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Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games ( Tic-tac-toe , Chess , Connect 4 , etc.).
Bruce Ballard was the first to develop a technique, called *-minimax, that enables alpha-beta pruning in expectiminimax trees. [3] [4] The problem with integrating alpha-beta pruning into the expectiminimax algorithm is that the scores of a chance node's children may exceed the alpha or beta bound of its parent, even if the weighted value of each child does not.
MuZero (MZ) is a combination of the high-performance planning of the AlphaZero (AZ) algorithm with approaches to model-free reinforcement learning. The combination allows for more efficient training in classical planning regimes, such as Go, while also handling domains with much more complex inputs at each stage, such as visual video games.
An aspiration window is a heuristic used in pair with alpha-beta pruning in order to reduce search time for combinatorial games by supplying a window (or range) around an estimated score guess. Use of an aspiration window allows alpha-beta search to compete in the terms of efficiency against other pruning algorithms .
Alpha–beta pruning works best when the best moves are considered first. This is because the best moves are the ones most likely to produce a cutoff , a condition where the game-playing program knows that the position it is considering could not possibly have resulted from best play by both sides and so need not be considered further.
MTD(f) is an alpha-beta game tree search algorithm modified to use ‘zero-window’ initial search bounds, and memory (usually a transposition table) to reuse intermediate search results. MTD(f) is a shortened form of MTD(n,f) which stands for Memory-enhanced Test Driver with node ‘n’ and value ‘f’. [ 1 ]
Alpha–beta pruning speeds the minimax algorithm by identifying cutoffs, points in the game tree where the current position is so good for the side to move that best play by the other side would have avoided it. Since such positions could not have resulted from best play, they and all branches of the game tree stemming from them can be ignored.
Since he had only a very limited amount of available computer memory, Samuel implemented what is now called alpha-beta pruning. [12] Instead of searching each path until it came to the game's conclusion, Samuel developed a scoring function based on the position of the board at any given time.