1.1 CAS CS 460/660 Introduction to Database Systems Fall 2015.
CS 460 Spring 2011
description
Transcript of CS 460 Spring 2011
![Page 1: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/1.jpg)
CS 460Spring 2011
Lecture 4
![Page 2: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/2.jpg)
Overview
• Review• Adversarial Search / Game Playing– (chap 5 3rd ed, chap 6 2nd ed)
![Page 3: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/3.jpg)
Review• Evaluation of strategies
– Completeness, time & space complexity, optimality• Informed Search
– Best First– Greedy Best First– Heuristics: A*
• Admissible, Consistent• Relaxed problems• Dominance
• Local Search– Hill climbing / gradient ascent– Simulated annealing– K-beam– Genetic algorithms
![Page 4: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/4.jpg)
Game playing /Adversarial search
![Page 5: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/5.jpg)
![Page 6: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/6.jpg)
![Page 7: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/7.jpg)
Game tree (2-player, deterministic, turns)
![Page 8: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/8.jpg)
![Page 9: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/9.jpg)
Minimax
![Page 10: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/10.jpg)
Properties of minimaxComplete? Yes (if tree is finite)•• Optimal? Yes (against an optimal opponent)•• Time complexity? O(bm)•• Space complexity? O(bm) (depth-first exploration)•
• For chess, b ≈ 35, m ≈100 for "reasonable" games exact solution completely infeasible
• Do we need to explore every path?•
![Page 11: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/11.jpg)
α-β pruning example
![Page 12: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/12.jpg)
α-β pruning example
![Page 13: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/13.jpg)
α-β pruning example
![Page 14: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/14.jpg)
α-β pruning example
![Page 15: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/15.jpg)
α-β pruning example
![Page 16: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/16.jpg)
Properties of α-βPruning does not affect final result•
Good move ordering improves effectiveness of pruning•
• With "perfect ordering," time complexity = O(bm/2) doubles solvable depth of search
• A simple example of the value of reasoning about which computations are relevant (a form of metareasoning)
• Unfortunately, 35**50 is still an impossible number of searches•
![Page 17: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/17.jpg)
Why is it called α-β?
α is the value of the best (i.e., highest-value) choice found so far at any choice point along the path for max•• If v is worse than α, max will avoid it•• prune that branch
Define β similarly for min•
![Page 18: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/18.jpg)
Alpha-beta algorithm
![Page 19: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/19.jpg)
![Page 20: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/20.jpg)
![Page 21: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/21.jpg)
![Page 22: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/22.jpg)
![Page 23: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/23.jpg)
![Page 24: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/24.jpg)
![Page 25: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/25.jpg)
![Page 26: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/26.jpg)
![Page 27: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/27.jpg)
![Page 28: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/28.jpg)
![Page 29: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/29.jpg)
![Page 30: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/30.jpg)
![Page 31: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/31.jpg)
![Page 32: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/32.jpg)
![Page 33: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/33.jpg)
![Page 34: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/34.jpg)
![Page 35: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/35.jpg)
![Page 36: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/36.jpg)
![Page 37: CS 460 Spring 2011](https://reader035.fdocuments.net/reader035/viewer/2022062410/568162af550346895dd3326c/html5/thumbnails/37.jpg)