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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. - PowerPoint PPT Presentation
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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
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