Reinforcement learning and simulation-based search in computer go

Abstract

Learning and planning are two fundamental problems in artificial intelligence. The learning problem can be tackled by reinforcement learning methods, such as temporal-difference learning, which update a value function from real experience, and use function approximation to generalise across states. The planning problem can be tackled by simulation-based search methods, such as Monte-Carlo tree search, which update a value function from simulated experience, but treat each state individually. We introduce a new method, temporal-difference search, that combines elements of both reinforcement learning and simulation-based search methods. In this new method the value function is updated from simulated experience, but it uses function approximation to efficiently generalise across states. We also introduce the Dyna-2 architecture, which combines temporal-difference learning with temporal-difference search. Whereas temporal-difference learning acquires general domain knowledge from its past experience, temporal-difference search acquires local knowledge that is specialised to the agent's current state, by simulating future experience. Dyna-2 combines both forms of knowledge together. We apply our algorithms to the game of 9 × 9 Go. Using temporal-difference learning, with a million binary features matching simple patterns of stones, and using no prior knowledge except the grid structure of the board, we learnt a fast and effective evaluation function. Using temporal-difference search with the same representation produced a dramatic improvement: without any explicit search tree, and with equivalent domain knowledge, it achieved better performance than a vanilla Monte-Carlo tree search. When combined together using the Dyna-2 architecture, our program outperformed all handcrafted, traditional search, and traditional machine learning programs on the 9 × 9 Computer Go Server. We also use our framework to extend the Monte-Carlo tree search algorithm. By forming a rapid generalisation over subtrees of the search space, and incorporating heuristic pattern knowledge that was learnt or handcrafted offline, we were able to significantly improve the performance of the Go program MoGo . Using these enhancements, MoGo became the first 9 × 9 Go program to achieve human master level.