Computer Go

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Computer go is the field of artificial intelligence (AI) dedicated to creating a computer program that plays go, an ancient board game.

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[edit] Performance

Go has long been considered a difficult challenge in the field of AI and has not yielded as easily as Chess. The first Go program was written by Albert Zobrist in 1968 as part of his thesis on pattern recognition. It introduced an influence function to estimate territory and Zobrist hashing to detect ko. Recent developments have brought the best programs to good dan level on the small 9x9 board; however, while the techniques which have brought such progress in the 9x9 case have been applied on the 19x19 board with some success, dan level play has not yet been reached.

Currently, the best Go programs are ranked as (1-3 kyu). Only a decade ago, very strong players were able to beat computer programs at handicaps of 25-30 stones, an enormous handicap that few human players would ever take. There is a case where the winning program in the 1994 World Computer Go Championship, Go Intellect, lost all 3 games against the youth players on a 15 stone handicap.[1] In general, players who understand and exploit a program's weaknesses can win with much larger handicaps than typical players.[2] It is not yet known how efficient such exploits are against modern programs like Crazystone or Mogo, which when running on fast hardware, achieve ratings in the high to very high single digit kyu range on go servers.

[edit] Obstacles to high level performance

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Go is unlike chess, where the massive computing power of modern computer systems (and in particular dedicated chess machines like Hydra) together with relatively simple search and evaluation heuristics have proven marginally superior to the best human players. It is possible that techniques learned in the course of developing a strong Go program would transfer to more general problems in artificial intelligence to a greater degree than has been the case with chess.[3]

Although the rules of the game are simple, to write a program capable of automatically determining the winner of a game is no trivial matter. The amount of effort put into researching this field is comparable to many other board games, although the development effort going into computer chess systems continues to be at least an order of magnitude larger. This is evidenced by the existence of literally hundreds of freely available and about a dozen relatively successful commercially sold chess engines, as well as by the fact that computer chess, unlike computer go, still sometimes manages to get access to supercomputers.

[edit] Board is too large

The large board (19x19, 361 intersections) is often noted as one of the primary reasons why a strong program is hard to create. The large board size is a problem to the extent that it prevents an alpha-beta searcher without significant search extensions or pruning heuristics from achieving deep look-ahead.

So far, the largest game of Go being completely solved has been played on a 5×5 board. It was achieved in 2002, with black winning by 25 points (the entire board), by a computer program called MIGOS (MIni GO Solver).[4]

[edit] Most moves are possible

Continuing the comparison to chess, Go moves are not limited by the rules of the game. For the first move in chess, the player has twenty choices. Go players begin with a choice of 55 distinct legal moves, accounting for symmetry. This number rises quickly as symmetry is broken and soon almost all of the 361 points of the board must be evaluated. Some are much more popular than others, some are almost never played, but all are possible.

[edit] Additive nature of the game

As a chess game progresses (as well as most other games such as checkers, draughts, and backgammon), pieces disappear from the board, simplifying the game. Each new Go move, on the contrary, adds new complexities and possibilities to the situation, at least until an area becomes developed to the point of being 'settled'.

[edit] Techniques in chess that cannot be applied to Go

The fact that computer Go programs are significantly weaker than computer chess programs has served to generate research into many new programming techniques. The techniques which proved to be the most effective in computer chess have generally shown to be mediocre at Go.

A simple material counting evaluation is not sufficient for decent play in chess. Writing a good chess evaluation function is not an easy task. However, many more subtle considerations like isolated pawns, rooks on open verticals, pawns in the center of the board etc. can be formalised easily, providing a reasonably good evaluation function that can run quickly.

So far, the most success has been made by programs which utilise large amounts of expert knowledge, but new techniques are continually being researched, developed, and improved.

Still, material counting is the backbone of a chess evaluation function, with all positional factors combined typically scaled so as not exceed the value of a single pawn.[citation needed]

[edit] Evaluation function

Another problem comes from the difficulty of creating a good evaluation function for Go. More than one move can be regarded as the best depending on how you use that stone and what your strategy is. In order to choose a move, the computer must evaluate different possible outcomes and decide which is best. This is difficult due to the delicate trade-offs present in Go. For example, it may be possible to capture some enemy stones at the cost of strengthening the opponent's stones elsewhere. Whether this is a good trade or not can be a difficult decision, even for human players.

[edit] Combinatorial problems

Sometimes it is mentioned in this context that various difficult combinatorial problems (in fact, any NP-complete problem) can be converted to Go problems; however, the same is true for other abstract board games, including chess, when suitably generalised to a board of arbitrary size. NP-complete problems do not tend in their general case to be easier for unaided humans than for suitably programmed computers: it is doubtful that unaided humans would be able to compete successfully against computers in solving, for example, instances of the subset sum problem. Hence, the idea that we can convert some NP-complete problems into Go problems does not help in explaining the present human superiority in Go.

[edit] Endgame

Given that the endgame contains fewer possible moves than the opening or middle game, one could suppose that it was easier to play, and thus that computers should be easily able to tackle it. In chess, computer programs perform worse in endgames because the ideas are long-term; unless the number of pieces is reduced to an extent that allows taking advantage of solved endgame tablebases.

The application of surreal numbers to the endgame in Go, a general game analysis pioneered by John H. Conway, has been further developed by Elwyn R. Berlekamp and David Wolfe and outlined in their book, Mathematical Go (ISBN 1-56881-032-6). While not of general utility in most playing circumstances, it greatly aids the analysis of certain classes of positions.

Nonetheless, although elaborate study has been conducted, Go endgames have been proven to be PSPACE-hard. There are many reasons why they are so hard:

  • Even if a computer can play each local endgame area flawlessly, we cannot conclude that its plays would be flawless in regards to the entire board. Additional areas of consideration in endgames include Sente and Gote relationships, prioritisation of different local endgames, territory counting & estimation, and so on.
  • The endgame may involve many other aspects of Go, including 'life and death' which are also known to be NP-hard.
  • Each of the local endgame areas may affect one another. In other words, they are dynamic in nature although visually isolated. This makes it much more difficult for computers to deal with. This nature leads to some very complex situations like Triple Ko, Quadruple Ko, Molasses Ko and Moonshine Life.

Thus, it is very unlikely that it will be possible to program a reasonably fast algorithm for playing the Go endgame flawlessly, let alone the whole Go game.[5]

In those rare Go positions known as "ishi-no-shita", in which stones are repeatedly captured and re-played on the same points, humans have reading problems, while they are easy for computers.

[edit] Tactical search

One of the main concerns for a Go player is which groups of stones can be kept alive and which can be captured. This general class of problems is known as life and death. The most direct strategy for calculating life and death is to perform a tree search on the moves which potentially affect the stones in question, and then to record the status of the stones at the end of the main line of play.

However, within time and memory constraints, it is not generally possible to determine with complete accuracy which moves could affect the 'life' of a group of stones. This implies that some heuristic must be applied to select which moves to consider. The net effect is that for any given program, there is a trade-off between playing speed and life and death reading abilities.

[edit] State representation

A problem that all Go programs must solve is how to represent the current state of the game. For programs that use extensive searching techniques, this representation needs to be copied and modified for each new hypothetical move considered. This need places the additional constraint that the representation should either be small enough to be copied quickly or flexible enough that a move can be made and undone easily.

The most direct way of representing a board is as a 1 or 2-dimensional array, where each space in the array represents a point on the board, and can take on a value corresponding to a white stone, a black stone, or an empty space. Additional data is needed to store how many stones have been captured, whose turn it is, and which spaces are illegal due to Ko rule.

Most programs, however, use more than just the raw board information to evaluate positions. Data such as which stones are connected in strings, which strings are associated with each other, which groups of stones are in risk of capture and which groups of stones are effectively dead is necessary to make an accurate evaluation of the position. While this information can be extracted from just the stone positions, much of it can be computed more quickly if it is updated in an incremental, per-move basis. This incremental updating requires more information to be stored as the state of the board, which in turn can make copying the board take longer. This kind of trade-off is very indicative of the problems involved in making fast computer Go programs.

An alternative method is to have a single board and make and takeback moves so as to minimise the demands on computer memory and have the results of the evaluation of the board stored. This avoids having to copy the information over and over again.

[edit] System design

[edit] New approaches to problems

Historically, GOFAI (Good Old Fashioned AI) techniques have been used to approach the problem of Go AI. More recently, neural networks are being looked at as an alternative approach. One example of a program which uses neural networks is WinHonte[6].

These approaches attempt to mitigate the problems of the game of Go having a high branching factor and numerous other difficulties.

Computer Go research results are being applied to other similar fields such as cognitive science, pattern recognition and machine learning.[7] Combinatorial Game Theory, a branch of applied mathematics, is a topic relevant to computer Go.[7]

[edit] Design philosophies

The only choice a program needs to make is where to place its next stone. However, this decision is made difficult by the wide range of impacts a single stone can have across the entire board, and the complex interactions various stones groups can have with each other. Various architectures have arisen for handing this problem. The most popular are using some form of tree search, the application of Monte-Carlo methods, the creation of knowledge-based systems, and the use of machine learning. Few programs use only one of these techniques exclusively; most combine portions of each into one synthetic system.

[edit] Minimax tree search

One traditional AI technique for creating game playing software is to use a minimax tree search. This involves playing out all hypothetical moves on the board up to a certain point, then using an evaluation function to estimate the value of that position for the current player. The move which leads to the best hypothetical board is selected, and the process is repeated each turn. While tree searches have been very effective in computer chess, they have seen less success in Computer Go programs. This is partly because it has traditionally been difficult to create an effective evaluation function for a Go board, and partly because the large number of possible moves each side can make each leads to a high branching factor. This makes this technique very computationally expensive. Because of this, many programs which use search trees extensively can only play on the smaller 9×9 board, rather than full 19×19 ones.

There are several techniques, which can greatly improve the performance of search trees in terms of both speed and memory. Pruning techniques such as Alpha-beta pruning, Principal Variation Search, and MTD-f can reduce the effective branching factor without loss of strength. Likewise, caching techniques, such as transposition tables can reduce the amount of repeated effort, especially when combined with an iterative deepening approach. In order to quickly store a full sized Go board in a transposition table, a hashing technique for mathematically summarizing is generally necessary. Zobrist hashing is very popular in Go programs because it has low collision rates, and can be iteratively updated at each move with just two XORs, rather than being calculated from scratch. Even using these performance-enhancing techniques, full tree searches on a full sized board are still prohibitively slow. Searches can be sped up by using large amounts of domain specific pruning techniques, such as not considering moves where your opponent is already strong, and selective extensions like always considering moves next to groups of stones which are about to be captured. However, both of these options introduce a significant risk of not considering a vital move which would have changed the course of the game.

Results of computer competitions show that pattern matching techniques for choosing a handful of appropriate moves combined with fast localized tactical searches (explained above) are sufficient to produce a competitive program. For example, GNU Go is competitive, yet does not have a full-board search.

[edit] Knowledge-based systems

Novices often learn a lot from the game records of old games played by master players. There is a strong hypothesis that suggests that acquiring Go knowledge is a key to make a strong computer Go. For example, Tim Kinger and David Mechner argue that "it is our belief that with better tools for representing and maintaining Go knowledge, it will be possible to develop stronger Go programs." They propose two ways: recognizing common configurations of stones and their positions and concentrating on local battles. "... Go programs are still lacking in both quality and quantity of knowledge."[8]

After implementation, the use of expert knowledge has been proved very effective in programming Go software. Hundreds of guidelines and rules of thumb for strong play have been formulated by both high level amateurs and professionals. The programmer's task is to take these heuristics, formalize them into computer code, and utilize pattern matching and pattern recognition algorithms to recognize when these rules apply. It is also important to have a system for determining what to do in the event that two conflicting guidelines are applicable.

Most of the relatively successful results come from programmers' individual skills at Go and their personal conjectures about Go, but not from formal mathematical assertions; they are trying to make the computer mimic the way they play Go. "Most competitive programs have required 5–15 person-years of effort, and contain 50–100 modules dealing with different aspects of the game."[9]

This method has until recently been the most successful technique in generating competitive Go programs on a full sized board. Some example of programs which have relied heavily on expert knowledge are Handtalk (later known as Goemate), The Many Faces of Go, Go Intellect, and Go++, each of which has at some point been considered the world's best go program.

Nevertheless, adding knowledge of Go sometimes weakens the program because some superficial knowledge might bring mistakes: "the best programs usually play good, master level moves. However, as every games player knows, just one bad move can ruin a good game. Program performance over a full game can be much lower than master level."[9]

[edit] Monte-Carlo methods

One major alternative to using hand-coded knowledge and searches is the use of Monte-Carlo methods. This is done by generating a list of potential moves, and for each move playing out thousands of games at random on the resulting board. The move which leads to the best set of random games for the current player is chosen as the best move. The advantage of this technique is that it requires very little domain knowledge or expert input, the tradeoff being increased memory and processor requirements. However, because the moves used for evaluation are generated at random it is possible that a move which would be excellent except for one specific opponent response would be mistakenly evaluated as a good move. The result of this are programs which are strong in an overall strategic sense, but are weak tactically. This problem can be mitigated by adding some domain knowledge in the move generation and a greater level of search depth on top of the random evolution. Some programs which use Monte-Carlo techniques are MoGo, CrazyStone, Olga and Gobble.

In 2006, a new search technique, upper confidence bounds applied to trees (UCT), was developed and applied to many 9x9 Monte-Carlo Go programs with excellent results. UCT uses the results of the play outs collected so far to guide the search along the more successful lines of play, while still allowing alternative lines to be explored. The UCT technique along with many other optimizations for playing on the larger 19x19 board has led MoGo to become one of the strongest research programs. Successful applications of UCT methods to 19x19 go include MoGo, CrazyStone and Mango. MoGo won the 2007 Computer Olympiad and won one (out of three) blitz game against Guo Juan, 5th Dan Pro, in 9x9 Go.

In 2007, Rémi Coulom developed a new method of generating candidate moves for the UCT algorithm based upon machine analysis of ELO scores/past games. [10]

In 2008, thanks to an efficient message-passing parallelization, MoGo won one game (out of three) against Catalin Taranu, 5th Dan Pro, in 9x9 with standard time settings (30 minutes per side). MoGo was running on a cluster provided by Bull (32 nodes with 8 cores per node, 3 GHz); the machine was down during one of the lost games. The results of this event were approved by the French Federation of Go. MoGo also played a 19x19 Game against Catalin Taranu and lost in spite of 9 stones handicap. However, MoGo was in good position during most of the game, and lost due to a bad choice in a ko situation at the end. The machine used for this event (the IAGO challenge, organized by the company "Recitsproque") is a good one, but far from the top level in industry - as the speed-up curve is linear until at least 32 nodes, we can guess that much better results are possible with bigger machines.

[edit] Machine learning

While knowledge-based systems have been very effective at Go, their skill level is closely linked to the knowledge of their programmers and associated domain experts. One way to break this limitation is to use machine learning techniques in order to allow the software to automatically generate rules, patterns, and/or rule conflict resolution strategies.

This is generally done by allowing a neural network or genetic algorithm to either review a large database of professional games, or play many games against itself or other people or programs. These algorithms are then able to utilize this data as a means of improving their performance. Machine learning techniques can also be used in a less ambitious context to tune specific parameters of programs which rely mainly on other techniques. Notable programs using neural nets are NeuroGo and WinHonte.

[edit] Competitions among computer Go programs

Several annual competitions take place between Go computer programs, the most prominent being the Go event at the Computer Olympiad and the Gifu Challenge in Japan. Regular, less formal, competitions between programs occur on the Kiseido Go Server and the Computer Go Ladder.

Prominent go-playing programs include ZhiXing Chen's Handtalk, Michael Reiss's Go++ and David Fotland's Many Faces of Go. GNU Go is a free computer go implementation.

[edit] History

The first computer Go competitions were sponsored by USENIX. They ran from 1984-1988. These competitions introduced Nemesis, the first competitive go program from Bruce Wilcox, and G2.5 by David Fotland, which would later evolve into Cosmos and The Many Faces of Go.

One of the early drivers of computer go research was the Ing Prize, a relatively large money award sponsored by Taiwanese banker Ing Chang-ki, offered annually between 1985 and 2000 at the World Computer Go Congress (or Ing Cup). The winner of this tournament was allowed to challenge young professionals at a handicap in a short match. If the computer won the match, the prize was awarded and a new prize announced: a larger prize for beating the professionals at a lesser handicap. The series of Ing prizes was set to expire either 1) in the year 2000 or 2) when a program could beat a 1-dan professional at no handicap for 40,000,000 NT dollars. The last winner was Handtalk in 1997, claiming 250,000 NT dollars for winning an 11-stone handicap match against three 8-9 year old professionals. At the time the prize expired in 2000, the unclaimed prize was 550,000 NT dollars for winning a 9-stone handicap match.

Many other large regional Go tournaments ("congresses") had an attached computer Go event. The European Go Congress has sponsored a computer tournament since 1987, and the USENIX event evolved into the US/North American Computer Go Championship, held annually from 1988-2000 at the US Go Congress.

Surprisingly, Japan has only recently started sponsoring its own computer Go competitions. The FOST Cup was held annually from 1995-1999 in Tokyo. That tournament has been supplanted by the Gifu Challenge, which has been held annually since 2003 in Ogaki City.

[edit] Problems in computer-computer games

When two computers play a game of Go against each other, the ideal is to treat the game in a manner identical to two humans playing. However, this can be difficult especially during the end game. The main problem is that Go playing software has no capacity to communicate in a dialog with its opponents. So if there is a disagreement about the status of a group of stones, there is no general way for two different programs to “talk it out” and resolve the conflict. One method for resolving this problem is to have an expert human or well-crafted piece of software judge the final board. However, this introduces subjectivity into the results and the risk that the expert would miss something the program saw. An alternative method is to send a special command to the two programs that indicates they should continue placing stones until there is no question about the status of any particular group. The main problem with this system is that some rule sets (such as the traditional Japanese rules) penalize the players for making these extra moves. Additionally this introduces the risk that a program which was in a winning position at the traditional end of the game (when both players have passed), could be penalized for poor play that is made after the game was technically over.

[edit] Notes and references

  1. ^ See http://www.itee.uq.edu.au/~janetw/Computer%20Go/CS-TR-339.html#6.2
  2. ^ See for instance http://www.intgofed.org/history/computer_go_dec2005.pdf
  3. ^ Read this article for more explanations on why computer go is so hard to write
  4. ^ 5×5 Go is solved by MIni GO Solver
  5. ^ See Computer Go and Computer Go Programming pages at Sensei's Library
  6. ^ WinHonte 2.01
  7. ^ a b Müller, Martin. Computer Go, Artificial Intelligence 134 (2002): p150
  8. ^ Müller, Martin. Computer Go, Artificial Intelligence 134 (2002): p151
  9. ^ a b Müller, Martin. Computer Go, Artificial Intelligence 134 (2002): p148
  10. ^ Computing Elo Ratings of Move Patterns in the Game of Go, Rémi Coulom http://remi.coulom.free.fr/Amsterdam2007/

[edit] Academic articles

[edit] Related websites

[edit] Computer programs

See also: Go software
  • AYA by Hiroshi Yamashita
  • CrazyStone by Rémi Coulom
  • GNU Go, the strongest open source Go program
  • Go++ by Michael Reiss (sold as Strongest Go or Tuyoi Igo in Japan)
  • Go Intellect by Ken Chen
  • Handtalk/Goemate, developed in China by Zhixing Chen (sold as Shudan Taikyoku in Japan)
  • Haruka by Ryuichi Kawa (sold as Saikouhou in Japan)
  • Indigo by Bruno Bouzy
  • Katsunari by Shin-ichi Sei
  • KCC Igo, from North Korea (sold as Silver Star or Ginsei Igo in Japan)
  • The Many Faces of Go by David Fotland (sold as AI Igo in Japan)
  • MoGo by Sylvain Gelly; parallel version [1] by many people.
  • Smart Go by Anders Kierulf, inventor of the Smart Game Format

[edit] See also

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