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Minmax Algorithm In Artificial Intelligence slides
The mini-max algorithm is a recursive decision-making strategy used in game theory, where two players (max and min) aim to optimize their respective scores by exploring a game tree. It performs a depth-first search to evaluate all possible game states and backtracks to maximize or minimize scores based on terminal node values. While it guarantees a solution in finite search trees and is optimal under perfect play, its time and space complexity is O(bm), making it inefficient for complex games with high branching factors, which can be mitigated through alpha-beta pruning.
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Introduction to the Mini-Max algorithm in Artificial Intelligence for decision-making and game theory.
Details on how the Mini-Max algorithm uses recursion, game-tree searching, and player roles (MAX and MIN) in games.
Explains the completeness, optimality, time complexity (O(bm)), and space complexity (O(bm)) of the Mini-Max algorithm.
Discusses the limitations of the Mini-Max algorithm, particularly its inefficiency in complex games with high branching factors.
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Minmax Algorithm In Artificial Intelligence slides
- 1.Mini-Max Algorithm inArtificialIntelligence
- 2. Mini-max algorithmis a recursive or backtracking algorithm whichis used in decision-making and game theory. Mini-Max algorithm uses recursion to search through the game-tree. In this algorithm two players play the game, one is called MAXand other is called MIN.
- 3. Both theplayers fight it as the opponent player gets the minimum benefit while they getthe maximum benefit. The minimax algorithm performs a depth-first search algorithm for the exploration of thecomplete game tree. The minimax algorithm proceeds all the way down to the terminal node of the tree, thenbacktrack the tree as the recursion.
- 4.Working An exampleof game-tree which is representing the two-player game. In this example, there are two players one is called Maximizer and other iscalled Minimizer. Maximizer will try to get the Maximum possible score, and Minimizer willtry to get the minimum possible score.
- 5. This algorithmapplies DFS, so in this game-tree, we have to go all the way through theleaves to reach the terminal nodes. At the terminal node, the terminal values are given so we will compare those value andbacktrack the tree until the initial state occurs.
- 10.Properties Complete- Min-Maxalgorithm is Complete. It will definitely find asolution (if exist), in the finite search tree. Optimal- Min-Max algorithm is optimal if both opponents are playingoptimally. Time complexity- As it performs DFS for the game-tree, so the timecomplexity of Min-Max algorithm is O(bm), where b is branching factor ofthe game-tree, and m is the maximum depth of the tree. Space Complexity- Space complexity of Mini-max algorithm is also similarto DFS which is O(bm).
- 11.Limitation The maindrawback of the minimax algorithm is that it gets really slow forcomplex games such as Chess, go, etc. This type of games has a hugebranching factor, and the player has lots of choices to decide. Thislimitation of the minimax algorithm can be improved from alpha-betapruning.