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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
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CS 460Spring 2011 Lecture 4
Overview • Review • Adversarial Search / Game Playing • (chap 5 3rded, chap 6 2nded)
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
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?
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
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?