a complex systems introduction to gohistory rules emergence computers future background image by...
TRANSCRIPT
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A Complex Systems Introduction to Go
Eric JankowskiCSAAW
10-22-2007
History Rules Emergence Computers FutureBackground image by Wikpedia user Donar Resikoffer
Wei Chi, Go, Baduk...
• Oldest board game in the world (maybe)
• Developed by Chinese monks
• Spread to Japan by monks
• Popularized in Japan
• Spread back to China and Korea
History
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Recent History
• Go spreads West ~ last 200 years
• First Western pro (1978) - Manfred Wimmer
• First American pro (1981) - Michael Redmond
• First computer go tournament - 1984
• Hikaru No Go bringing new young players
History
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Go is simple
No Suicide
No Infinite loops
Whoever has more, wins
Rules
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Definitions
• Group: 1 or more touching stones of the same color
• Touching: When two stones share an edge
• Liberty: An empty node adjacent to a group
Rules
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How’s it played?
• Players alternate turns
• You can play a stone or pass
• Restrictions on stone placement:
• After removing enemy stones, can’t have any groups with zero liberties
• Can’t repeat the same board position twice
• Score = Prisoners + Territory (Japanese)
• Score = Stones + Territory (Chinese)
Rules
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Wait... that’s it?
• Yes.
• Add stones to the board
• Try and make territory
• Can’t kill yourself or repeat a position
• And this is the greatest game in the history of the world.
Emergence
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You have got to be kidding
• No. Seriously.
• It’s totally sweet.
• From those simple rules emerges incredible complexity
Emergence
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Eyes and Life
• Invincible groups: Two eyes guarantees life!
• Seki: Life for groups without two eyes?!
Emergence
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Ko Fights
• Arise from the “no repeats” rule
• Can make non-local positions matter
• Are pretty common
Emergence
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Ladders
Emergence
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Strategy
• “Good shape” and “bad shape”
• Balance between:
• Greed and safety
• Attack and defense
• Correctness and complexity
Emergence
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Go is complex
• From 3 simple rules, way more possible games than particles in the universe
• Lots of different patterns emerge:
• live/dead groups
• ways of capturing stones
• ko’s create nonlocal interactions
Emergence
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in siligo
• 1997 - Kasparov loses to Deeper Blue. People freak out as they slowly realize this means they will be inevitably enslaved by superintelligent robot overlords.
• Skeptics of robot uprising point to Go: “Computers will never beat people at Go, stop investing in EMP devices and get back to work.”
Computers
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Challenges of Go AI
• Huge branching factor
• Game has about 200 moves- so you average about 200 move choices per turn
• Difficult move evaluation
• Very abstract for non-endgame positions
• Non-trivial for endgame positions
Computers
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Current methods
• alpha-beta algorithm
• Upper confidence bounds applied to trees (UCT)
• Null-move pruning
• Expert information for common positions
Computers
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alpha-beta
• Reduces branching factor out to some depth
• alpha = best result after opponent moves
• beta = worst case scenario for opponent
• Assume opponent makes best response
• Toss out any moves < alpha
• Toss out any moves > beta
• Efficiency depends on order of search
Computers
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UCT
• UCT math is kinda complicated
• Builds lookahead tree with biased Monte Carlo sampling
• Ensures only “interesting” moves looked at
• Each state is a multi-armed bandit, each move is an arm to the bandit
• Does better than alpha-beta, requires lots of memory
Computers
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UCT
• Given state s, depth d, and some position evaluation function...
• Initialize: Randomly generate some moves, evaluate them, d--;
• Values of arms = X(j)’s
• Loop: play move that maximizes X(ave) + sqrt( (2log n)/T(j,n) )
Computers
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Null-move pruning
• What’s the worst possible situation if I pass?
• If I’m ok after a shallow search, sweet!
• Means that this is a really good move
• Null move pruning + alpha-beta reduces branching by ~ square root
Computers
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MoGo
• Current world champion program
• UCT + expert knowledge to build lookahead trees
• Monte Carlo move evaluation
• Currently about 4k (30k-1k, 1d-9d)
Computers
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Computer go to come...
• Improve and combine currently used methods
• UCT to build search trees
• Null-move pruning
• Newer and more specialized hardware
• “re-use” information from tree branches, transposing them to other locations
• F.S. Hsu thinks 100 trillion searches per second will be able to beat pros
Future
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Robot overlords?
• Perhaps some serial brute-forcing can get eventually get close to human strength
• No immediate danger of robots enslaving us
• Human brains do a really good job (pattern recognition) with really hard stuff (go)
• Play go: it makes robots cry (if they had feelings)
Future
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Advertisements
• www.umich.edu/~goclub
• www.usgo.org
• AADL; 2:00pm-3:00pm on Sunday!
• Michigan League: Dec 1: Tournament!
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Some references
• http://www.lri.fr/~gelly/MoGo.htm - MOGO
• http://videolectures.net/otee06_gelly_umc/ - some nice talks on UCT and MOGO
• http://www.spectrum.ieee.org/print/5552 - article by Hsu on computer go