Artificial Intelligence

Transcription

1 Artificial Intelligence Jeff Clune Assistant Professor Evolving Artificial Intelligence Laboratory

2 Please speak up if you don t get something! When traveling, people always say yes or nod even when they don t know the question Very difficult! are you sure this gun isn t loaded? can I slap you in the face?

3 Probability When to add vs. multiply? Probability of rolling: - P(1 ^ 2 ^ 3 ^4 ^ 5) in order for 5 rolls of one die - P(1 v 2 v 3 v 4 v 5) in 1 roll of one die On your own

4 Probability When to add vs. multiply? Intuition: X AND Y = less likely - stranger is tall AND fat AND bald AND funny X OR Y = more likely - stranger is tall OR fat OR bald OR funny Probability of rolling: - 1 ^ 2 ^ 3 ^4 ^ 5? - 1 v 2 v 3 v 4 v 5?

5 The Gambler Every gambler knows that the secret to survivin' Is knowin' what to throw away and knowing what to keep 'Cause every hand's a winner and every hand's a loser

6 The Gambler Every gambler knows that the secret to survivin' Is knowin' what to throw away and knowing what to keep 'Cause every hand's a winner and every hand's a loser And the best that you can hope for is to die in your sleep to maximize expected reap!

7 AI Challenge Two! Due Sept. 18th this Sunday! because we split a large one into two

8 Overview Breadth-First Search Depth-First Search Image credit: Wikipedia

9 Problem Difficulty (for Graphs) b: branching factor Goal: 23 maximum number of successors per node - e.g. chess: 35 (average, not max) d: depth shallowest goal node m: maximum length of any path in the state space What are b, d, & m?

10 Depth-First Search: Complexity (Graph) time: O(b m ) space: O(b m ) visited = [0] * V DFS(v): visited[v] = 1 for node in connectedto(v): if!visited[node]: DFS(w)

11 Depth-First Search: Complexity (Tree) time: O(b m ) space: O(b m ) size of example space: Chess: ~ (Shannon 1950) Branching factor ply typical (ply = each piece moved) Go: branching factor ~361

12 Modified Depth-First Search? Only works for trees, not graphs time: O(b m ) space: O(bm)!! Space w/ Deep Blue d = 20 b = ~ vs. 2.2 trillion!! visited = [0] * N DFS(v): visited[v] = 1 for node in connectedto(v): if!visited[node]: DFS(w)

13 Backtracking Depth-First Search Only works for trees, not graphs time: O(b m ) space: O(m) If each node tells you which child to expand next, you don t store b nodes at each depth m, hence O(m)

14 Breadth-First Search Breadth-First Search Depth-First Search

15 Breadth-First Search same colors intentionally vague shortest path! put start node in queue, with pathlength 0, mark gray for node at start of queue: add non-visited node.neighbors to queue, with node.pathlength +1, mark gray/visited remove node from queue r s t u Queue: s r w t x v u y v w x y

16 Shortest Path DFS DFS BFS

17 Breadth-First Search spanning tree r s t u s w r t x v v w x y u y

18 Breadth-First Search: Complexity r s t u time: O(b d ) space: O(b d ) v w x y time same as (unmodified) DFS i.e. same on graphs (with cycles) space much larger than modified DFS i.e. on trees.dfs has no space advantage on graphs

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20 Review of BFS vs. DFS Breadth-First Search Depth-First Search many short paths Prioritizes fewer long paths (slight victory) Time Complexity O(b d ) O(b m ) O(b d ) Space Complexity graph: O(b m ), tree: O(m) (slight victory) Optimal? (Shortest Path?) Complete? (Guaranteed Solution?) Spanning Tree Queue Data Structure Stack

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22 Uniform Cost Search Extension of BFS that expands node with cheapest path cost first Note Goal check when expanded, not when added Replace in frontier if lowerpath cost discovered Try it in pairs! Start: Sibiu Goal: Bucharest

23 Uniform Cost Search Extension of BFS that expands node with cheapest path cost first Should have found: S to RV to P to B

24 Uniform Cost Search Extension of BFS that expands node with cheapest path cost first Previously we did not find the shortest path to Bucharest!

25 Uniform Cost Search Extension of BFS that expands node with cheapest path cost first Optimal with Variable Path Cost Time & Space Complexity a Bit Complicated: See p. 85 in Book

26 Depth-Limited Search Easy solution for cycles in DFS: limit depth

27 Iterative Deepening DFS for i=1 to infinityandbeyond! limiteddfs(i) Optimal? Complete? Time Complexity? Space Complexity?

28 Iterative Deepening DFS for i=1 to infinityandbeyond! limiteddfs(i) Optimal? Yes (if path cost does not decrease with depth) Complete? Yes (when b is finite) Time Complexity? O(b d ) [surprising! and better than b m ] Space Complexity? O(d) [assumes backtracking DFS]

29 Iterative Deepening DFS Number of nodes expanded at depth d

30 Iterative Deepening DFS Combines best of DFS and BFS without much overhead Generally the preferred uninformed search algorithm for large search spaces when d is unknown

31 Review of uninformed search

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