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Lecture

Connect Four: Alpha-Beta Pruning and Monte-Carlo Tree Search

Description

This lecture presents the application of game theory to solve Connect Four using the minimax algorithm, optimizing it with alpha-beta pruning, and comparing it with the Monte-Carlo tree search algorithm. The lecture discusses the principles of alpha-beta pruning, the performance comparison with minimax, and the working principles of Monte-Carlo. It also contrasts Monte-Carlo with alpha-beta, highlighting their respective computational characteristics. Special thanks are given to Anna Maddux, Giulio Salizzoni, and Professor Maryam Kamgarpour for their support.

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Related concepts (32)

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Alpha–beta pruning

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.). It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further.

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

Quantum complexity theory

Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA.

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