Deep or Wide? Learning Policy and Value Neural Networks for Combinatorial Games

The success in learning how to play Go at a professional level is based on training a deep neural network on a wider selection of human expert games and raises the question on the availability, the limits, and the possibilities of this technique for other combinatorial games, especially when there is a lack of access to a larger body of additional expert knowledge. As a step towards this direction, we trained a value network for Tic-TacToe, providing perfect winning information obtained by retrograde analysis. Next, we trained a policy network for the SameGame, a challenging combinatorial puzzle. Here, we discuss the interplay of deep learning with nested rollout policy adaptation (NRPA), a randomized algorithm for optimizing the outcome of single-player games. In both cases we observed that ordinary feed-forward neural networks can perform better than convolutional ones both in accuracy and efficiency.