A Complex Systems Introduction to Go

Transcription

1 A Complex Systems Introduction to Go Eric Jankowski CSAAW Background image by Juha Nieminen

2 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 Rules Emergence Computers Future

3 Recent History Go spreads West ~ last 200 years First Western pro (1978) - Manfred Wimmer First American pro (1981) - Michael Redmond First computer go tournament Hikaru No Go bringing new young players History Rules Emergence Computers Future

4 Go is simple No Suicide No Infinite loops Whoever has more, wins History Rules Emergence Computers Future

5 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 History Rules Emergence Computers Future

6 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) History Rules Emergence Computers Future

7 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. History Rules Emergence Computers Future

8 You have got to be kidding No. Seriously. It s totally sweet. From those simple rules emerges incredible complexity History Rules Emergence Computers Future

9 Eyes and Life Invincible groups: Two eyes guarantees life! Seki: Life for groups without two eyes?! History Rules Emergence Computers Future

10 Ko Fights Arise from the no repeats rule Can make non-local positions matter Are pretty common History Rules Emergence Computers Future

11 Ladders History Rules Emergence Computers Future

12 Strategy Good shape and bad shape Balance between: Greed and safety Attack and defense Correctness and complexity History Rules Emergence Computers Future

13 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 History Rules Emergence Computers Future

14 in siligo 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. History Rules Emergence Computers Future

15 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 History Rules Emergence Computers Future

16 Current methods alpha-beta algorithm Upper confidence bounds applied to trees (UCT) Null-move pruning Expert information for common positions History Rules Emergence Computers Future

17 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 History Rules Emergence Computers Future

18 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 History Rules Emergence Computers Future

19 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) ) History Rules Emergence Computers Future

20 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 History Rules Emergence Computers Future

21 MoGo Current world champion program UCT + expert knowledge to build lookahead trees Monte Carlo move evaluation Currently about 4k (30k-1k, 1d-9d) History Rules Emergence Computers Future

22 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 History Rules Emergence Computers Future

23 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) History Rules Emergence Computers Future

24 Advertisements AADL; 2:00pm-3:00pm on Sunday! Michigan League: Dec 1: Tournament! History Rules Emergence Computers Future

25 Some references - MOGO - some nice talks on UCT and MOGO - article by Hsu on computer go History Rules Emergence Computers Future