1 Uninformed Search Strategies Slides drawn from Andrew Moore’s Machine Learning Tutorials:

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5 What problems do you think are like this?

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7 There are, however, a lot of search problems that DON’T fit this definition. Can you name some?? Definition of a Search Problem

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9 This is a game against an adversary This is a game of chance This one has hidden state This one has an infinite number of states This one  has all of the problems above

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24 What’s another way to search that avoids the need for pointers?

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50 AlgorithmComplete?Optimal?Time Complexity Space Complexity BFS UCS

51 AlgorithmComple te OptimalTime Complexity Space Complexity BFSYY ( if all transitions cost the same) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L )

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57 AlgorithmCompl ete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFS

58 AlgorithmCompl ete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFSNNN/A

59 OK, assume an ACYCLIC GRAPH AlgorithmCompl ete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFS**

60 OK, assume an ACYCLIC GRAPH AlgorithmCompl ete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFS**YNO(B LMAX )O(LMAX)

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62 Which might be the best solution? When?

63 AlgorithmComp lete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) PCDFS MEMDFS

64 AlgorithmComp lete Optim al Time Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) PCDFSYNO(B LMAX )O(LMAX) MEMDFSYNO(min(N,B LMAX ))

65 N S EW startWhat would BFS do?

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69 AlgorithmCompleteOptimalTime Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFS**YNO(B LMAX )O(LMAX) Iterative Deepening Back to judging the search algorithms

70 AlgorithmCompleteOptimalTime Complexity Space Complexity BFSYY ( if...) O(min(N,B L )) UCSYYO(log(Q)*min(N,B L ))O(min(N),B L ) DFS**YNO(B LMAX )O(LMAX) Iterative Deepening YY (if all transitions cost the same) O(B L )O(L) Back to judging the search algorithms

71 Heuristic Search In the searches we have covered so far, we never determine which states look most promising for expansion at a given time point. We never “look-ahead” to the goal. Often, however, we have some knowledge about the merit of states.

72 Heuristic functions We can encode each notion of the “ merit” of a state into a heuristic function, h(s). For planning a path through a maze? For solving a Rubick’s cube?

73 Euclidean distance as h(s) Say we want to plan a path from Arad to Bucharest, and we know the straight line distance from each city to our goal. This lets us plan our trip by picking cities at each time point that minimize the distance to our goal (or maximize our heuristic).

74 Greedy best first search This search strategy is called greedy best first search. How can it possibly go wrong??

75 Greedy best first search In red is the path we selected. In green is the shortest path between Arad and Bucharest. What happened?