The Implementation of Machine Learning in the Game of Checkers

Billy Melicher

Computer Systems lab 08-09

Abstract• Machine learning uses past information

to predict future states• Can be used in any situation where the

past will predict the future• Will adapt to situations

Introduction

• Checkers is used to explore machine learning

• Checkers has many tactical aspects that make it good for studying

Background

• Minimax• Heuristics • Learning

Minimax

• Method of adversarial search• Every pattern(board) can be given a fitness

value(heuristic)• Each player chooses the outcome that is best

for them from the choices they have

Minimax

Chart from wikipedia

Minimax

• Has exponential growth rate• Can only evaluate a certain number of actions

into the future – ply

Heuristic

• Heuristics predict out come of a board• Fitness value of board, higher value, better

outcome• Not perfect• Requires expertise in the situation to create

Heuristics• H(s) = c0F0(s) + c1F1(s) + … + cnFn(s)

• H(s) = heuristic

• Has many different terms

• In checkers terms could be:

Number of checkers

Number of kings

Number of checkers on an edge

How far checkers are on board

Learning by Rote

• Stores every game played• Connects the moves made for each board• Relates the moves made from a particular board to

the outcome of the board• More likely to make moves that result in a win, less

likely to make moves resulting in a loss• Good in end game, not as good in mid game

How I store dataI convert each checker board into a 32 digit base 5 number where each digit corresponds to a playable square and each number corresponds to what occupies that square.

Learning by Generalization

• Uses a heuristic function to guide moves• Changes the heuristic function after games

based on the outcome• Good in mid game but not as good in early

and end games• Requires identifying the features that affect

game

Development

• Use of minimax algorithm with alpha beta pruning

• Use of both learning by Rote and Generalization

• Temporal difference learning

Temporal Difference Learning

• In temporal difference learning, you adjust the heuristic based on the difference between the heuristic at one time and at another

• Equilibrium moves toward ideal function• U(s) <-- U(s) + α( R(s) + γU(s') - U(s))

Temporal Difference Learning

• No proof that prediction closer to the end of the game will be better but common sense says it is

• Changes heuristic so that it better predicts the value of all boards

• Adjusts the weights of the heuristic

Alpha Value

• The alpha value decreases the change of the heuristic based on how much data you have

• Decreasing returns• Necessary for ensuring rare occurrences do not

change heuristic too much

Development

• Equation for learning applied to each weight:• w=(previous-current)(previous+current/2)• Equation for alpha value:• a=50/(49+n)

Results

• Value of weight reaches equilibrium• Changes to reflect the learning of the program• Occasionally requires programmer intervention

when it reaches a false equilibrium

Results

Results

Results

Results

• Learning by rote requires a large data set• Requires large amounts of memory• Necessary for determining alpha value in

temporal difference learning

Conclusions

• Good way to find equilibrium weight• Sometimes requires intervention• Doesn't require much memory• Substantial learning could be achieved with

relativelly few runs• Learning did not require the program to know

strategies but does require it to play towards a win