Simulation-Based Algorithms for Markov Decision Processes: Monte Carlo Tree Search from AlphaGo to AlphaZero

AlphaGo and its successors AlphaGo Zero and AlphaZero made international headlines with their incredible successes in game playing, which have been touted as further evidence of the immense potential of artificial intelligence, and in particular, machine learning. AlphaGo defeated the reigning human world champion Go player Lee Sedol 4 games to 1, in March 2016 in Seoul, Korea, an achievement that surpassed previous computer game-playing program milestones by IBM’s Deep Blue in chess and by IBM’s Watson in the U.S. TV game show Jeopardy. AlphaGo then followed this up by defeating the world’s number one Go player Ke Jie 3-0 at the Future of Go Summit in Wuzhen, China in May 2017. Then, in December 2017, AlphaZero stunned the chess world by dominating the top computer chess program Stockfish (which has a far higher rating than any human) in a 100-game match by winning 28 games and losing none (72 draws) after training from scratch for just four hours! The deep neural networks of AlphaGo, AlphaZero, and all their incarnations are trained using a technique called Monte Carlo tree search (MCTS), whose roots can be traced back to an adaptive multistage sampling (AMS) simulation-based algorithm for Markov decision processes (MDPs) published in Operations Research back in 2005 [Chang, HS, MC Fu, J Hu and SI Marcus (2005). An adaptive sampling algorithm for solving Markov decision processes. Operations Research, 53, 126–139.] (and introduced even earlier in 2002). After reviewing the history and background of AlphaGo through AlphaZero, the origins of MCTS are traced back to simulation-based algorithms for MDPs, and its role in training the neural networks that essentially carry out the value/policy function approximation used in approximate dynamic programming, reinforcement learning, and neuro-dynamic programming is discussed, including some recently proposed enhancements building on statistical ranking & selection research in the operations research simulation community.