Lesson2 - The Checkers Problem - A well posed learning problem

To explain the concept of a well-posed learning problem, let's use the game of checkers.

Checkers: A Classic Game for All Ages

Checkers, also known as draughts, is a simple yet strategic board game enjoyed by people of all ages for centuries. 

Equipment:

• Checkers board: An 8x8 grid alternating light and dark squares.

• Checkers pieces: 12 light pieces and 12 dark pieces.

Objective:

The objective of checkers is to capture all of your opponent's pieces or render them immobile, leaving them with no legal moves.

Setup:

• Place the board so that a light square lies in the bottom right corner.

• Each player places their 12 pieces on the dark squares of the first three rows closest to them.

Movement:

• Players take turns moving their pieces.

• A piece can move one square diagonally forward onto an unoccupied dark square.

• A piece cannot move over other pieces.

Capturing:

• If a piece lands directly next to an opponent's piece in a diagonal direction and there is an unoccupied dark square beyond it, the capturing piece can jump over the opponent's piece and remove it from the board.

• A piece can continue to make multiple captures in the same turn as long as it jumps over an opponent's piece and lands on an unoccupied dark square beyond it.

Kinging:

• When a piece reaches the opposite side of the board (the last row), it becomes a "king."

• A king can move diagonally forward or backward one square onto an unoccupied dark square.

• Kings can also capture opponents' pieces by jumping over them in both directions.

Winning:

• A player wins when their opponent has no legal moves remaining or has lost all their pieces.

Additional Rules:

• If a player has multiple legal captures, they must make the capture that results in the most captured pieces.

• If two or more pieces can make the same capture, the capturing piece is chosen by the player.

• A player cannot move a piece if it does not result in a capture or move the piece closer to the opponent's side of the board.

Tips for Players:

• Focus on controlling the center of the board.

• Try to capture your opponent's pieces early on.

• Don't be afraid to sacrifice a piece if it means gaining a strategic advantage.

Additional Resource

https://www.wikihow.com/Play-Checkers

Checkers as a Well Posed Learning Problem

The checkers game can be considered a well-posed learning problem due to the following characteristics:

1. Clearly Defined Task:

The objective of checkers is explicitly defined as capturing all of your opponent's pieces or rendering them immobile. This clear goal provides a concrete target for learning algorithms to optimize towards.

2. Observable Environment:

The state of the checkers game is fully observable to both players. Each player can see the positions of all pieces on the board, enabling them to make informed decisions based on the current game state.

3. Performance Measure:

The outcome of a checkers game, win or loss, serves as a clear and unambiguous measure of performance. This allows learning algorithms to evaluate the effectiveness of their strategies and adjust accordingly.

4. Finite Action Space:

Each player has a finite set of possible actions they can take on their turn, limited to moving their pieces according to the rules of the game. This finite action space simplifies the problem for learning algorithms to explore and exploit.

5. Diverse Training Data:

With numerous possible moves and board states, checkers offers a vast amount of diverse training data for learning algorithms. This diversity helps to ensure that the learned strategies are generalizable and resilient to unexpected situations.

6. Efficient Evaluation:

The outcome of a checkers game can be determined relatively quickly and efficiently. This allows for rapid feedback and evaluation of learning algorithms, enabling them to learn and improve at a faster rate.

7. Reproducible Results:

The rules of checkers are well-defined and consistent, ensuring that the results of learning algorithms are reproducible and reliable. This allows for fair comparisons and verification of performance across different learning methods.

8. Availability of Data and Tools:

Datasets of checkers games and open-source implementations of checkers engines are readily available. This readily accessible data and tools facilitate research and development of new learning algorithms for checkers.

Complexities

While checkers possesses most of the characteristics of a well-posed learning problem, it is worth noting that some complexities exist, such as:

• Evaluating long-term strategies: 

Evaluating the effectiveness of a move often requires considering its impact on the future game state, adding a layer of complexity.

• Dealing with randomness: 

While the game rules are deterministic, the initial setup and player choices introduce randomness, which learning algorithms need to handle effectively.

• Accounting for opponent variability: 

Different opponents may have different playing styles, requiring learning algorithms to adapt their strategies accordingly.

Despite these complexities, checkers remains a valuable testbed for developing and evaluating learning algorithms due to its well-defined rules, observable environment, and clear performance measure. As research in the field of artificial intelligence continues, checkers will likely remain a crucial benchmark for measuring the progress of learning algorithms in the domain of strategic board games.