Artificial Intelligence

Transcription

1 Artificial Intelligence Jeff Clune Assistant Professor Evolving Artificial Intelligence Laboratory

2 AI Challenge One Transform to graph Explore the graph, looking for? dust unexplored squares

3 Some good solutions 2013 champ: 0.97 AI Challenge One Move greedily towards dust or unexplored tiles in sensor range. Otherwise start a BFS toward nearest unexplored tile champ: 0.98 BFS with a maximum depth of 2 towards either dust or unexplored tile If nothing found: run simple reflex agent (move randomly for the most part) Ross (2015): 0.998!!!!! Uniform Cost Search (effectively BFS) toward dust first, if no known dust UCS toward unexplored tile instead

4 How was it? AI Challenge Two?

5 AI Challenge Three! Due: Sept. 27th This Sunday!

6 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

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

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

9 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

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

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

12 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]

13 Iterative Deepening DFS Number of nodes expanded at depth d

14 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

15 Review of uninformed search

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17 Informed Search Best-first most important - Greedy search - A* Tree Search/Graph Search - expand according to evaluation function - e.g cheapest first - a heuristic is used - e.g. straight-line distance

18 Greedy Search aka best-first expand the node closest to the goal

19 Greedy Search aka best-first Try It! expand the node closest to the goal (Bucharest)

20 Greedy Search Expand closest node to Bucharest first: Arad, Sibiu, Fagaras, Bucharest - not optimal! - Arad, Sibiu, Vilcea, Pitesti, Bucharest is shorter

21 Greedy Search Also not complete From Iasi, get to Fagaras - Neamt, Iasi, Neamt, Iasi, ad infinitum - Problem: solution requires moving away from the goal - remind you of anything? (EC people?) - note: graph search version is complete

22 A* pronounced A-star node evaluation: f(n): g(n) + h(n) - g(n): cost to reach node - h(n): heuristic estimate for node to goal

23 A* if the heuristic follows certain conditions, it s both optimal complete

24 Heuristic conditions (1 of 2) A* never overestimates the distance (i.e. err on the side of optimism) - i.e. I know with certainty that it takes at least X - critical because you trust the heuristic to decide which nodes *not* to expand - if h(n) overestimates an unexplored node and its wrong, that node may be a better path - which you d fail to discover, meaning incompleteness Imagine: First day of work, never heard of an elevator h(n) = 45 min h(n) = 2 hours If you get to the bottom in < 2 hours and you trust g(n) you d never try the elevator!

25 is straight-line distance admissible? A*

26 A* let s run a* on this map together use h(n) = as the crow flies Try it!

27 Note: Bucharest added to frontier in step e, but not expanded because the cost was not the cheapest - meaning there might still be a cheaper route

28 A* is setting the heuristic h(n) = 1 for each city admissible?

29 A* is setting the heuristic h(n) = 1 for each city admissible? why not just do that? try it in groups

30 A* is setting the heuristic g(n) = 1 for each city admissible? why not just do that? try it in groups was it better? worse?

31 A* is setting the heuristic g(n) = 1 for each city admissible? why not just do that? try it in groups was it better? worse? more accurate heuristics save time goal: be as accurate as possible while remaining admissible