ErrFreeYttrium
·

Start Quiz

Study Flashcards

## 10 Questions

### What is the purpose of the alpha-beta algorithm in game search space generation?

To prune large chunks of the trees

### Why is the alpha-beta algorithm considered impractical for real-time decisions?

It still requires beta to traverse the entire tree

### In the context of game evaluation, what does 'eval(s)' represent?

An evaluation function to estimate the value of current board configurations

### What is the primary function of an ideal evaluation function in gaming scenarios?

To rank terminal states like the true utility function

### How are nonterminal nodes converted into terminal leaves in game evaluation?

By using an evaluation function like 'eval(s)'

### What is a common strategy to craft an effective evaluation function in gaming scenarios?

Define features and create a linear weighted sum of these features

### How does Deep Blue utilize domain knowledge in making game predictions?

By defining thousands of features based on chess domain knowledge

~6,000

### 'Minimax' and 'alpha-beta algorithm' are primarily utilized for optimizing which aspect of gaming?

Game search space generation efficiency

### 'Cut off search' is implemented to address what challenge in real-time decision-making processes?

'Move time constraints' requirement

## Study Notes

### The 8 Queens Puzzle

• The 8 queens puzzle is a problem where a queen attacks any piece in the same row, column, or diagonal.
• The goal is to find a solution where 8 queens can be placed on a chessboard without attacking each other.

### The Travelling Problem

• The initial state is In(Arad), with applicable actions being {Go(Sibiu), Go(Timisoara), Go(Zerind)}.
• The transition model is specified by the function RESULT(s, a), which returns the state that results from action a in state s.
• The goal state is {In(Bucharest)}, and the path cost is a function that assigns a numeric cost to each path.

### Search Trees

• A node denotes some state or value.
• The root is the top node in a tree, and a child is a node directly connected to another node when moving away from the root.
• A parent is the converse notion of a child, and a leaf is a node with no children.
• An internal node is a node with at least one child.
• An edge is the connection between one node and another.
• The depth is the distance between a node and the root, and the level is the number of edges between a node and the root +1.
• The height is the number of edges on the longest path between a node and a descendant leaf, and the breadth is the number of leaves.

### Minimax Algorithm

• Minimax is a search algorithm used for decision-making in games like chess and tic-tac-toe.
• The algorithm assumes that both players, Max and Min, play optimally.
• The minimax value is the best achievable utility against an optimal adversary.
• The minimax algorithm computes the utility of being in a state, assuming both players play optimally from there until the end of the game.
• The algorithm propagates minimax values up the tree once terminal nodes are discovered.

• Adversarial search is a search algorithm used for decision-making in games like chess and tic-tac-toe.
• The algorithm assumes that both players, Max and Min, play optimally.
• The algorithm computes the utility of being in a state, assuming both players play optimally from there until the end of the game.
• The algorithm propagates minimax values up the tree once terminal nodes are discovered.

### Minimax Example

• If the state is a terminal node, the value is the utility of the state.
• If the state is a Max node, the value is the highest value of all successor node values.
• If the state is a Min node, the value is the lowest value of all successor node values.

### Properties of Minimax

• The minimax algorithm is optimal and complete, meaning it will find the best move if the game tree is finite.
• The time complexity of the algorithm is O(bd), where b is the branching factor and d is the depth of the game tree.
• The space complexity of the algorithm is O(bd).

### Alpha-Beta Pruning

• Alpha-beta pruning is a variant of the minimax algorithm that reduces the number of nodes to be evaluated.
• The algorithm keeps track of two bounds, α and β, which are the current lower bound on Max's outcome and the current upper bound on Min's outcome, respectively.
• The algorithm propagates α and β values down during the search to be used for pruning.
• The algorithm updates α and β values by propagating upwards values of terminal nodes.
• The algorithm prunes any remaining branches whenever α ≤ β.

### Real-time Decisions

• Real-time decisions are necessary in games like chess, where moves have to be made in a reasonable amount of time.
• One solution is to bound the depth of search and replace utility(s) with eval(s), an evaluation function that estimates the value of current board configurations.
• The evaluation function is a heuristic that ranks terminal states in the same way as the true utility function.
• The evaluation function is typically a linear weighted sum of features, which are domain-specific characteristics of the game.

Test your knowledge on finding the optimal strategy for Max using the minimax algorithm in adversarial search. Understand the depth-first search of the game tree, the minimax principle, and propagating minimax values up the tree.

## Make Your Own Quizzes and Flashcards

Convert your notes into interactive study material.

## More Quizzes Like This

5 questions
16 questions
30 questions
Use Quizgecko on...
Browser
Information:
Success:
Error: