CS 460Spring 2011

Lecture 4

Overview

• Review• Adversarial Search / Game Playing– (chap 5 3rd ed, chap 6 2nd ed)

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

Game playing /Adversarial search

Game tree (2-player, deterministic, turns)

Minimax

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?•

α-β pruning example

α-β pruning example

α-β pruning example

α-β pruning example

α-β pruning example

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•

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•

Alpha-beta algorithm