igb go —— a self-learning go program

IGB GO—— A self-learning GO program

Lin WUInformation & Computer Science

University of California, Irvine

12/02/2003Lin WU, [email protected]

Outline

Background:– What is GO?– Existing GO programs

IGB GO Past work:

– Three past scenarios– Present scenario

Discussion Conclusion Demon.


What is GO

Black and white player play alternatively.

Black plays first. Basic concepts:

– Liberty– Eye– Territory– Unconditional live– Position


What is GO (cont.)

Rules– Stone(s) are captured, if the liberty becomes 0.– Captured stones are removed from board– Winner is determined by counting the territory


Existing GO programs

There are many existing GO programs– KCC Igo– HARUKA– Go++– Goemate– Hand talk– The Many Faces of Go: www.smart-games.com– GNU GO: www.gnu.org/software/gnugo/gnugo.html– NeuroGo: www.markus-enzenberger.de/neurogo.html– etc.

None of them can beat average amateur players.


Conceptual Architecture

Pattern libraries:– Library for opening– Library of corner– Library for the internal part of the board– Libraries for attack, defense, connection, etc.

Engine: match the board position against the libraries Evaluation: determine the best, if there are multiple hits


Architecture I

The many faces of GO (1981- now)– Knowledge Representation in The Many Faces of

Go, David Fotland, February 27, 1993– Joseki database of standard corner patterns (36,000

moves)– a pattern database of 8x8 patterns (4,000 moves)– a rule based expert system with about 200 rules that

suggests plausible moves for full board evaluation


Architecture II

GNU GO (1989.3 – now)– GNU GO documentation– Pattern libraries

General: patterns.db, patterns2.db Fuseki (opening): fuseki.db Eyes: eyes.db Connection: conn.db Influence: influence.db, barriers.db Etc

– GNU Go engine: calculate states of different level, pattern matching, move reasoning.


Why pattern based system?

Simple rules doesn’t mean simple game– Simple rules means extremely huge searching space

Board evaluation is hard, especially in the middle of the game

– The representation space is extremely huge– The evaluation function is sensitive to small difference of input– Result: to get reliable evaluation results, the level of search

have to be very high Pattern based system

– Avoid search by pattern matching


Complexity —— Search time

Search Level

5x5 7x7 9x9 19x19

1 25 49 81 361

2 625 2,401 6,561 130,321

3 15,625 117,649 531,441 4.7 E 7

4 390,625 5.7 E 6 4.3 E 7 2.1 E 8


Problems of pattern based system

Everything is manual work As system become larger, it’s harder to improve the

pattern database. As database becomes larger, more likely to be

inconsistent.

Results:– Performance improves slower as the performance becomes

better.


Outline


IGB GO Past work:




IGB GO

http://contact.ics.uci.edu/go.html A GO program which can improve its

performance automatically How?

– Use artificial neural networks to learn the evaluation function.

– Improving the quality of the neural networks by improving the quality of training data.


Architecture of the neural networks

6 planes– 1 input plane– 1 output plane– 4 transmission

Use recurrent neural network to learn two functions

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How to improving the training data

1. Initiate a group of neural networks

2. Let neural networks play against each other

3. Identify the set of good moves

4. Train neural networks over those good moves

5. Repeat 2.


Two key issues of this system

Given the neural networks, how to identify “the good moves”

Given the good moves, how to improve neural networks’ performance efficiently


Outline


IGB GO Past work:




Play against itself

1. Randomly initiate a neural network

2. The neural network plays against itself over a set of initial setups.

3. If black(or white) wins, learn the black(or white) moves.

4. Update weights, repeat 2.


Play against itself — Good move identification

Win: the color who gets larger territory Good moves: all the moves played by wining

color


Play against itself — Results

Results– First, improve– Then, begin to get worse– Last, learn a very deterministic and bad pattern

Improvement: No guarantee.


Group playing

1. Initiate a group of neural networks (18)2. Randomly assign a neural network to another

as a pair.3. Members in a pair play against each other4. Identify the set of good moves5. Train the loser neural networks over those

good moves6. Repeat 2.


Group playing — Good move identification

Each pair has two players (A and B) Game1: A plays black, B plays white, get a

result R1 Game2: B plays black, A plays white, get a

result R2 If R1 > R2, then A is better player. B is the

loser. So B learn all the moves played by A.


Group playing — Results

Results– Improve at beginning.– If a player dominates, the whole system degrades

as “play against itself”.– No indication of converge till now. (9 machines, 1

month on 9 by 9 board)

Improvement: No guarantee.


ABC scenario

1. Initiate a group of neural networks

2. Randomly assign three different neural networks (A,B,C) in a group

3. Let A and B play against each other

4. Identify the set of good moves

5. Train neural networks over those good moves

6. Repeat 2.


ABC scenario — Good move identification

For a given pair with player A and player B– Suppose B is the loser.

Randomly assign a teacher C– C will tell B, what move C will make for every B’s turn

C’s suggested move is the same as that of B C’s suggested move is different from B

Based on C’s suggest move, A play with B again– Better: understandable good move– The same– Worse

The set of good moves is all the understandable good moves


ABC scenario — Results

Results– It took 1 week to get a best player from 3 randomly

initialized players– The best player was beaten by another randomly

initialized player.– The speed of improving became slower as the

performance increased. Improvement: guarantee. Training Speed: unacceptable slow


Present scenario

Output representation:– Two papers:

Temporal Difference Learning of Position Evaluation in the Game of Go, Nicol N. Schraudolph, Peter Dayan, and Terrence J. Sejnowski, Advances in Neural Information Processing 6, 1994

Learning to evaluate GO positions via temporal difference methods, Nicol N. Schraudolph, Peter Dayan, and Terrence J. Sejnowski, Soft Computing Techniques in Game Playing, 2000

– Each intersection has an output: real number [0,1]– The likelihood to make a move => the likelihood of securing that

intersection as black territory at the end of the game.– Reinforcement learning

Good move identification: reinforcement learning identify good moves automatically


Present scenario — Results

Improvement: guarantee. Training Speed: better than ABC scenario, but

still slow Results

– 5x5: 3 - 4 hours training: beat random player 100% 1 - 2 weeks (168-336 h): comparable to GNUGO Prediction accuracy is >90% after the board is occupied >50%

– 7x7: after 1 month of training, GNUGO beats it without any difficulty


Outline


IGB GO Past work:




Why better results

Old architecture– Target is inconsistent– Target is harder to learn,

spatial complexity 325 / 8 ( 105911076180.375) for 5x5

– Quality of training data is bad

New architecture– Target is consistent, and

at the end of the game, it’s true target.

– Target correlates mainly to local information, so the complexity should be much less than 325 / 8

– Quality of training data is determined by the neural network itself.


Is present arch. enough — search time complexity

Board Size

2(25%) 3(25%) 2(50%) 3(50%)

5x5 64 729 4,096 531,441

7x7 4,096 531,441 1.6E7 2.8E11

9x9 1E6 3.5E9 1E12 1.2E19

19x19 1.2E27 8.7E42 1.5E54 7.6E85


Known Problems

Intrinsic hard problems:– No complexity bounds for the number of iterations to

get a better player

– Representation space is extremely huge


Known Problems — Technical

Temporary technical problems:– Lack position-level evaluation method– Unable to respond to some unusual cases correctly

Unable to AUTOMATICALLY identify the unusual cases, which will cause problems

– Time complexity per iteration: Play a match: O(n6W) Learn a match: O(n4W) for TD0, O(n6W) for Q-Learning (19/5)6 = 3011


Bounds for iteration

Maybe exponential Observation:

– Human being: the complexity increases as the level of player increases.

– Present implementation: same as above

Important to know– How fast the complexity increases, as the level of

player increases?


The complexity could be exponential

– Suppose, one player dominate the whole system, or a small group of players dominate the whole system

– How much time is needed for obtaining a better new player or a better group?

– Repeat the experiment, with the same amount of time, there is a 50% chance to get a better one, due to the symmetry

– At least exponential to 2.


Position-level performance evaluation

With it– Study the iteration bounds empirically– The evaluation results can be used to find good

tradeoff between performance and searching space

Without it– Every method is trial and error, but there exists

infinite number of potential methods to try.


Time complexity per iteration

Separate “play” and “learn”– A database of training data– Training data:

Best players play against each other Online server Manually find ways to beat the best player.

– All players learn the generated training data


Unusual move identification

Difficulty– Search space is huge Hard to identify

automatically

Possible solution– Use database to record all such moves, once they

appear Can be implemented the same as training database


Why it’s so hard

No method touches the tough problem explicitly.– Key problems:

extremely huge searching space hard to evaluate positions

Present strategy is to reduce the searching space by improve evaluation function.


Why it’s so hard (cont.)

Reinforcement learning may not be enough– Nicol N. Schraudolph, 6 years without any observable progress– Arthur Samuel, “no progress has been made in overcoming [this

defect]” (11 years, 1956-1967) (Blondie24, p146-147) Neural network may not learn

– Why? Representation space is huge even for the last move 90% occupied, 9x9 board, equal number of black and white

– Solution Generalization ability Automatically identify features

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Lesson I

Ability to improve The best?– The speed of improving:

5x5: 3 - 4 hours training to beat random

1 - 2 weeks (168-336 h) to be comparable to GNUGO 7x7: after 1 month of training, GNUGO is still able to win.

==?


Lesson II

Deterministic function between input and output

Neural network can learn it without any difficulty

No– The intrinsic complexity of the function– Neural network can only learn the correlation between the

input and the output, as a result of hill climbing

==?


Conclusion

A self-learning GO program is possible but exists several technically difficult problems– Automatic feature discovery– Automatic learning from failure– Position-level performance evaluation


Demon.http://contact.ics.uci.edu/go.html


Thanks for coming

igb go —— a self-learning go program

Documents

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functionslin wu

territorylin wu

search timelin wu

board evaluationlin

multiple hitslin wu

pattern matching

level of search