A New ComputationalApproach to the Game of

Go

Amol Khedkar

Aims

Investigate neural networksApplication of neural networks to GoLook at combining hard AI and soft AI with reference to GoAssess the success of such a combination

What Is Go?

Ancient oriental game19 by 19 board of intersectionsPlayers take turns placing black and white stonesSurround territoryCapture opponents stones

What Is Go?

Liberties

Capture

Comparison With Chess

More moves to consider Average of 180 legal move choices

per turn

LookaheadLarger boardLarger search spaceTherefore brute force is impractical

State of the Art

Many Faces Of Go – David FotlandBrute force search with all the trimmings: Minimax game tree search Alpha-Beta pruning Transposition table

Pattern matchingRule based expert system ~250 move suggesters

Neural Networks

Modelled on the brain

Neural Networks

Trained to recognise inputAbility to generaliseLearning Algorithms Back Propagation Network (BPN)

Application to Go

Use neural network to suggest and score plausible movesUse Minimax search to investigate suggested plausible movesBenefits Fast and efficient move filter Look-ahead

Evaluation functions – liberty count

Development

Manager functionMinimax implementation MTD(f) Alpha-Beta variation Iterative Deepening framework Transposition Table Best Move First Enhanced Transposition Cutoffs

Development

Neural network implementation Training algorithm

BPN Training data Interface method – 81-45-1

architecture

Area Finder Network 361-90-9 architecture

Short range specialist networks

Development

Results

Successful combination of Alpha-Beta and neural networksPlayed against GNU Go Performance improved when using

combination of techniques

Results

Configuration Score (we play black)

1. 9x9 Network B-8, W-49

2. 9x9 Network+Area Finder

B-3, W-21

3. Alpha-Beta B-9, W-12 (Not Complete)

4. 9x9 Network+Alpha-Beta

B-9, W-25

5. 9x9 Network+Alpha-Beta+Area Finder

B-7, W-18

Conclusions

Human players and computer playersFilled in own territory, including eyes of safe groupsOpening game poor Short range networks promising

Evaluation function limits Alpha-Beta

Future Work

Further development of different grain networks and different range and specialisationEvaluation function Temporal Difference network

Investigate alternative neural network architectures and algorithms