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Register a new userMonte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups
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Added by
Marc Lanctot
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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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.
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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.
This paper introduces Monte Carlo *-Minimax Search (MCMS), a Monte Carlo search algorithm for turned-based, stochastic, two-player, zero-sum games of perfect information. The algorithm is designed for the class of of densely stochastic games; that is, games where one would rarely expect to sample the same successor state multiple times at any particular chance node. Our approach combines sparse sampling techniques from MDP planning with classic pruning techniques developed for adversarial expectimax planning. We compare and contrast our algorithm to the traditional *-Minimax approaches, as well as MCTS enhanced with the Double Progressive Widening, on four games: Pig, EinStein Wurfelt Nicht!, Cant Stop, and Ra. Our results show that MCMS can be competitive with enhanced MCTS variants in some domains, while consistently outperforming the equivalent classic approaches given the same amount of thinking time.
Circuit routing is a fundamental problem in designing electronic systems such as integrated circuits (ICs) and printed circuit boards (PCBs) which form the hardware of electronics and computers. Like finding paths between pairs of locations, circuit routing generates traces of wires to connect contacts or leads of circuit components. It is challenging because finding paths between dense and massive electronic components involves a very large search space. Existing solutions are either manually designed with domain knowledge or tailored to specific design rules, hence, difficult to adapt to new problems or design needs. Therefore, a general routing approach is highly desired. In this paper, we model the circuit routing as a sequential decision-making problem, and solve it by Monte Carlo tree search (MCTS) with deep neural network (DNN) guided rollout. It could be easily extended to routing cases with more routing constraints and optimization goals. Experiments on randomly generated single-layer circuits show the potential to route complex circuits. The proposed approach can solve the problems that benchmark methods such as sequential A* method and Lees algorithm cannot solve, and can also outperform the vanilla MCTS approach.
We consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Processes (MDPs) and Partially Observable MDPs (POMDPs), and the well-known Upper Confidence bound for Trees (UCT) algorithm. In UCT, a tree with nodes (states) and edges (actions) is incrementally built by the expansion of nodes, and the values of nodes are updated through a backup strategy based on the average value of child nodes. However, it has been shown that with enough samples the maximum operator yields more accurate node value estimates than averaging. Instead of settling for one of these value estimates, we go a step further proposing a novel backup strategy which uses the power mean operator, which computes a value between the average and maximum value. We call our new approach Power-UCT, and argue how the use of the power mean operator helps to speed up the learning in MCTS. We theoretically analyze our method providing guarantees of convergence to the optimum. Finally, we empirically demonstrate the effectiveness of our method in well-known MDP and POMDP benchmarks, showing significant improvement in performance and convergence speed w.r.t. state of the art algorithms.
Monte Carlo tree search (MCTS) has achieved state-of-the-art results in many domains such as Go and Atari games when combining with deep neural networks (DNNs). When more simulations are executed, MCTS can achieve higher performance but also requires enormous amounts of CPU and GPU resources. However, not all states require a long searching time to identify the best action that the agent can find. For example, in 19x19 Go and NoGo, we found that for more than half of the states, the best action predicted by DNN remains unchanged even after searching 2 minutes. This implies that a significant amount of resources can be saved if we are able to stop the searching earlier when we are confident with the current searching result. In this paper, we propose to achieve this goal by predicting the uncertainty of the current searching status and use the result to decide whether we should stop searching. With our algorithm, called Dynamic Simulation MCTS (DS-MCTS), we can speed up a NoGo agent trained by AlphaZero 2.5 times faster while maintaining a similar winning rate. Also, under the same average simulation count, our method can achieve a 61% winning rate against the original program.
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