Non-Linear Monte-Carlo Search in Civilization II

Abstract

This paper presents a new Monte-Carlo search algorithm for very large sequential decision-making problems. Our approach builds on the recent success of Monte-Carlo tree search algorithms, which estimate the value of states and actions from the mean outcome of random simulations. Instead of using a search tree, we apply non-linear regression, online, to estimate a state-action value function from the outcomes of random simulations. This value function generalizes between related states and actions, and can therefore provide more accurate evaluations after fewer simulations. We apply our Monte-Carlo search algorithm to the game of Civilization II, a challenging multi-agent strategy game with an enormous state space and around $10^{21}$ joint actions. We approximate the value function by a neural network, augmented by linguistic knowledge that is extracted automatically from the official game manual. We show that this non-linear value function is significantly more efficient than a linear value function. Our non-linear Monte-Carlo search wins 80\% of games against the handcrafted, built-in AI for Civilization II.