1. Computer Go : A Go player Rohit Gurjar CS365 Project Proposal, IIT Kanpur rgurjar@iitk.ac.in Guided By – Prof. Amitabha Mukerjee

2. Introduction to the game A two player board game Around 3000 years old Players have white and black stones A stone (or a group) is captured if it is completely surrounded by enemy stones Goal is to surround territories (empty points or enemy stones) by with one’s own stones Image ref : http://www.sente.ch/software/goban/BoardBig.jpg

3. Past work done A lot of work has been done to develop a Computer Go player But the best Go programs are ranked only as 1-3 kyu (equivalent to a intermediate amateur) Go is an extremely difficult game for computers to play well. Four main factor causes failure of standard AI techniques 1) The state space of the game of go is intractably huge. 2) The branching factor of go is intractably huge. 3) It is difficult to construct a heuristic function to evaluate board states. 4) Proper go strategy requires an extremely deep look-ahead. Ref : A machine learning approach to computer Go (2007) – Jeffrey Bagdis

4. Algorithms used for Move Generation Two components were necessary – Evaluation Function – A tree search Finding a good evaluation function is very hard Solution- Generate goals Choose a specific EF related to one goal and associate a specific move generator with this goal. (Reduced complexity) What if more than one goal is relevant to winning the game? Computer Go, an AI oriented survey- Bruno Bouzy, Tristan Cazenave (2000)

5. Tree search In classical games tree search uses the EF to find out the best possible move High branching factor is a problem (~200) Local TS – Selecting moves localized on a part of the board – Problems Defining locality criterion Given the results of local TS, reconstruction of the global result Independence of local situations

6. Tree search Splitting the game into sub-games was proved to be useful in the endgame. * Problem – finding independent sub-games Alpha-Beta pruning. – as the tree being searched, cut off some sections of the tree from consideration, without at all reducing the optimality of accuracy of an exhaustive search. * M.Müller, Decomposition search: A combinatorial games approach to game tree search, with applications to solving Go endgames (1999)

7. Machine Learning Previous algorithms are inadequate for developing a Go player. Machine learning through neural network technique A function(nonlinear) maps a vector(board state) to a scalar(0-1) which shows the probability of winning The perceptron - simplified computational model of the biological neurons Ref : A machine learning approach to computer Go (2007) – Jeffrey Bagdis

8. Perceptron A single perceptron can be trained to produce a certain output for a corresponding input by adjusting its input weights appropriately. In order to achieve a more precise approximation, perceptrons can be connected together to form Multi-layer networks - perceptrons can be connected together to form multi-layer networks Ref : A machine learning approach to computer Go (2007) – Jeffrey Bagdis

9. Multilayer Network Ref : A machine learning approach to computer Go (2007) – Jeffrey Bagdis

10. Conclusion This approach seems effective at producing an approximation of a value function that can be used to play go. But this value function is not by itself sufficient for strong play Combination of this with some of the previously shown algorithms may give good results.

11. Algorithms used for go Finding a good evaluation function is very hard – Concrete EF With the high branching factor of Go computers cannot search down to the depth of terminating the game – Conceptual EF used by program Indigo To observe human players, and capture the useful concepts