Information Compression and Performance Evaluation of Tic-Tac-Toe's Evaluation Function Using Singular Value Decomposition
This work addresses compression of board game strategies for AI applications, but it is incremental as it applies known tensor methods to a specific, simple game.
The study approximated Tic-Tac-Toe's evaluation function using singular value decomposition (SVD) and higher-order SVD (HOSVD), finding that information could be reduced by 70% without significant performance loss, with HOSVD yielding a higher winning rate than SVD at the same compression ratio.
We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe and performed low-rank approximation by considering the evaluation function as a ninth-order tensor. We found that we can reduce the amount of information of the evaluation function by 70% without significantly degrading the performance. Approximation accuracy and winning rate were strongly correlated but not perfectly proportional. We also investigated how the decomposition method of the evaluation function affects the performance. We considered two decomposition methods: simple SVD regarding the evaluation function as a matrix and the Tucker decomposition by higher-order SVD (HOSVD). At the same compression ratio, the strategy with the approximated evaluation function obtained by HOSVD exhibited a significantly higher winning rate than that obtained by SVD. These results suggest that SVD can effectively compress board game strategies and an optimal compression method that depends on the game exists.