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G51I AI Introduction to AI Andrew Parkes Game Playing 2: Alpha-Beta Search and General Issues

Game Playing – Summary So Far ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

= terminal position = agent = opponent 1 MAX MIN MAX A Recap of (depth-bounded) minimax: D E F G 4 -5 -5 1 -7 2 -3 -8 4 1 2 -3 1 -3 B C

Game Playing – Beyond Minimax ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Improving Efficiency ,[object Object],[object Object]

Game Playing – Minimax using DFS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

A 6 5 8 MAX MIN 6 >=8 MAX <=6 = agent = opponent On discovering util( D ) = 6 we know that util( B ) <= 6 On discovering util( J ) = 8 we know that util( E ) >= 8 STOP! What else can you deduce now!? STOP! What else can you deduce now!? Can stop expansion of E as best play will not go via E Value of K is irrelevant – prune it! STOP! What else can you deduce now!? B C D E H I J K

Game Playing – Pruning nodes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Self-Study Suggestion ,[object Object],[object Object],[object Object]

Game Playing – Improving Efficiency ,[object Object],[object Object],[object Object]

Game Playing – Node-ordering ,[object Object],[object Object],[object Object],[object Object],[object Object]

A 6 5 2 MAX MIN 6 >=2 MAX <=6 = agent = opponent On discovering util( D ) = 6 we know that util( B ) <= 6 On discovering util( K ) = 2 we know that util( E ) >= 2 STOP! What else can you deduce now!? STOP! What else can you deduce now!? Can NOT stop expansion of E as best play might still go via E Value of J is relevant – no pruning STOP! What else can you deduce now!? 8 B C D E H I K J

Game Playing – Node-ordering ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

A 6 5 8 MAX MIN 6 >=8 MAX 6 = agent = opponent 2 1 2 <=2 >=6 B C D E F G H I J K L M

Game Playing – Alpha-Beta Implementation ,[object Object],[object Object],[object Object],[object Object]

A 6 5 8 MAX MIN 6 α = 8 MAX β = 6 = agent = opponent 2 1 2 2 6 beta pruning as α (E) > β (B) alpha pruning as β (C) < α (A) Alpha-beta Pruning B C D E F G H I J K L M

Game Playing – Deficiencies of Minimax ,[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Non-Quiescence ,[object Object],[object Object]

= terminal position = agent = opponent 4 direct, but 1 by minimax MIN MAX A B Utility values of “terminal” positions obtained by an evaluation function Example of non-quiescence Direct evaluation does not agree with one more expansion and then using of minimax 1 -3 B C

Game Playing – Quiescence Search ,[object Object],[object Object],[object Object]

Game Playing – Horizon Effect ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Beyond alpha-beta ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Game Classification ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Playing – Game Classification ,[object Object],[object Object],[object Object],[object Object]

Game Playing – Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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