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CS 460 Spring 2011

Review of game playing and adversarial search strategies. Evaluating completeness, complexity, and optimality. Introduction to informed search techniques like A* with admissible and consistent heuristics. Overview of local search algorithms including hill climbing and genetic algorithms.

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CS 460 Spring 2011

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  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

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