Erik C. D. van der Werf

Local move prediction in Go

The paper presents a system that learns to predict local strong expert moves in the game of Go at a level comparable to that of strong human kyu players. This performance is achieved by four techniques. First, our training algorithm is based on a relative-target approach that avoids needless weight adaptations characteristic of most neural-network classifiers. Second, we reduce dimensionality through state-of-the-art feature extraction, and present two new feature-extraction methods, the Move Pair Analysis and the Modified Eigenspace Separation Transform. Third, informed pre-processing is used to reduce state-space complexity and to focus the feature extraction on important features. Fourth, we introduce and apply second-phase training, i.e., the retraining of the trained network with an augmented input constituting all pre-processed features. Experiments suggest that local move prediction will be a significant factor in enhancing the strength of Go programs.

Enhanced forward pruning

In this paper forward-pruning methods, such as multi-cut and null move, are tested at so-called ALL nodes. We improved the principal variation search by four small but essential additions. The new PVS algorithm guarantees that forward pruning is safe at ALL nodes. Experiments show that multi-cut at ALL nodes (MC-A) when combined with other forward-pruning mechanisms give a significant reduction of the number of nodes searched. In comparison, a (more) aggressive version of the null move (variable null-move bound) gives less reduction at expected ALL nodes. Finally, it is demonstrated that the playing strength of the lines of action program MIA is significantly (scoring 21% more winning points than the opponent) increased by MC-A.

Learning to score final positions in the game of Go

This article investigates the application of machine-learning techniques for the task of scoring final positions in the game of Go. Neural network classifiers are trained to classify life and death from labelled 9 × 9 game records. The performance is compared to standard classifiers from statistical pattern recognition. A recursive framework for classification is used to improve performance iteratively. Using a maximum of four iterations our cascaded scoring architecture (CSA*) scores 98.9% of the positions correctly. Nearly all incorrectly scored positions are recognised (they can be corrected by a human operator). By providing reliable score information CSA* opens the large source of Go knowledge implicitly available in human game records for automatic extraction. It thus paves the way for a successful application of machine learning in Go.

Learning to predict life and death from Go game records

This article presents a new learning system for predicting life and death in the game of Go. It is called Gone. The system uses a multi-layer perceptron classifier which is trained on learning examples extracted from game records. Blocks of stones are represented by a large amount of features which enable a rather precise prediction of life and death. On average, Gone correctly predicts life and death for 88% of all the blocks that are relevant for scoring. Towards the end of a game the performance increases up to 99%. A straightforward extension for full-board evaluation is discussed. Experiments indicate that the predictor is an important component for building a strong full-board evaluation function.

Learning to estimate potential territory in the game of go

This paper investigates methods for estimating potential territory in the game of Go. We have tested the performance of direct methods known from the literature, which do not require a notion of life and death. Several enhancements are introduced which can improve the performance of the direct methods. New trainable methods are presented for learning to estimate potential territory from examples. The trainable methods can be used in combination with our previously developed method for predicting life and death [25]. Experiments show that all methods are greatly improved by adding knowledge of life and death.

Solving Go for Rectangular Boards

In 2003, the solution for the 5×5 Go board was published in this journal. The current article presents the game-theoretic values for rectangular boards up to a surface of 30 intersections under Chinese rules. The result was achieved by improving the αβ-based solver MIGOS. Moreover, the article identifies errors in published human solutions by comparing them with our computer solutions.

The relative history heuristic

In this paper a new method is described for move ordering, called the relative history heuristic. It is a combination of the history heuristic and the butterfly heuristic. Instead of only recording moves which are the best move in a node, we also record the moves which are applied in the search tree. Both scores are taken into account in the relative history heuristic. In this way we favour moves which on average are good over moves which are sometimes best. Experiments in LOA show that our method gives a reduction between 10 and 15 per cent of the number of nodes searched. Preliminary experiments in Go confirm this result. The relative history heuristic seems to be a valuable element in move ordering.