# Train on Small, Play the Large: Scaling Up Board Games with AlphaZero and GNN

arXiv: https://arxiv.org/abs/2107.08387 · HTML: https://mlsanity.com/paper/2107.08387/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 18 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learning](https://mlsanity.com/paper/1807.08058/) (2018)

## Built on by (most cited first, 6 of 6)

- [Scaling Laws Under the Microscope: Predicting Transformer Performance from Small Scale Experiments](https://mlsanity.com/paper/2202.06387/) (2022)
- [Online 3D Bin Packing Reinforcement Learning Solution with Buffer](https://mlsanity.com/paper/2208.07123/) (2022)
- [Brick Tic-Tac-Toe: Exploring the Generalizability of AlphaZero to Novel Test Environments](https://mlsanity.com/paper/2207.05991/) (2022)
- [From Images to Connections: Can DQN with GNNs learn the Strategic Game of Hex?](https://mlsanity.com/paper/2311.13414/) (2023)
- [Towards Faster Matrix Diagonalization with Graph Isomorphism Networks and the AlphaZero Framework](https://mlsanity.com/paper/2407.00779/) (2024)
- [Enhancing Chess Reinforcement Learning with Graph Representation](https://mlsanity.com/paper/2410.23753/) (2024)

## Abstract (arXiv)

Playing board games is considered a major challenge for both humans and AI researchers. Because some complicated board games are quite hard to learn, humans usually begin with playing on smaller boards and incrementally advance to master larger board strategies. Most neural network frameworks that are currently tasked with playing board games neither perform such incremental learning nor possess capabilities to automatically scale up. In this work, we look at the board as a graph and combine a graph neural network architecture inside the AlphaZero framework, along with some other innovative improvements. Our ScalableAlphaZero is capable of learning to play incrementally on small boards, and advancing to play on large ones. Our model can be trained quickly to play different challenging board games on multiple board sizes, without using any domain knowledge. We demonstrate the effectiveness of ScalableAlphaZero and show, for example, that by training it for only three days on small Othello boards, it can defeat the AlphaZero model on a large board, which was trained to play the large board for 30 days.