深度學習用於愛因斯坦棋研發之初步探討

Abstract

愛因斯坦棋，是於西元2004年由德國中部耶拿(Jena)鎮的一位數學教授—Ingo Althöfer所發明的兩人骰棋類遊戲。 在5x5的棋盤中放入雙方各六個棋子，雙方必須利用擲骰子的方式，來決定當前回合可以移動的棋子編號，透過各種不同的策略，減少我方或敵方的棋子，使我方比敵方優先達成勝利條件，以獲取勝利。雖然此遊戲的遊戲盤面尺寸、棋子數目較其他棋盤遊戲小、少，但是由於融入了骰子這個不確定的要素，大大地增加此遊戲的複雜度，同時也增加了耐玩性與挑戰性。 本研究將嘗試利用蒙地卡羅演算法、卷積式類神經網路的方法，嘗試使用、尋找各種不同的特徵，將這些特徵互相搭配以形成不同的feature map，藉此訓練類神經網路各個節點的參數(權重)，期望新的方法可以達到、擁有，甚至是超越目前其他強力的愛因斯坦棋下棋程式的棋力。EinStein würfelt nicht! is a dice board game for two players which was invented by a professor of applied mathematics, Ingo Althöfer, who lives in Jena, Germany. In this game, initially each player has six pieces, numbered 1 to 6, on a board with size 5x5. Each player needs to roll a dice in turns to move one of his/her pieces forward to the goal. Each player also needs to use different policies to reduce his/her own pieces or enemy’s pieces in order to win the game. Compared to other games, EinStein würfelt nicht! has smaller board size and fewer number of pieces. But it has a very important element, dice, that makes the game more complex, more fun and full of challenges and amazements. This research will try to apply Monte Carlo method and convolutional neural network to explore different features and use different methods to combine these features to form different feature maps. Then base on these feature maps to train the weights of the neural network and expect that the new method can make the new EinStein würfelt nicht! program more powerful than the traditional approach.