點格棋中小盤面模型取代大盤面模型訓練之可行性研究

Abstract

點格棋（Dots and Boxes）是款零和、完全資訊並公正的雙人遊戲，雖然棋盤小卻有較高的複雜度。本論文以3×3盤面的點格棋作為研究主題，實現訓練好的小盤面的AlphaZero神經網路模型取代大盤面的AlphaZero神經網路模型。在實作上，我們採用基於AlphaGo Zero論文實現的AlphaZero General的開源框架專案，透過方便理解的Python開源專案，讓使用者可以輕鬆的在AlphaGo Zero的架構上實作遊戲及訓練神經網路，省去從頭開始開發的成本，能較專注於其他研究中。從實驗結果可以得知，在1天、2天及3天的訓練神經網路時間下，3×3盤面AlphaZero General代理人以平均處理合併policy的方式，在與相同訓練時間的4×4盤面AlphaZero General代理人的對戰中，分別取得64%、58%、57%的勝率。因此在訓練時間限制3天的情況下，可以使用訓練好的小盤面的AlphaZero神經網路模型取代大盤面的AlphaZero神經網路模型。

Dots and Boxes is a zero-sum, perfect information, and impartial two-player game. Despite its small board size, it exhibits high game complexity. This study focuses on the 3×3 board of the game and employs the AlphaZero neural network model adapted for smaller boards, replacing the model originally designed for larger boards.For implementation, we utilized the AlphaZero General open-source framework, which is based on the principles outlined in the AlphaGo Zero paper. This Python-based framework facilitates straightforward game implementation and neural network training, following the AlphaGo Zero architecture. By leveraging this existing framework, we reduced the development costs and could allocate resources to other research areas.Experimental results demonstrate that, across various training durations (1 day, 2 days, and 3 days), the 3×3 board AlphaZero General agent, employing average processing to merge policy, outperforms its 4×4 board AlphaZero General agent. It achieved respective winning rates of 64%, 58%, and 57%. Therefore, within a limited training timeframe of 3 days, the compact AlphaZero neural network model proves effective in substituting the larger-capacity model originally used.