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 data I 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

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