Scaling Monte Carlo Tree Search on Intel Xeon Phi

Many algorithms have been parallelized successfully on the Intel Xeon Phi coprocessor, especially those with regular, balanced, and predictable data access patterns and instruction flows. Irregular and unbalanced algorithms are harder to parallelize efficiently. They are, for instance, present in artificial intelligence search algorithms such as Monte Carlo Tree Search (MCTS). In this paper we study the scaling behavior of MCTS, on a highly optimized real-world application, on real hardware. The Intel Xeon Phi allows shared memory scaling studies up to 61 cores and 244 hardware threads. We compare work-stealing (Cilk Plus and TBB) and work-sharing (FIFO scheduling) approaches. Interestingly, we find that a straightforward thread pool with a work-sharing FIFO queue shows the best performance. A crucial element for this high performance is the controlling of the grain size, an approach that we call Grain Size Controlled Parallel MCTS. Our subsequent comparing with the Xeon CPUs shows an even more comprehensible distinction in performance between different threading libraries. We achieve, to the best of our knowledge, the fastest implementation of a parallel MCTS on the 61 core Intel Xeon Phi using a real application (47 relative to a sequential run).Comment: 8 pages, 9 figure

Monte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups

Monte Carlo Tree Search (MCTS) has improved the performance of game engines in domains such as Go, Hex, and general game playing. MCTS has been shown to outperform classic alpha-beta search in games where good heuristic evaluations are difficult to obtain. In recent years, combining ideas from traditional minimax search in MCTS has been shown to be advantageous in some domains, such as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new way to use heuristic evaluations to guide the MCTS search by storing the two sources of information, estimated win rates and heuristic evaluations, separately. Rather than using the heuristic evaluations to replace the playouts, our technique backs them up implicitly during the MCTS simulations. These minimax values are then used to guide future simulations. We show that using implicit minimax backups leads to stronger play performance in Kalah, Breakthrough, and Lines of Action.Comment: 24 pages, 7 figures, 9 tables, expanded version of paper presented at IEEE Conference on Computational Intelligence and Games (CIG) 2014 conferenc

TreeQN and ATreeC: Differentiable Tree-Structured Models for Deep Reinforcement Learning

Combining deep model-free reinforcement learning with on-line planning is a promising approach to building on the successes of deep RL. On-line planning with look-ahead trees has proven successful in environments where transition models are known a priori. However, in complex environments where transition models need to be learned from data, the deficiencies of learned models have limited their utility for planning. To address these challenges, we propose TreeQN, a differentiable, recursive, tree-structured model that serves as a drop-in replacement for any value function network in deep RL with discrete actions. TreeQN dynamically constructs a tree by recursively applying a transition model in a learned abstract state space and then aggregating predicted rewards and state-values using a tree backup to estimate Q-values. We also propose ATreeC, an actor-critic variant that augments TreeQN with a softmax layer to form a stochastic policy network. Both approaches are trained end-to-end, such that the learned model is optimised for its actual use in the tree. We show that TreeQN and ATreeC outperform n-step DQN and A2C on a box-pushing task, as well as n-step DQN and value prediction networks (Oh et al. 2017) on multiple Atari games. Furthermore, we present ablation studies that demonstrate the effect of different auxiliary losses on learning transition models

Continuous Monte Carlo Graph Search

In many complex sequential decision making tasks, online planning is crucial for high-performance. For efficient online planning, Monte Carlo Tree Search (MCTS) employs a principled mechanism for trading off between exploration and exploitation. MCTS outperforms comparison methods in various discrete decision making domains such as Go, Chess, and Shogi. Following, extensions of MCTS to continuous domains have been proposed. However, the inherent high branching factor and the resulting explosion of search tree size is limiting existing methods. To solve this problem, this paper proposes Continuous Monte Carlo Graph Search (CMCGS), a novel extension of MCTS to online planning in environments with continuous state and action spaces. CMCGS takes advantage of the insight that, during planning, sharing the same action policy between several states can yield high performance. To implement this idea, at each time step CMCGS clusters similar states into a limited number of stochastic action bandit nodes, which produce a layered graph instead of an MCTS search tree. Experimental evaluation with limited sample budgets shows that CMCGS outperforms comparison methods in several complex continuous DeepMind Control Suite benchmarks and a 2D navigation task.Comment: Under review as a conference paper at ICLR 202