1 / 37

CS 460 Spring 2011

CS 460 Spring 2011. Lecture 4. Overview. Review Adversarial Search / Game Playing (chap 5 3 rd ed , chap 6 2 nd ed ). Review. Evaluation of strategies Completeness, time & space complexity, optimality Informed Search Best First Greedy Best First Heuristics: A* Admissible, Consistent

freya
Download Presentation

CS 460 Spring 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS 460Spring 2011 Lecture 4

  2. Overview • Review • Adversarial Search / Game Playing • (chap 5 3rded, chap 6 2nded)

  3. 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

  4. Game playing /Adversarial search

  5. Game tree (2-player, deterministic, turns)

  6. Minimax

  7. Properties of minimax • Complete? 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?

  8. α-β pruning example

  9. α-β pruning example

  10. α-β pruning example

  11. α-β pruning example

  12. α-β pruning example

  13. Properties of α-β • Pruning 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

  14. 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 Why is it called α-β?

  15. Alpha-beta algorithm

More Related