep keep track track of of previous previous solutions solutions Instead Instead itit keeps keeps track track of of current current solution solution current current state state Uses Uses aa method method of of generating generating alternative alternative solution solution candidates candidates Advantages Advantages Use Use aa small small amount amount of of memory memory usually usually constant constant amount amount They They can can find find reasonable reasonable note note we we aren t aren t saying saying optimal optimal solutions solutions in in infinite infinite search search spaces spaces Optimization Problems Objective Objective Function Function A A function function with with vector vector inputs inputs and and scalar scalar output output goal goal is is to to search search through through candidate candidate input input vectors vectors in in order order to to minimize minimize or or maximize maximize objective objective function function Example Example ff q q d d n n 1 000 000 1 000 000 ifif q 0 25 q 0 25 d 0 1 d 0 1 n 0 05 n 0 05 17 45 17 45 qq nn dd otherwise otherwise minimize minimize ff Search Space The The realm realm of of feasible feasible input input vectors vectors Also Also called called state state space space landscape landscape Usually Usually described described by by number number of of dimensions dimensions 3 3 for for our our change change example example domain domain of of dimensions dimensions q q is is discrete discrete from from 00 to to 69 69 nature nature of of relationship