Showing papers on "Game tree published in 2018"

Superhuman AI for heads-up no-limit poker: Libratus beats top professionals

Abstract: No-limit Texas hold’em is the most popular form of poker. Despite artificial intelligence (AI) successes in perfect-information games, the private information and massive game tree have made no-limit poker difficult to tackle. We present Libratus, an AI that, in a 120,000-hand competition, defeated four top human specialist professionals in heads-up no-limit Texas hold’em, the leading benchmark and long-standing challenge problem in imperfect-information game solving. Our game-theoretic approach features application-independent techniques: an algorithm for computing a blueprint for the overall strategy, an algorithm that fleshes out the details of the strategy for subgames that are reached during play, and a self-improver algorithm that fixes potential weaknesses that opponents have identified in the blueprint strategy.

Solving Imperfect-Information Games via Discounted Regret Minimization

Abstract: Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfect-information games In this paper we introduce novel CFR variants that 1) discount regrets from earlier iterations in various ways (in some cases differently for positive and negative regrets), 2) reweight iterations in various ways to obtain the output strategies, 3) use a non-standard regret minimizer and/or 4) leverage "optimistic regret matching" They lead to dramatically improved performance in many settings For one, we introduce a variant that outperforms CFR+, the prior state-of-the-art algorithm, in every game tested, including large-scale realistic settings CFR+ is a formidable benchmark: no other algorithm has been able to outperform it Finally, we show that, unlike CFR+, many of the important new variants are compatible with modern imperfect-information-game pruning techniques and one is also compatible with sampling in the game tree

GLEAM: a graph clustering framework based on potential game optimization for large-scale social networks

Abstract: With the growing explosion of online social networks, the study of large-scale graph clustering has attracted considerable interest Most of traditional methods view the graph clustering problem as an optimization problem based on a given objective function; however, there are few methodical theories for the emergence of clusters over real-life networks In this paper, each actor in online social networks is viewed as a selfish player in a non-cooperative game The strategy associated with each node is defined as the cluster membership vector, and each one's incentive is to maximize its own social identity by adopting the most suitable strategy The definition of utility function in our game model is inspired by the conformity psychology, which is defined as the weighted average of one's social identity by participating different clusters With this setting, the proposed game can well match a potential game So that the cluster could be shaped by the actions of those closely interactive users who adopt the same strategy in a Nash equilibrium To this end, we propose a novel Graph cLustering framework based on potEntial gAme optiMization (GLEAM) for parallel graph clustering It first utilize the cosine similarity to weight each edge in the original network Then, an initial partition, including a number of clusters dominated by those potential "leader nodes", is created by a fast heuristic process Third, a potential game-based weighted Modularity optimization is used to improve the initial partition Finally, we introduce the notion of potentially attractive cluster, and then discover the overlapping partition of the graph using a simple double-threshold procedure Three phases in GLEAM are carefully designed for parallel execution Experiments on real-world networks analyze the convergence inside GLEAM, and demonstrate the high performance of GLEAM by comparing it with the state-of-the-art community detection approaches in the literature

Computational Results for Extensive-Form Adversarial Team Games

Abstract: We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary. We define three different scenarios according to the communication capabilities of the team. In the first, the teammates can communicate and correlate their actions both before and during the play. In the second, they can only communicate before the play. In the third, no communication is possible at all. We define the most suitable solution concepts, and we study the inefficiency caused by partial or null communication, showing that the inefficiency can be arbitrarily large in the size of the game tree. Furthermore, we study the computational complexity of the equilibrium-finding problem in the three scenarios mentioned above, and we provide, for each of the three scenarios, an exact algorithm. Finally, we empirically evaluate the scalability of the algorithms in random games and the inefficiency caused by partial or null communication.

Playing Multiaction Adversarial Games: Online Evolutionary Planning Versus Tree Search

Abstract: We address the problem of playing turn-based multiaction adversarial games, which include many strategy games with extremely high branching factors as players take multiple actions each turn This leads to the breakdown of standard tree search methods, including Monte Carlo tree search (MCTS), as they become unable to reach a sufficient depth in the game tree In this paper, we introduce online evolutionary planning (OEP) to address this challenge, which searches for combinations of actions to perform during a single turn guided by a fitness function that evaluates the quality of a particular state We compare OEP to different MCTS variations that constrain the exploration to deal with the high branching factor in the turn-based multiaction game Hero Academy While the constrained MCTS variations outperform the vanilla MCTS implementation by a large margin, OEP is able to search the space of plans more efficiently than any of the tested tree search methods as it has a relative advantage when the number of actions per turn increases

A cooperative game framework for detecting overlapping communities in social networks

Abstract: Community detection in social networks is a challenging and complex task, which received much attention from researchers of multiple domains in recent years. The evolution of communities in social networks happens merely due to the self-interest of the nodes. The interesting feature of community structure in social networks is the multi membership of the nodes resulting in overlapping communities. Assuming the nodes of the social network as self-interested players, the dynamics of community formation can be captured in the form of a game. In this paper, we propose a greedy algorithm, namely, Weighted Graph Community Game (WGCG), in order to model the interactions among the self-interested nodes of the social network. The proposed algorithm employs the Shapley value mechanism to discover the inherent communities of the underlying social network. The experimental evaluation on the real-world and synthetic benchmark networks demonstrates that the performance of the proposed algorithm is superior to the state-of-the-art overlapping community detection algorithms.

Deep Counterfactual Regret Minimization

Abstract: Counterfactual Regret Minimization (CFR) is the leading framework for solving large imperfect-information games. It converges to an equilibrium by iteratively traversing the game tree. In order to deal with extremely large games, abstraction is typically applied before running CFR. The abstracted game is solved with tabular CFR, and its solution is mapped back to the full game. This process can be problematic because aspects of abstraction are often manual and domain specific, abstraction algorithms may miss important strategic nuances of the game, and there is a chicken-and-egg problem because determining a good abstraction requires knowledge of the equilibrium of the game. This paper introduces Deep Counterfactual Regret Minimization, a form of CFR that obviates the need for abstraction by instead using deep neural networks to approximate the behavior of CFR in the full game. We show that Deep CFR is principled and achieves strong performance in large poker games. This is the first non-tabular variant of CFR to be successful in large games.

Interference-Aware Spectrum Access Self-Organization: A Weighted Graph Game Perspective

Abstract: We investigate the spectrum access problem in wireless canonical networks, where several network access points (NAPs) share some spectrum in a self-organization manner. A key feature enabling spectrum spatial reuse across nodes is the local interaction, that is, the interferences or direct influences only occur among neighboring nodes. Traditional works model the local interaction relationship by graphs, which, however, fails to characterize the diversity in the interference relationships and results in degradation in the spectrum utilization efficiency. In this paper, we incorporate the interference-awareness into spectrum access. Specifically, we extent the existing graph models to weighted graphs, where the degree of interference is explored and abstracted as the edge weight. On this basis, we formulate the spectrum access self-organization problem as a weighted graph game and analyze the existence and performance bounds of its Nash equilibriums. Finally, an interference-aware spectrum access algorithm achieving Nash equilibriums is proposed, where NAPs select channels according to the number of effectively interfering users instead of the number of interfering NAPs. Simulation results verified the superiority of the weighted graph game and the effectiveness of the spectrum access algorithm.

Generating Win-Win Strategies for Software Businesses Under Coopetition: A Strategic Modeling Approach

Abstract: Interorganizational coopetition describes a phenomenon in which businesses cooperate and compete simultaneously. Such behavior is commonplace among software firms wherein vendors concomitantly deal with each other both as partners and as rivals. Sustainable coopetitive relationships are predicated on the logic of win-win strategies. Conversely, win-lose or lose-lose strategies do not lead to durable coopetitive relationships. This aspect of coopetition requires decision-makers in coopeting software businesses to generate and analyze win-win strategies. This paper proposes a strategic modeling approach to systematically search for alternatives and generate win-win strategies. This approach synergistically combines i* goal-modeling to analyze the distributed intentional structures of actors and Game Tree decision-modeling to reason about the moves and countermoves of actors. An illustrative example of a published case study is presented to demonstrate the strengths and weaknesses of this methodology.

Avoiding game‐tree pathology in 2‐player adversarial search

Abstract: Adversarial search, or game‐tree search, is a technique for analyzing an adversarial game to determine what moves a player should make in order to win a game. Until recently, lookahead pathology (in which deeper game‐tree search results in worse play) has been thought to be quite rare. We provide an analysis that shows that every game should have some sections that are locally pathological, assuming that both players can potentially win the game.

DDT: Deep Driving Tree for Proactive Planning in Interactive Scenarios

Abstract: We consider long-term planning problems for autonomous vehicles in complex traffic scenarios where vehicles and pedestrians interact. The decisions of an autonomous vehicle can influence surrounding other participants in these scenarios. Therefore, planning algorithms that preprocess the long-term prediction of other participants restrict freedom in action. In this paper, we process both problems of long-term planning and prediction at the same time. Our approach which we call DDT (Deep Driving Tree) is based on game tree accumulating a short-term prediction. Machine learning techniques are applied to this short-term prediction instead of model-based techniques that depends on domain knowledge. In contrast to Q-learning, this prediction part is trained off-line and does not require feedback from collision data. Our approach using a game tree models multiple future states of other participants to decide a proactive action taking uncertainties of their intentions into consideration. This approach is demonstrated in a left turning scenario at an intersection of left-hand traffic with oncoming vehicles without V2V communication.

Practical exact algorithm for trembling-hand equilibrium refinements in games

Abstract: Nash equilibrium strategies have the known weakness that they do not prescribe rational play in situations that are reached with zero probability according to the strategies themselves, for example, if players have made mistakes Trembling-hand refinements---such as extensive-form perfect equilibria and quasi-perfect equilibria---remedy this problem in sound ways Despite their appeal, they have not received attention in practice since no known algorithm for computing them scales beyond toy instances In this paper, we design an exact polynomial-time algorithm for finding trembling-hand equilibria in zero-sum extensive-form games It is several orders of magnitude faster than the best prior ones, numerically stable, and quickly solves game instances with tens of thousands of nodes in the game tree It enables, for the first time, the use of trembling-hand refinements in practice

Getting to Win-Win in Industrial Collaboration Under Coopetition: A Strategic Modeling Approach

Abstract: Interorganizational coopetition describes a relationship in which two or more organizations cooperate and compete simultaneously. Actors under coopetition cooperate to achieve collective objectives and compete to maximize their individual benefits. Such relationships are based on the logic of win-win strategies that necessitate decision-makers in coopeting organizations to develop relationships that yield favorable outcomes for each actor. We follow a strategic modeling approach that combines i* goal-modeling to explore strategic alternatives of actors with Game Tree decision-modeling to evaluate the actions and payoffs of those players. In this paper, we elaborate on the method, illustrating one particular pathway towards a positive-sum outcome - through the introduction of an intermediary actor. This paper demonstrates the activation of one component in this guided approach of systematically searching for alternatives to generate a new win-win strategy. A hypothetical industrial scenario drawn from practitioner and scholarly literatures is used to explain this approach. This illustration focuses on the Industrial Data Space which is a platform that can help organizations to overcome obstacles to data sharing in a coopetitive ecosystem.

Improving Game Modeling for the Quoridor Game State Using Graph Databases

Abstract: Artificial intelligence has gained great importance in the last decades because based on its techniques, it is possible to make autonomous systems. In addition, it is possible to make those systems able to learn based on the previous interactions with users. This paper presents one proposal for an agent to play the Quoridor game based on some improvements in the graph model of the board. It is done by using artificial intelligence techniques to provide the capacity to learn through games played against users. Thus, learning is achieved through the use of game trees, where some of the nodes are going to be stored using a graph database. Since graph databases are one of the subgroup of the noSQL databases, which focuses in the relation representation between nodes, such databases are suitable for this kind of approaches.

Application of complex game-tree structures for the hsu graph in the analysis of automatic transmission gearboxes

Abstract: In the article was discussed the possibility of structures and information systems complex game trees for the analysis of automatic gearboxes. The purpose of modelling an automatic gearbox with graphs can be versatile, namely: determining the transmission ratio of individual gears, analysing the speed and acceleration of individual rotating elements. In a further step, logic tree-decision methods can be used to analyse functional schemes of selected transmission gears. Instead, for graphs that are models of transmission, parametrically acting tree structures can be used. This allows for the generalization and extension of the algorithmic approach, furthermore in the future it will allow further analyses and syntheses, such as checking the isomorphism of the proposed solutions, determining the validity of construction and / or operating parameters of the analysed gears. The game tree structure describes a space of possible solutions in order to find optimum objective functions. There is the connection with other graphical structures which can be graphs in another sense, or even decision trees with node and/or branch coding.

A Hybrid Gomoku Deep Learning Artificial Intelligence

Abstract: Gomoku is an ancient board game. The traditional approach to solving the Gomoku is to apply tree search on a Gomoku game tree. Although the rules of Gomoku are straightforward, the game tree complexity is enormous. Unlike other board games such as chess and Shogun, the Gomoku board state is more intuitive. This feature is similar to another famous board game, the game of Go. The success of AlphaGo [5, 6] inspired us to apply a supervised learning method and deep neural network in solving the Gomoku game. We designed a deep convolutional neural network model to help the machine learn from the training data. In our experiment, we got 69% accuracy on the training data and 38% accuracy on the testing data. Finally, we combined the trained deep neural network model with a hard-coded convolution-based Gomoku evaluation function to form a hybrid Gomoku artificial intelligence (AI) which further improved performance.

Facing Multiple Attacks in Adversarial Patrolling Games with Alarmed Targets.

Abstract: We focus on adversarial patrolling games on arbitrary graphs, where the Defender can control a mobile resource, the targets are alarmed by an alarm system, and the Attacker can observe the actions of the mobile resource of the Defender and perform different attacks exploiting multiple resources. This scenario can be modeled as a zero-sum extensive-form game in which each player can play multiple times. The game tree is exponentially large both in the size of the graph and in the number of attacking resources. We show that when the number of the Attacker's resources is free, the problem of computing the equilibrium path is NP-hard, while when the number of resources is fixed, the equilibrium path can be computed in poly-time. We provide a dynamic-programming algorithm that, given the number of the Attacker's resources, computes the equilibrium path requiring poly-time in the size of the graph and exponential time in the number of the resources. Furthermore, since in real-world scenarios it is implausible that the Defender knows the number of attacking resources, we study the robustness of the Defender's strategy when she makes a wrong guess about that number. We show that even the error of just a single resource can lead to an arbitrary inefficiency, when the inefficiency is defined as the ratio of the Defender's utilities obtained with a wrong guess and a correct guess. However, a more suitable definition of inefficiency is given by the difference of the Defender's utilities: this way, we observe that the higher the error in the estimation, the higher the loss for the Defender. Then, we investigate the performance of online algorithms when no information about the Attacker's resources is available. Finally, we resort to randomized online algorithms showing that we can obtain a competitive factor that is twice better than the one that can be achieved by any deterministic online algorithm.

When Does “Knowing More is Less” Happen in Real Games

Abstract: Coevolution in combinatorial games is how players evolve their search strategy and evaluation function according to their opponents. Evaluation function is used to measure the performance of non-final states which embodies major characteristics of a player. Using Five-in-a-Row as a platform, we study how player's winning probability will change after she knows opponent's evaluation function and thus changes search method and we scrutinize the relations between this change and the performance of evaluation functions. We create 45 evaluation functions to contest with each other and build an index called absolute winning probability based on computer simulation to mark the fitness of evaluation functions. We refine the phenomenon of “knowing more is less” and elaborate when “knowing more is less” and “knowing more is more” will happen in Five-in-a-Row. We find that the superior one will win more after knowing the other and the inferior one is possible to lose more after knowing the other. An empirical transformation formula is given to transform absolute winning probability to evaluation function to explain the phenomenon of “knowing more is less” by theoretical game tree model.

A Dynamic-Logical Characterization of Solutions to Sight-limited Extensive Games

Abstract: An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution for a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions of these games via formulas of this logic. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.

A dual-tree Monte Carlo search algorithm for sequential synchronous games

Abstract: The invention discloses a dual-tree Monte Carlo search algorithm for solving a large-scale sequential synchronous game problem. Compared with a sequential synchronous Monte Carlo search based on single tree structure, the invention has the advantages that two trees are established to represent the state transition of both sides of the game, which greatly reduces the selection branches of the gametree and reduces the size of the game tree while maintaining the characteristics of synchronous operation, the explosion problem caused by synchronous action is eliminated and the searching depth is increased, the quality of the solution is ensured, and also the efficiency of the solution is improved. Specific technical means include: through the construction of a Nash equilibrium support library,the problem that synchronous Nash equilibrium online calculation time is too long is solved; a deep strategy net and a deep valuation net of a sequential synchronous game are designed, realizing knowledge guidance of sequential synchronous search; research on environment-oriented reinforcement learning solves the decision-making problem under the condition of state transition or lack of benefits.

Adaptation of Alpha-Beta Search Algorithm for Real-Time Strategy Game

Abstract: Real-time strategy(RTS)[1] game is known for its large action space, rapid response speed, and subtle game scenarios, and it has proven to be a very challenging application area in artificial intelligence research. In the RTS game, the search time increases exponentially as the number of units increases. So it is not possible to achieve a complete search for the game tree in the strict circumstances of time constraints. In this paper, we propose a new tree model, and named T-AlphaBeta search algorithm. It can reduce the interval of Alpha and Beta appropriately by use the dynamic T value in the AlphaBeta[2] [3] algorithm. It can return to the better results at the same time of fast search, so that there is a balance between search depth and search time. We use SparCraft as our test platform, which shows that our approach can achieve better results.

A sequential synchronous sequential Monte Carlo search algorithm

Abstract: A sequential synchronous sequential Monte Carlo search algorithm is provided. The search algorithm is adapted to a search system. The searching system comprises a searching server, a searching entry and a searching device. The searching algorithm comprises the following steps: designing a game tree structure, changing the meaning of the information stored in the node and the connecting edge of thestandard Monte Carlo game tree, and compressing the multi-layer nodes on the standard Monte Carlo game tree containing the information of the game parties to the same layer; and dividing the nodes ineach layer of the new game tree into fixed time periods. In the aspect of problem model, the search algorithm realizes the good modeling of sequential synchronization decision-making problem. In theaspect of searching process, the search algorithm makes the searching more close to the synchronization characteristic of the sequential synchronization decision-making game problem.

Novel threat-based AI strategies that incorporate adaptive data structures for multi-player board games

Abstract: This paper considers the problem of designing novel techniques for multi-player game playing, in a range of board games and configurations. Compared to the well-known case of two-player game playing, multi-player game playing is a more complex problem with unique requirements. To address the unique challenges of this domain, we examine the potential of employing techniques inspired by Adaptive Data Structures (ADSs) to rank opponents based on their relative threats, and using this information to achieve gains in move ordering and tree pruning. We name our new technique the Threat-ADS heuristic. We examine the Threat-ADS’ performance within a range of game models, employing a number of different, well-understood update mechanisms for ADSs. We then extend our analysis to specifically consider intermediate board states, which are more interesting than the initial board state, as we do not assume the availability of “Opening book” moves, and where substantial variation can exist, in terms of available moves and threatening opponents. We expand this analysis to include an exploration of the Threat-ADS heuristic’s performance in deeper ply game trees, to confirm that it maintains its benefits even when lookahead is greater, and with an expanded examination of how the number of players present in the game impacts the performance of the Threat-ADS heuristic. We find that in nearly all environments, the Threat-ADS heuristic is able to produce meaningful, statistically significant improvements in tree pruning, demonstrating that it serves as a very reliable move ordering heuristic for multi-player game playing under a wide range of configurations, thus motivating the use of ADS-based techniques within the field of game playing.

Best play in Dots and Boxes endgames

Abstract: We give very simple algorithms for best play in the simplest kind of Dots & Boxes endgames: those that consist entirely of loops and long chains. In every such endgame we compute the margin of victory, assuming both players maximize the number of boxes they capture, and specify a move that leads to that result. We improve on results of Buzzard and Ciere on the same problem: our algorithms examine only the current position and do not need to consider the game tree at all.

Applying Game Theoretic Techniques to Improve the Accuracy of Tree-based Classification Results

Abstract: The application of game-theoretic techniques to enhance data mining results in financial applications has been widely explored. While results have been promising, further investigation is needed to generate a more robust model and minimize errors. In this work, a two-step, data mining and game-theoretic analysis model is examined to reduce classification error and improve predictions. Using credit-worthiness and loan applications from the German Credit dataset, we are able to reduce classification errors using payoff tables, game trees, and associated binomial distributions. Our results show that applying game-theoretic techniques after data mining results in a combined model can improve overall accuracy and enhance decision accuracy.

Object-Oriented Modeling of Matching to Systemic Classifiers

Abstract: In this paper we present a version of object-oriented implementation of models of constructive regularized mental systems, mentals, and systemic classifiers introduced in [1] as well as algorithms for matching them to situations. We experiment the adequacy of the models and algorithms for the chess representing kernels of the class of combinatorial problems, where space of solutions can be represented by Reproducible Game Trees (RGT).

Polynomial time winning strategies for three variants of ( s , t )-Wythoff’s game

Abstract: In this paper, we provide polynomial time winning strategies for three variants of (s, t)-wythoff’s game using some special numeration systems. The first one is the game of Liu and Zhou (Discrete Applied Math 179:28–43, 2014), which is an extension of (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The second one is a restriction of (s, t)-Wythoff’s game, investigated by Liu and Li (Electron J Combin 21(2): $$\sharp $$ P2.44, 2014), where players are restricted to take even tokes in every move. The final one is new defined and obtained from the second one by adjoining to it some of its P-positions as additional moves.