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

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Learning from Monte Carlo Rollouts with Opponent Models for Playing Tron

This paper describes a novel reinforcement learning system for learning to play the game of Tron. The system combines Q-learning, multi-layer perceptrons, vision grids, opponent modelling, and Monte Carlo rollouts in a novel way. By learning an opponent model, Monte Carlo rollouts can be effectively applied to generate state trajectories for all possible actions from which improved action estimates can be computed. This allows to extend experience replay by making it possible to update the state-action values of all actions in a given game state simultaneously. The results show that the use of experience replay that updates the Q-values of all actions simultaneously strongly outperforms the conventional experience replay that only updates the Q-value of the performed action. The results also show that using short or long rollout horizons during training lead to similar good performances against two fixed opponents

A hybridisation technique for game playing using the upper confidence for trees algorithm with artificial neural networks

In the domain of strategic game playing, the use of statistical techniques such as the Upper Confidence for Trees (UCT) algorithm, has become the norm as they offer many benefits over classical algorithms. These benefits include requiring no game-specific strategic knowledge and time-scalable performance. UCT does not incorporate any strategic information specific to the game considered, but instead uses repeated sampling to effectively brute-force search through the game tree or search space. The lack of game-specific knowledge in UCT is thus both a benefit but also a strategic disadvantage. Pattern recognition techniques, specifically Neural Networks (NN), were identified as a means of addressing the lack of game-specific knowledge in UCT. Through a novel hybridisation technique which combines UCT and trained NNs for pruning, the UCTNN algorithm was derived. The NN component of UCT-NN was trained using a UCT self-play scheme to generate game-specific knowledge without the need to construct and manage game databases for training purposes. The UCT-NN algorithm is outlined for pruning in the game of Go-Moku as a candidate case-study for this research. The UCT-NN algorithm contained three major parameters which emerged from the UCT algorithm, the use of NNs and the pruning schemes considered. Suitable methods for finding candidate values for these three parameters were outlined and applied to the game of Go-Moku on a 5 by 5 board. An empirical investigation of the playing performance of UCT-NN was conducted in comparison to UCT through three benchmarks. The benchmarks comprise a common randomly moving opponent, a common UCTmax player which is given a large amount of playing time, and a pair-wise tournament between UCT-NN and UCT. The results of the performance evaluation for 5 by 5 Go-Moku were promising, which prompted an evaluation of a larger 9 by 9 Go-Moku board. The results of both evaluations indicate that the time allocated to the UCT-NN algorithm directly affects its performance when compared to UCT. The UCT-NN algorithm generally performs better than UCT in games with very limited time-constraints in all benchmarks considered except when playing against a randomly moving player in 9 by 9 Go-Moku. In real-time and near-real-time Go-Moku games, UCT-NN provides statistically significant improvements compared to UCT. The findings of this research contribute to the realisation of applying game-specific knowledge to the UCT algorithm

Scalable Neural Network Decoders for Higher Dimensional Quantum Codes

Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be evaluated by dedicated hardware which is very fast and consumes little power. Machine learning has been previously applied to decode the surface code. However, these approaches are not scalable as the training has to be redone for every system size which becomes increasingly difficult. In this work the existence of local decoders for higher dimensional codes leads us to use a low-depth convolutional neural network to locally assign a likelihood of error on each qubit. For noiseless syndrome measurements, numerical simulations show that the decoder has a threshold of around $7.1\%$ when applied to the 4D toric code. When the syndrome measurements are noisy, the decoder performs better for larger code sizes when the error probability is low. We also give theoretical and numerical analysis to show how a convolutional neural network is different from the 1-nearest neighbor algorithm, which is a baseline machine learning method

Contributions to Monte Carlo Search

This research is motivated by improving decision making under uncertainty and in particular for games and symbolic regression. The present dissertation gathers research contributions in the field of Monte Carlo Search. These contributions are focused around the selection, the simulation and the recommendation policies. Moreover, we develop a methodology to automatically generate an MCS algorithm for a given problem. For the selection policy, in most of the bandit literature, it is assumed that there is no structure or similarities between arms. Thus each arm is independent from one another. In several instances however, arms can be closely related. We show both theoretically and empirically, that a significant improvement over the state-of-the-art selection policies is possible. For the contribution on simulation policy, we focus on the symbolic regression problem and ponder on how to consistently generate different expressions by changing the probability to draw each symbol. We formalize the situation into an optimization problem and try different approaches. We show a clear improvement in the sampling process for any length. We further test the best approach by embedding it into a MCS algorithm and it still shows an improvement. For the contribution on recommendation policy, we study the most common in combination with selection policies. A good recommendation policy is a policy that works well with a given selection policy. We show that there is a trend that seems to favor a robust recommendation policy over a riskier one. We also present a contribution where we automatically generate several MCS algorithms from a list of core components upon which most MCS algorithms are built upon and compare them to generic algorithms. The results show that it often enables discovering new variants of MCS that significantly outperform generic MCS algorithms

Low-resource learning in complex games

This project is concerned with learning to take decisions in complex domains, in games in particular. Previous work assumes that massive data resources are available for training, but aside from a few very popular games, this is generally not the case, and the state of the art in such circumstances is to rely extensively on hand-crafted heuristics. On the other hand, human players are able to quickly learn from only a handful of examples, exploiting specific characteristics of the learning problem to accelerate their learning process. Designing algorithms that function in a similar way is an open area of research and has many applications in today’s complex decision problems. One solution presented in this work is design learning algorithms that exploit the inherent structure of the game. Specifically, we take into account how the action space can be clustered into sets called types and exploit this characteristic to improve planning at decision time. Action types can also be leveraged to extract high-level strategies from a sparse corpus of human play, and this generates more realistic trajectories during planning, further improving performance. Another approach that proved successful is using an accurate model of the environment to reduce the complexity of the learning problem. Similar to how human players have an internal model of the world that allows them to focus on the relevant parts of the problem, we decouple learning to win from learning the rules of the game, thereby making supervised learning more data efficient. Finally, in order to handle partial observability that is usually encountered in complex games, we propose an extension to Monte Carlo Tree Search that plans in the Belief Markov Decision Process. We found that this algorithm doesn’t outperform the state of the art models on our chosen domain. Our error analysis indicates that the method struggles to handle the high uncertainty of the conditions required for the game to end. Furthermore, our relaxed belief model can cause rollouts in the belief space to be inaccurate, especially in complex games. We assess the proposed methods in an agent playing the highly complex board game Settlers of Catan. Building on previous research, our strongest agent combines planning at decision time with prior knowledge extracted from an available corpus of general human play; but unlike this prior work, our human corpus consists of only 60 games, as opposed to many thousands. Our agent defeats the current state of the art agent by a large margin, showing that the proposed modifications aid in exploiting general human play in highly complex games