삼목 게임에 적용된 몬테카를로 트리탐색

Fuegito is an educational software package for learning about programming two player games. The package provides a simple, yet flexible and extensible framework which allows students to study the core search algorithms of computer game-playing, and extend them easily in projects. The current version of Fuegito supports alphabeta and Monte Carlo Tree Search as main game tree search methods, as well as a number of simple playing algorithms.

Tree search algorithms are widely applied methods to model and solve sequential decision problems. In particular, the family of sampling-based tree search algorithms called Monte Carlo Tree Search (MCTS) has had great success in problems with large branching factors. However, Real-Time Strategy (RTS) games offer a challenging testbed for tree search algorithms due to their large combinatorial action spaces, partial observability, simultaneous moves, and other factors, making them beyond the grasp of even current MCTS algorithms. This thesis makes contributions towards scaling MCTS algorithms to become more effective and efficient in the domain of RTS games. Specifically, this thesis contributes on the following problems. Firstly, we explore the problem of the integration of MCTS and domain knowledge, in the form of unit-action probability distributions, state evaluation functions, and scripted bots. Secondly, we investigate the optimization of gameplay/rollout policies for MCTS. Third, we study methods for self-learning in MCTS, where tree and/or rollout policies are bootstrapped directly from MCTS behavior iteratively.

Monte Carlo Tree Search (MCTS) is a sampling best-first method to search for optimal decisions. The success of MCTS depends heavily on how the tree is built and the selection process plays a fundamental role in this. One particular selection mechanism that has proved to be reliable is based on the Upper Confidence Bounds for Trees (UCT). The UCT attempts to balance exploration and exploitation by considering the values stored in the statistical tree of the MCTS. However, some tuning of the MCTS UCT is necessary for this to work well. In this work, we use Evolutionary Algorithms (EAs) to evolve mathematical expressions with the goal to substitute the UCT formula and use the evolved expressions in MCTS. More specifically, we evolve expressions by means of our proposed Semantic-inspired Evolutionary Algorithm in MCTS approach (SIEA-MCTS). This is inspired by semantics in Genetic Programming (GP), where the use of fitness cases is seen as a requirement to be adopted in GP. Fitness cases are normally used to determine the fitness of individuals and can be used to compute the semantic similarity (or dissimilarity) of individuals. However, fitness cases are not available in MCTS. We extend this notion by using multiple reward values from MCTS that allow us to determine both the fitness of an individual and its semantics. By doing so, we show how SIEA-MCTS is able to successfully evolve mathematical expressions that yield better or competitive results compared to UCT without the need of tuning these evolved expressions. We compare the performance of the proposed SIEA-MCTS against MCTS algorithms, MCTS Rapid Action Value Estimation algorithms, three variants of the *-minimax family of algorithms, a random controller and two more EA approaches. We consistently show how SIEA-MCTS outperforms most of these intelligent controllers in the challenging game of Carcassonne, whose state-space complexity is, approx., 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{40}$</tex-math></inline-formula> .

The construction of approximate replication strategies for pricing and hedging of derivative contracts in incomplete markets is a key problem of financial engineering. Recently Reinforcement Learning algorithms for hedging under realistic market conditions have attracted significant interest. While research in the derivatives area mostly focused on variations of $Q$-learning, in artificial intelligence Monte Carlo Tree Search is the recognized state-of-the-art method for various planning problems, such as the games of Hex, Chess, Go,... This article introduces Monte Carlo Tree Search as a method to solve the stochastic optimal control problem behind the pricing and hedging tasks. As compared to $Q$-learning it combines Reinforcement Learning with tree search techniques. As a consequence Monte Carlo Tree Search has higher sample efficiency, is less prone to over-fitting to specific market models and generally learns stronger policies faster. In our experiments we find that Monte Carlo Tree Search, being the world-champion in games like Chess and Go, is easily capable of maximizing the utility of investor's terminal wealth without setting up an auxiliary mathematical framework.

Recently, theory of collective intelligence (CI) evolution is proposed as a meta algorithm toward artificial general intelligence. But the only implementation of the CI algorithm of the theory is the Monte Carlo tree search (MCTS) used by AlphaZero. Since ant colony optimization (ACO) is an extensively used CI algorithm, it is useful to implement CI evolution using ACO. A genetic version of ACO is adapted to satisfy the CI evolution theory by two methods. One method is realized by using a policy network, namely policy network guided ACO (P-ACO). The other method is realized by using a policy network and a value network, namely policy and value network guided ACO (PV-ACO). Both methods of ACO evolution algorithm are applied to Tic-Tac-Toe and Four in a Row, where traditional ACO played poorly compared to the tree search algorithm, e.g., MCTS. Computational experiments are done to compare both methods with pure ACO and MCTS. As a result, the intelligence level of ACO evolution algorithm quickly exceeds pure ACO and MCTS. In this article, the performance of ACO evolution algorithm is analyzed and the feasibility of applying the CI evolution theory to a specific application is verified.

Monte Carlo Tree Search (MCTS) is widely used for planning in domains where the potential actions can be represented as a tree of sequential decisions. To efficiently select an action, MCTS usually needs to perform many simulations to build a reliable tree representation of the decision space. As such, a bottleneck to MCTS arises when enough simulations cannot be performed between action selections. This is particularly highlighted in continuously running tasks, for which the time available to perform simulations between actions tends to be limited due to the environment's state constantly changing. In this paper, we present an approach that extends the time available for Monte Carlo simulations when allowed. Our approach is to effectively balance the prospect of selecting the right action with the time that can be spared to perform MCTS simulations before the next action selection. For that, we considered the simulation time as a decision variable to be selected alongside an action. We extended the Hierarchical Optimistic Optimization applied to Tree (HOOT) method to adapt our approach to environments with a continuous decision space. We evaluated our approach on tasks with a continuous decision space using OpenAI gym's Pendulum and Continuous Mountain Car environments and on those with discrete action space using the arcade learning environment (ALE) platform. The evaluation results show that, with variable simulation times, the proposed approach outperforms the conventional MCTS in the evaluated continuous decision space tasks and improves the performance of MCTS in most of the ALE tasks.

Monte Carlo Tree Search (MCTS) is a powerful approach to designing game-playing bots or solving sequential decision problems. The method relies on intelligent tree search that balances exploration and exploitation. MCTS performs random sampling in the form of simulations and stores statistics of actions to make more educated choices in each subsequent iteration. The method has become a state-of-the-art technique for combinatorial games. However, in more complex games (e.g. those with a high branching factor or real-time ones) as well as in various practical domains (e.g. transportation, scheduling or security) an efficient MCTS application often requires its problem-dependent modification or integration with other techniques. Such domain-specific modifications and hybrid approaches are the main focus of this survey. The last major MCTS survey was published in 2012. Contributions that appeared since its release are of particular interest for this review.

The dominant approach for programs playing the game of Go is nowadays Monte-Carlo Tree Search (MCTS). While MCTS allows for fine-grained time control, little has been published on time management for MCTS programs under tournament conditions. This paper investigates the effects that various time-management strategies have on the playing strength in Go. We consider strategies taken from the literature as well as newly proposed and improved ones. We investigate both semi-dynamic strategies that decide about time allocation for each search before it is started, and dynamic strategies that influence the duration of each move search while it is already running. In our experiments, two domain-independent enhanced strategies, EARLY-C and CLOSE-N, are tested; each of them provides a significant improvement over the state of the art.KeywordsTime ManagementSearch TimeTime AllocationDynamic StrategyGood MoveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Monte Carlo tree search (MCTS) is a search paradigm that has been remarkably successful in computer games like Go. It uses Monte Carlo simulation to evaluate the values of nodes in a search tree. The node values are then used to select the actions during subsequent simulations. The performance of MCTS heavily depends on the quality of its default policy, which guides the simulations beyond the search tree. In this paper, we propose an MCTS improvement, called incentive learning, which learns the default policy online. This new default policy learning scheme is based on ideas from combinatorial game theory, and hence is particularly useful when the underlying game is a sum of games. To illustrate the efficiency of incentive learning, we describe a game named Heap-Go and present experimental results on the game.

This tutorial provides an introduction to Monte Carlo tree search (MCTS), which is a general approach to solving sequential decision-making problems under uncertainty using stochastic (Monte Carlo) simulation. MCTS is most famous for its role in Google DeepMind’s AlphaZero, the recent successor to AlphaGo, which defeated the (human) world Go champion Lee Sedol in 2016 and world #1 Go player Ke Jie in 2017. Starting from scratch without using any domain-specific knowledge (other than the rules of the game), AlphaZero was able to defeat not only its predecessors in Go but also the best AI computer programs in chess (Stockfish) and shogi (Elmo), using just 24 hours of training based on MCTS and reinforcement learning. We demonstrate the basic mechanics of MCTS via decision trees and the game of tic-tac-toe.

In this paper, Monte Carlo tree search (MCTS) is introduced for controlling the Pac-Man character in the real-time game Ms Pac-Man. MCTS is used to find an optimal path for an agent at each turn, determining the move to make based on the results of numerous randomized simulations. Several enhancements are introduced in order to adapt MCTS to the real-time domain. Ms Pac-Man is an arcade game, in which the protagonist has several goals but no conclusive terminal state. Unlike games such as Chess or Go there is no state in which the player wins the game. Instead, the game has two subgoals, 1) surviving and 2) scoring as many points as possible. Decisions must be made in a strict time constraint of 40 ms. The Pac-Man agent has to compete with a range of different ghost teams, hence limited assumptions can be made about their behavior. In order to expand the capabilities of existing MCTS agents, four enhancements are discussed: 1) a variable-depth tree; 2) simulation strategies for the ghost team and Pac-Man; 3) including long-term goals in scoring; and 4) reusing the search tree for several moves with a decay factor gamma. The agent described in this paper was entered in both the 2012 World Congress on Computational Intelligence (WCCI'12, Brisbane, Qld., Australia) and the 2012 IEEE Conference on Computational Intelligence and Games (CIG'12, Granada, Spain) Pac-Man Versus Ghost Team competitions, where it achieved second and first places, respectively. In the experiments, we show that using MCTS is a viable technique for the Pac-Man agent. Moreover, the enhancements improve overall performance against four different ghost teams.

Monte Carlo Tree Search (MCTS) parallelization is one of the many possible enhancements for MCTS algorithms. However, no work has been done on evaluating these methods in the rather new area of General Video Game Playing (GVGP), an area that challenges the creation of agents that can play any videogame even without prior knowledge about the video game they are going to play. To address this gap, this paper proposes the implementation and evaluation of the three main MCTS parallelization methods as agents of the General Video Game AI framework, a popular framework for GVGP agents evaluation. This paper is not focused on comparing the parallel MCTS agents to other existing GVGP agents, but rather on exploring how the MCTS parallelization methods compare between themselves. This paper also presents a testing methodology for evaluating these agents, which is based on a set of three experiments focused on different aspects of the parallel MCTS algorithms. In these experiments, the overall best results were achieved by the root parallelization method using the sum merging technique and the UCT’s sigma value of \( \sqrt 2 \).

Monte Carlo Tree Search (MCTS) is a novel machine learning paradigm that is used to find good solutions for complex optimization problems with very large search spaces (like playing GO). We combine MCTS with Covariance Matrix Adaptation Evolution Strategies (CMA-ES) to efficiently optimize real-parameter single objective problems by balancing the exploitation of promising areas with the exploration of new regions of the search space. The novel algorithm is called hierarchical CMA-ES and it is influenced by both machine learning and evolutionary computation research areas. Like in evolutionary computation, we use a population of individuals to explore the commonalities of CMA-ES solvers. These CMA-ES solvers are structured using a MCTS tree like structure. Our experiments compare the performance of hierarchical CMA-ES solvers with two other algorithms: the standard CMA-ES optimizer, and an adaptation of MCTS to solve real-parameter problems. The hierarchical CMA-ES optimizer has the best empirical performance on several benchmark problems.

This research is based on the idea that certain cognitive-intensive tasks typically carried out by structural engineers—such as choosing how to effectively arrange a building’s structure—can be successfully automated. In this article we investigate two techniques widely used in the field of Artificial Intelligence, namely Monte Carlo Tree Search (MCTS) and Genetic Algorithm (GA). Following a tabula rasa approach, according to which no hints nor external data are used as a reference for navigating the search space, we demonstrate how structural designs of two-dimensional multi-storey reinforced concrete structures can be generated, with no human intervention, by implementing and combining the two techniques from a reinforcement-learning perspective. The design tasks assigned to the developed software agents concern civil structures under static and seismic loads, and the basis for comparison is represented by a combination of construction cost and greenhouse gas emissions associated with the making of the structures. In the article, based on the main concepts of Computational Mechanics, a theoretical framework is introduced, which allows to represent both structures and design tasks in a simple, analytical way. The process of gamification, to which MCTS is often associated, is then described, so that structural design is reduced to the concepts of state, actions and payoff.. Finally, case studies are presented in which different agents—based respectively on GA, MCTS, and a combination of both—are tested. The results suggest that hybrid approaches, where GA operates first followed by MCTS, are the most effective.

Monte-Carlo Tree Search (MCTS) grows a partial game tree and uses a large number of random simulations to approximate the values of the nodes. It has proven effective in games with such as Go and Hex where the large search space and difficulty of evaluating positions cause difficulties for standard methods. The best MCTS players use carefully hand-crafted rules to bias the random simulations. Obtaining good hand-crafting rules is a very difficult process, as even rules promoting better simulation play can result in a weaker MCTS system [12]. Our Hivemind system uses evolution strategies to automatically learn effective rules for biasing the random simulations. We have built a MCTS player using Hivemind for the game Hex. The Hivemind learned rules result in a 90% win rate against a baseline MCTS system, and significant improvement against the computer Hex world champion, MoHex.