In imperfect-information games, agents must make decisions based on partial knowledge of the game state. The Belief Stochastic Game model addresses this challenge by delegating state estimation to the game model itself. This allows agents to operate on externally provided belief states, thereby reducing the need for game-specific inference logic. This paper investigates two approaches to represent beliefs in games with hidden piece identities: a constraint-based model using Constraint Satisfaction Problems and a probabilistic extension using Belief Propagation to estimate marginal probabilities. We evaluated the impact of both representations using general-purpose agents across two different games. Our findings indicate that constraint-based beliefs yield results comparable to those of probabilistic inference, with minimal differences in agent performance. This suggests that constraint-based belief states alone may suffice for effective decision-making in many settings.

There are several different game description languages (GDLs), each intended to allow wide ranges of arbitrary games (i.e., general games) to be described in a single higher-level language than general-purpose programming languages. Games described in such formats can subsequently be presented as challenges for automated general game playing agents, which are expected to be capable of playing any arbitrary game described in such a language without prior knowledge about the games to be played. The language used by the Ludii general game system was previously shown to be capable of representing equivalent games for any arbitrary, finite, deterministic, fully observable extensive-form game. In this paper, we prove its universality by extending this to include finite non-deterministic and imperfect-information games.

Automatically generating novel and interesting games is a complex task. Challenges include representing game rules in a computationally workable form, searching through the large space of potential games under most such representations, and accurately evaluating the originality and quality of previously unseen games. Prior work in automated game generation has largely focused on relatively restricted rule representations and relied on domain-specific heuristics. In this work, we explore the generation of novel games in the comparatively expansive Ludii game description language, which encodes the rules of over 1000 board games in a variety of styles and modes of play. We draw inspiration from recent advances in large language models and evolutionary computation in order to train a model that intelligently mutates and recombines games and mechanics expressed as code. We demonstrate both quantitatively and qualitatively that our approach is capable of generating new and interesting games, including in regions of the potential rules space not covered by existing games in the Ludii dataset.

In many board games and other abstract games, patterns have been used as features that can guide automated game-playing agents. Such patterns or features often represent particular configurations of pieces, empty positions, etc., which may be relevant for a game's strategies. Their use has been particularly prevalent in the game of Go, but also many other games used as benchmarks for AI research. In this paper, we formulate a design and efficient implementation of spatial state-action features for general games. These are patterns that can be trained to incentivise or disincentivise actions based on whether or not they match variables of the state in a local area around action variables. We provide extensive details on several design and implementation choices, with a primary focus on achieving a high degree of generality to support a wide variety of different games using different board geometries or other graphs. Secondly, we propose an efficient approach for evaluating active features for any given set of features. In this approach, we take inspiration from heuristics used in problems such as SAT to optimise the order in which parts of patterns are matched and prune unnecessary evaluations. This approach is defined for a highly general and abstract description of the problem—phrased as optimising the order in which propositions of formulas in disjunctive normal form are evaluated—and may therefore also be of interest to other types of problems than board games. An empirical evaluation on 33 distinct games in the Ludii general game system demonstrates the efficiency of this approach in comparison to a naive baseline, as well as a baseline based on prefix trees, and demonstrates that the additional efficiency significantly improves the playing strength of agents using the features to guide search.

Local, spatial state-action features can be used to effectively train linear policies from self-play in a wide variety of board games. Such policies can play games directly, or be used to bias tree search agents. However, the resulting feature sets can be large, with a significant amount of overlap and redundancies between features. This is a problem for two reasons. Firstly, large feature sets can be computationally expensive, which reduces the playing strength of agents based on them. Secondly, redundancies and correlations between features impair the ability for humans to analyse, interpret, or understand tactics learned by the policies. We look towards decision trees for their ability to perform feature selection, and serve as interpretable models. Previous work on distilling policies into decision trees uses states as inputs, and distributions over the complete action space as outputs. In contrast, we propose and evaluate a variety of decision tree types, which take state-action pairs as inputs, and provide various different types of outputs on a per-action basis. An empirical evaluation over 43 different board games is presented, and two of those games are used as case studies where we attempt to interpret the discovered features.

Many games often share common ideas or aspects between them, such as their rules, controls, or playing area. However, in the context of General Game Playing (GGP) for board games, this area remains under-explored. We propose to formalise the notion of “game concept”, inspired by terms generally used by game players and designers. Through the Ludii General Game System, we describe concepts for several levels of abstraction, such as the game itself, the moves played, or the states reached. This new GGP feature associated with the ludeme representation of games opens many new lines of research. The creation of a hyper-agent selector, the transfer of AI learning between games, or explaining AI techniques using game terms, can all be facilitated by the use of game concepts. Other applications which can benefit from game concepts are also discussed, such as the generation of plausible reconstructed rules for incomplete ancient games, or the implementation of a board game recommender system.

This paper investigates the performance of different general-game-playing heuristics for games in the Ludii general game system. Based on these results, we train several regression learning models to predict the performance of these heuristics based on each game's description file. We also provide a condensed analysis of the games available in Ludii, and the different ludemes that define them.

Expert Iteration (ExIt) is an effective framework for learning game-playing policies from self-play. ExIt involves training a policy to mimic the search behaviour of a tree search algorithm -- such as Monte-Carlo tree search -- and using the trained policy to guide it. The policy and the tree search can then iteratively improve each other, through experience gathered in self-play between instances of the guided tree search algorithm. This paper outlines three different approaches for manipulating the distribution of data collected from self-play, and the procedure that samples batches for learning updates from the collected data. Firstly, samples in batches are weighted based on the durations of the episodes in which they were originally experienced. Secondly, Prioritized Experience Replay is applied within the ExIt framework, to prioritise sampling experience from which we expect to obtain valuable training signals. Thirdly, a trained exploratory policy is used to diversify the trajectories experienced in self-play. This paper summarises the effects of these manipulations on training performance evaluated in fourteen different board games. We find major improvements in early training performance in some games, and minor improvements averaged over fourteen games.

Accepted at ECAI 2020

This paper proposes using a linear function approximator, rather than a deep neural network (DNN), to bias a Monte Carlo tree search (MCTS) player for general games. This is unlikely to match the potential raw playing strength of DNNs, but has advantages in terms of generality, interpretability and resources (time and hardware) required for training. Features describing local patterns are used as inputs. The features are formulated in such a way that they are easily interpretable and applicable to a wide range of general games, and might encode simple local strategies. We gradually create new features during the same self-play training process used to learn feature weights. We evaluate the playing strength of an MCTS player biased by learnt features against a standard upper confidence bounds for trees (UCT) player in multiple different board games, and demonstrate significantly improved playing strength in the majority of them after a small number of self-play training games.

Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as Sudoku, but also enjoy the ability to check their solution easily once it's done. For this reason, using constraint programming is naturally suited to solve them. In this paper, we focus on logic puzzles described in the Ludii general game system and we propose using the XCSP formalism in order to solve them with any CSP solver.

Although General Game Playing (GGP) systems can facilitate useful research in Artificial Intelligence (AI) for game-playing, they are often computationally inefficient and somewhat specialised to a specific class of games. However, since the start of this year, two General Game Systems have emerged that provide efficient alternatives to the academic state of the art - the Game Description Language (GDL). In order of publication, these are the Regular Boardgames language (RBG), and the Ludii system. This paper offers an experimental evaluation of Ludii. Here, we focus mainly on a comparison between the two new systems in terms of two key properties for any GGP system: simplicity/clarity (e.g. human-readability), and efficiency.

In recent years, state-of-the-art game-playing agents often involve policies that are trained in self-playing processes where Monte Carlo tree search (MCTS) algorithms and trained policies iteratively improve each other. The strongest results have been obtained when policies are trained to mimic the search behaviour of MCTS by minimising a cross-entropy loss. Because MCTS, by design, includes an element of exploration, policies trained in this manner are also likely to exhibit a similar extent of exploration. In this paper, we are interested in learning policies for a project with future goals including the extraction of interpretable strategies, rather than state-of-the-art game-playing performance. For these goals, we argue that such an extent of exploration is undesirable, and we propose a novel objective function for training policies that are not exploratory. We derive a policy gradient expression for maximising this objective function, which can be estimated using MCTS value estimates, rather than MCTS visit counts. We empirically evaluate various properties of resulting policies, in a variety of board games.

Ludii is a general game system being developed as part of the ERC-funded Digital Ludeme Project (DLP). While its primary aim is to model, play, and analyse the full range of traditional strategy games, Ludii also has the potential to support a wide range of AI research topics and competitions. This paper describes some of the future competitions and challenges that we intend to run using the Ludii system, highlighting some of its most important aspects that can potentially lead to many algorithm improvements and new avenues of research. We compare and contrast our proposed competition motivations, goals and frameworks against those of existing general game playing competitions, addressing the strengths and weaknesses of each platform.

The Digital Ludeme Project (DLP) aims to reconstruct and analyse over 1000 traditional strategy games using modern techniques. One of the key aspects of this project is the development of Ludii, a general game system that will be able to model and play the complete range of games required by this project. Such an undertaking will create a wide range of possibilities for new AI challenges. In this paper we describe many of the features of Ludii that can be used. This includes designing and modifying games using the Ludii game description language, creating agents capable of playing these games, and several advantages the system has over prior general game software.

Symmetry detection is a promising approach for reducing the search tree of games. In General Game Playing (GGP), where any game is compactly represented by a set of rules in the Game Description Language (GDL), the state-of-the-art methods for symmetry detection rely on a rule graph associated with the GDL description of the game. Though such rule-based symmetry detection methods can be applied to various tree search algorithms, they cover only a limited number of symmetries which are apparent in the GDL description. In this paper, we develop an alternative approach to symmetry detection in stochastic games that exploits constraint programming techniques. The minimax optimization problem in a GDL game is cast as a stochastic constraint satisfaction problem (SCSP), which can be viewed as a sequence of one-stage SCSPs. Minimax symmetries are inferred according to themicrostructure complement of these one-stage constraint networks. Based on a theoretical analysis of this approach, we experimentally show on various games that the recent stochastic constraint solver MAC-UCB, coupled with constraint-based symmetry detection, significantly outperforms the standard Monte Carlo Tree Search algorithms, coupled with rule-based symmetry detection. This constraint-driven approach is also validated by the excellent results obtained by our player during the last GGP competition.