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Register a new userMonte-Carlo Tree Search as Regularized Policy Optimization
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The combination of Monte-Carlo tree search (MCTS) with deep reinforcement learning has led to significant advances in artificial intelligence. However, AlphaZero, the current state-of-the-art MCTS algorithm, still relies on handcrafted heuristics that are only partially understood. In this paper, we show that AlphaZeros search heuristics, along with other common ones such as UCT, are an approximation to the solution of a specific regularized policy optimization problem. With this insight, we propose a variant of AlphaZero which uses the exact solution to this policy optimization problem, and show experimentally that it reliably outperforms the original algorithm in multiple domains.
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Active Reinforcement Learning (ARL) is a twist on RL where the agent observes reward information only if it pays a cost. This subtle change makes exploration substantially more challenging. Powerful principles in RL like optimism, Thompson sampling, and random exploration do not help with ARL. We relate ARL in tabular environments to Bayes-Adaptive MDPs. We provide an ARL algorithm using Monte-Carlo Tree Search that is asymptotically Bayes optimal. Experimentally, this algorithm is near-optimal on small Bandit problems and MDPs. On larger MDPs it outperforms a Q-learner augmented with specialised heuristics for ARL. By analysing exploration behaviour in detail, we uncover obstacles to scaling up simulation-based algorithms for ARL.
Many of the strongest game playing programs use a combination of Monte Carlo tree search (MCTS) and deep neural networks (DNN), where the DNNs are used as policy or value evaluators. Given a limited budget, such as online playing or during the self-play phase of AlphaZero (AZ) training, a balance needs to be reached between accurate state estimation and more MCTS simulations, both of which are critical for a strong game playing agent. Typically, larger DNNs are better at generalization and accurate evaluation, while smaller DNNs are less costly, and therefore can lead to more MCTS simulations and bigger search trees with the same budget. This paper introduces a new method called the multiple policy value MCTS (MPV-MCTS), which combines multiple policy value neural networks (PV-NNs) of various sizes to retain advantages of each network, where two PV-NNs f_S and f_L are used in this paper. We show through experiments on the game NoGo that a combined f_S and f_L MPV-MCTS outperforms single PV-NN with policy value MCTS, called PV-MCTS. Additionally, MPV-MCTS also outperforms PV-MCTS for AZ training.
Monte Carlo Tree Search (MCTS) algorithms have achieved great success on many challenging benchmarks (e.g., Computer Go). However, they generally require a large number of rollouts, making their applications costly. Furthermore, it is also extremely challenging to parallelize MCTS due to its inherent sequential nature: each rollout heavily relies on the statistics (e.g., node visitation counts) estimated from previous simulations to achieve an effective exploration-exploitation tradeoff. In spite of these difficulties, we develop an algorithm, WU-UCT, to effectively parallelize MCTS, which achieves linear speedup and exhibits only limited performance loss with an increasing number of workers. The key idea in WU-UCT is a set of statistics that we introduce to track the number of on-going yet incomplete simulation queries (named as unobserved samples). These statistics are used to modify the UCT tree policy in the selection steps in a principled manner to retain effective exploration-exploitation tradeoff when we parallelize the most time-consuming expansion and simulation steps. Experiments on a proprietary benchmark and the Atari Game benchmark demonstrate the linear speedup and the superior performance of WU-UCT comparing to existing techniques.
Despite its groundbreaking success in Go and computer games, Monte Carlo Tree Search (MCTS) is computationally expensive as it requires a substantial number of rollouts to construct the search tree, which calls for effective parallelization. However, how to design effective parallel MCTS algorithms has not been systematically studied and remains poorly understood. In this paper, we seek to lay its first theoretical foundation, by examining the potential performance loss caused by parallelization when achieving a desired speedup. In particular, we discover the necessary conditions of achieving a desirable parallelization performance, and highlight two of their practical benefits. First, by examining whether existing parallel MCTS algorithms satisfy these conditions, we identify key design principles that should be inherited by future algorithms, for example tracking the unobserved samples (used in WU-UCT (Liu et al., 2020)). We theoretically establish this essential design facilitates $mathcal{O} ( ln n + M / sqrt{ln n} )$ cumulative regret when the maximum tree depth is 2, where $n$ is the number of rollouts and $M$ is the number of workers. A regret of this form is highly desirable, as compared to $mathcal{O} ( ln n )$ regret incurred by a sequential counterpart, its excess part approaches zero as $n$ increases. Second, and more importantly, we demonstrate how the proposed necessary conditions can be adopted to design more effective parallel MCTS algorithms. To illustrate this, we propose a new parallel MCTS algorithm, called BU-UCT, by following our theoretical guidelines. The newly proposed algorithm, albeit preliminary, out-performs four competitive baselines on 11 out of 15 Atari games. We hope our theoretical results could inspire future work of more effective parallel MCTS.
The real-time strategy game of StarCraft II has been posed as a challenge for reinforcement learning by Googles DeepMind. This study examines the use of an agent based on the Monte-Carlo Tree Search algorithm for optimizing the build order in StarCraft II, and discusses how its performance can be improved even further by combining it with a deep reinforcement learning neural network. The experimental results accomplished using Monte-Carlo Tree Search achieves a score similar to a novice human player by only using very limited time and computational resources, which paves the way to achieving scores comparable to those of a human expert by combining it with the use of deep reinforcement learning.
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