Yngvi Björnsson

Reykjavík University · School of Computer Science

Concept probing is one prominent methodology for interpreting and analyzing (deep) neural network models. It has, for example, formed the backbone of several recent works to understand better the high-level knowledge learned and employed by game-playing agents, particularly in chess. However, some recent theoretical and empirical studies have quest...

Chess, once famously referred to as the drosophila of artificial intelligence (AI) research, has been a significant domain for developing intelligent AI agents capable of achieving super-human performance in domains previously dominated by humans. However, the emphasis on unceasingly improved playing strength has come at the cost of neglecting othe...

One of the main appeals of AlphaZero-style game-playing agents, which combine deep learning and Monte Carlo Tree Search, is that they can be trained autonomously without external expert-level domain knowledge. However, training such agents is generally computationally expensive, with the most computationally time-consuming step being generating tra...

In recent years, the state-of-the-art agents for playing abstract board games, like chess and others, have moved from using intricate hand-crafted models for evaluating the merits of individual game states toward using neural networks (NNs). This development has eased the encapsulation of the relevant domain-specific knowledge and resulted in much-...

There is a trend in game-playing agents to move towards an Alpha-Zero-style architecture, including using a deep neural network as a model for evaluating game positions. Model interpretability in such agents is problematic. We evaluate the applicability and effectiveness of several saliency-map-based methods for improving the interpretability of a...

As computer game worlds get more elaborate the more visible pathfinding performance bottlenecks become. The heuristic functions typically used for guiding A*-based path inding are too simplistic to provide the search with the necessary guidance in such large and complex game worlds. This may result in A*-search exploring the entire game map in orde...

Video game worlds are getting increasingly large and complex. This poses challenges to the game AI for both pathfinding and strategic decisions, not least in real-time strategy games. One way to alleviate the problem is to manually pre-label the game maps with information about regions and critical choke points, which the game AI can then take adva...

Game playing is one of the oldest areas of investigation in artificial intelligence (AI) and has been at the forefront of AI research ever since the birth of the first computers, over half a century ago. The research focus was initially on developing general approaches for game playing, but gradually shifted towards building high-performance game-p...

Many real-world systems can be represented as formal state transition systems. The modeling process, in other words the process of constructing these systems, is a time-consuming and error-prone activity. In order to counter these difficulties, efforts have been made in various communities to learn the models from input data. One learning approach...

Game playing is one of the oldest areas of investigation in artificial intelligence (AI) and has been at the forefront of AI research ever since the birth of the first computers, over half a century ago. The research focus was initially on developing general approaches for game playing, but gradually shifted towards building high-performance game-p...

The aim of general game playing (GGP) is to create programs capable of playing a wide range of different games at an expert level, given only the rules of the game. The most successful GGP programs currently employ simulation-based Monte Carlo tree search (MCTS). The performance of MCTS depends heavily on the simulation strategy used. In this paper...

The variety of open-source game description language (GDL) reasoners available to newcomers to general game playing (GGP) lowers the technical barrier of entering the field. This variety, however, also makes it more complicated to decide on a fitting reasoner for a given GGP project, considering the project's objectives, ambitions, and technical co...

Monte-Carlo Tree Search (MCTS) has proved a re-markably effective decision mechanism in many different game domains, including computer Go and general game playing (GGP). However, in GGP, where many disparate games are played, cer-tain type of games have proved to be particularly problematic for MCTS. One of the problems are game trees with so-call...

Games have played a prominent role as a test bed for advancements in the field of artificial intelligence ever since its foundation over half a century ago, resulting in highly specialized world-class game-playing systems being developed for various games. The establishment of the International General Game Playing Competition in 2005, however, res...

Model checking is used to uncover errors by searching the state space of a model. Informed search algorithms use heuristic strategies with problem-specific knowledge to find solutions efficiently. Generally, such heuristics estimate the distance from a given state to a goal state. In this paper, we present seven heuristics for guiding search algori...

kEver since humans achieved some degree of civilization, they have played games. The two most important reasons for games to be played are their intellectual challenge and their entertainment value. For the rst reason games are used as a testing ground for computational intelligence. Since the 1950s the AI community compares the computer performanc...

The aim of general game playing (GGP) is to create programs capable of playing a wide range of different games at an expert level, given only the rules of the game. The most successful GGP programs currently employ simulation-based Monte Carlo tree search (MCTS). The performance of MCTS depends heavily on the simulation strategy used. In this paper...

General Game Playing (GGP) agents learn strategies to skillfully play a wide variety of games when given only the rules of the game. The rules are provided in a language called Game De- scription Language (GDL) and specify the initial game setup, what constitutes legal moves and how they update the game state when played, how the game terminates, a...

Monte-Carlo Tree Search (MCTS) is a recent paradigm for game-tree search, which gradually builds a game-tree in a best-first fashion based on the results of randomized simulation play-outs. The performance of such an approach is highly dependent on both the total number of simulation play-outs and their quality. The two metrics are, however, typica...

Effective search control is one of the key components of any successful simulation-based game-playing program. In General Game Playing (GGP), learning of useful search-control knowledge is a particularly challenging task because it must be done in real-time during online play. In here we describe the search-control techniques used in the 2010 versi...

Monte-Carlo Tree Search (MCTS) is a recent paradigm for game-tree search, which gradually builds a game-tree in a best-first fashion based on the results of randomized simulation play-outs. The performance of such an approach is highly dependent on both the total number of simulation play-outs and their quality. The two metrics are, however, typica...

The success of Monte Carlo tree search (MCTS) in many games, where αβ-based search has failed, naturally raises the question whether Monte Carlo simulations will eventually also outperform traditional game-tree search in game domains where αβ -based search is now successful. The forte of αβ-based search are highly tactical deterministic game domain...

Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence con- trolled agents must react quickly to user commands and to other agen...

Game pathfinding is a challenging problem due to a limited amount of per-frame CPU time com-monly shared among many simultaneously pathfinding agents. The challenge is rising with each new generation of games due to progressively larger and more complex environments and larger numbers of agents pathfinding in them. Algorithms based on A* tend to sc...

The aim of General Game Playing (GGP) is to create intelligent agents that can automatically learn how to play many different games at an expert level without any human intervention. One of the main challenges such agents face is to automatically learn knowledge-based heuristics in real-time, whether for evaluating game positions or for search guid...

One of the main challenges with selective search extensions is designing effective move categories (features). Usually, it is a manual trial-and-error task, which requires both intuition and expert human knowledge. Automating this task potentially enables the discovery of both more complex and more effective move categories. The current work introd...

Since the introduction of the LRTA* algorithm, real-time heuristic search algorithms have generally followed the same plan-act-learn cycle: an agent plans one or several actions based on locally available information, executes them and then updates (i.e., learns) its heuristic function. Algorithm evaluation has almost exclusively been empirical wit...

The aim of General Game Playing (GGP) is to cre- ate intelligent agents that can automatically learn how to play many different games at an expert level without any human intervention. One of the main challenges such agents face is to auto- matically learn knowledge-based heuristics in real- time, whether for evaluating game positions or for search...

One of the main challenges with selective search extensions is designing effective move categories (features). This is a manual trial and error task, which requires both intuition and expert human knowledge. Automating this task potentially enables the discovery of both more complex and more effective move categories. In this work we introduce Grad...

Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence controlled agents must react quickly to user commands and to other agents...

The aim of General Game Playing (GGP) is to create intelligent agents that can automatically learn how to play a wide variety of different games at an expert level without any human intervention. This requires that the agents be capable of learning diverse game-playing strategies from basic game rules without any game-specific knowledge being provi...

Recently, Monte-Carlo Tree Search (MCTS) has advanced the fleld of computer Go substantially. In the game of Lines of Action (LOA), which has been dominated in the past by fifl, MCTS is making an inroad. In this paper we investigate how to use a positional evaluation function in a Monte-Carlo simulation-based LOA program (MC-LOA). Four difierent si...

The aim of general game playing (GGP) is to create intelligent agents that can automatically learn how to play many different games at an expert level without any human intervention. The traditional design model for GGP agents has been to use a minimax-based game-tree search augmented with an automatically learned heuristic evaluation function. The...

Real-time heuristic search algorithms are used for planning by agents in situations where a constant- bounded amount of deliberation time is required for each action regardless of the problem size. Such al- gorithms interleave their planning and execution to ensure real-time response. Furthermore, to guar- antee completeness, they typically store i...

Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence controlled agents must react quickly to user commands and to other agents...

In this paper, we show that Realization Probability Search (RPS) significantly improves the playing strength of a world-class Lines-of-Action (LOA) computer program, even when used in combination with existing state-of-the-art αβ search enhancements. In a 600-game match, a RPS-based version of the program defeats the original one with a winning sco...

The search engines of high-performance game-playing pro- grams are becoming increasingly complex as more and more enhance- ments are added. To maintain and enhance such complex engines is a challenging task, and the risk of introducing bugs or other unwanted be- havior during modifications is substantial. In this paper we introduce the Game Tree Qu...

Recently, Monte-Carlo Tree Search (MCTS) has advanced the fleld of computer Go substantially. In this article we investigate the application of MCTS for the game Lines of Action (LOA). A new MCTS variant, called MCTS-Solver, has been designed to play narrow tactical lines better in sudden-death games such as LOA. The variant difiers from the tradit...

Real-time heuristic search is a challenging type of agent-centered search because the agent's planning time per action is bounded by a constant independent of problem size. A common problem that imposes such restrictions is pathfinding in modern computer games where a large number of units must plan their paths simultaneously over large maps. Commo...

The aim of General Game Playing (GGP) is to create intelligent agents that automatically learn how to play many different games at an expert level without any human intervention. The most successful GGP agents in the past have used traditional game-tree search com- bined with an automatically learned heuristic function for evaluating game states. I...

The game of checkers has roughly 500 billion billion possible positions (5 × 1020). The task of solving the game, determining the final result in a game with no mistakes made by either player, is daunting. Since 1989, almost continuously, dozens of computers have been working on solving checkers, applying state-of-the-art artificial intelligence te...

Real-time heuristic search methods, such as LRTA*, are used by situated agents in applications that require the amount of planning per action to be constant-bounded regardless of the problem size. LRTA* interleaves planning and execution, with a fixed search depth being used to achieve progress to- wards a fixed goal. Here we generalize the algorit...

In 1981 Claude Berge asked about combinatorial properties that might be used to solve Hex puzzles. In response, we establish properties of dead, or negligible, cells in Hex and the Shannon game. A cell is dead if the colour of any stone placed there is irrelevant to the theoretical outcome of the game. We show that dead cell recognition is NPcompl...

Endgame databases have previously been built based on complete analysis of endgame positions. In the domain of Checkers, where endgame databases consisting of 39 trillion positions have already been built, it would be beneficial to be able to build select portions of even larger databases, without fully computing portions of the database that will...

One of the main drawbacks of the LRTA* real-time heuris- tic search algorithm is slow convergence. Backtracking as introduced by SLA* is one way of speeding up the conver- gence, although at the cost of sacrificing first-trial perfor- mance. The backtracking mechanism of SLA* consists of back-propagating updated heuristic values to previously vis-...

We present an algorithm that determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm recursively searches the game-tree, combining fixed and dynamic game-state virtual connection composition rules to find a winning virtual connection for one of the two players. The search i...

AI has had notable success in building high- performance game-playing programs to compete against the best human players. However, the availability of fast and plentiful machines with large memories and disks creates the possibility of a game. This has been done before for simple or relatively small games. In this paper, we present new ideas and al...

The A* algorithm is the de facto standard used for pathfinding search. IDA* is a space-efficient version of A*, but it suffers from cycles in the search space (the price for using no storage), repeated visits to states (the overhead of iterative deepening), and a simplistic left- to-right traversal of the search tree. In this paper, the Fringe Sear...

Pathfinding on a map is a fundamental problem in many applications, including robotics and computer games. Typically a grid is superimposed over the map where each cell in the grid forms a unique state. A state-space-based search algorithm, such as A* or IDA*, is then used for finding the optimal (shortest) path. In this paper we analyze the search...

The strength of a program for playing an adversary game like chess or checkers is greatly influenced by how selectively it explores the various branches of the game tree. Typically, some branch paths are discontinued early while others are explored more deeply. Finding the best set of parameters to control these extensions is a difficult, time-cons...

In the half century since minimax was first suggested as a strategy for adversary game search, various search algorithms have been developed. The standard approach has been to use improvements to the Alpha–Beta (α–β) algorithm. Some of the more powerful improvements examine continuations beyond the nominal search depth if they are of special intere...

In this paper we take a general look at forward pruning in tree search. By identifying what we think are desirable characteristics of pruning heuristics, and what attributes are important for them to consider, we hope to understand better the shortcomings of existing techniques, and to provide some additional insight into how they can be improved....

The strength of a program for playing an adversary game like chess or checkers is greatly influenced by how selectively it explores the various branches of the game tree. Typically, some branch paths are discontinued early while others are explored more deeply.

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on mo...

This paper describes the design and development of two world-class Lines of Ac- tion game-playing programs: YL, a three time Computer Olympiad gold-medal winner, and Mona, which has dominated international e-mail correspondence play. The underlying design philosophy of the two programs is very different: the former emphasizes fast and efficient sea...

In 1993, the CHINOOK team completed the computation of the 2 through 8- piece checkers endgame databases, consisting of roughly 444 billion positions. Until recently, nobody had attempted to extend this work. In November 2001, we began an effort to compute the 9- and 10-piece databases. By June 2003, the entire 9-piece database and the 5-piece vers...

Speculative execution of information gathering plans can dramatically reduce the effect of source I/O latencies on overall performance. However, the utility of speculation is closely tied to how accurately data values are predicted at runtime. Caching ...

The efficiency of the ##-algorithm as a minimax search procedure can be attributed to its effective pruning at so-called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by also expanding some of the remaining moves. Our results sho...

The efficiency of the αβ-algorithm as a minimax search procedure can be attributed to its effective pruning at so-called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by also expanding some of the remaining moves. Our results sho...

This chapter provides a brief historical overview of how variable- depth-search methods have evolved in the last half a century of computer chess work. We focus mainly on techniques that have not only withstood the test of time but also embody ideas that are still relevant in contemporary game-playing programs. Pseudo code is provided for a special...

Recently there has been increased interest in applying machine learn- ing methods to adversary games. However, the emphases has been mainly on learning evaluation function parameters and opening book lines, with little attention given to other aspects of the game. In contrast, learning as applied in the domain of planning and scheduling has focusse...

In this paper we take a general look at forward pruning in tree search. By identifying what we think are desirable characteristics of pruning heuristics, and what attributes are important for them to consider, we hope to understand better the shortcomings of existing techniques, and to provide some additional insight into how they can be improved....

The efficiency of the αβ-algorithm as a minimax search procedure can be attributed to its effective pruning at so called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by expanding other move alternatives as well. Our results show...

Advances in technology allow for increasingly deeper searches in competitive chess programs. Several experiments with chess indicate a constant improvement in a program 's performance for deeper searches; a program searching to depth d + 1 scores roughly 80% of the possible points in a match with a program searching to depth d. In other board games...

The thinking process for playing chess by computer is significantly different from that used by humans. Although computer hardware and software have evolved considerably, computers still have difficulties to understand the more elaborate chess concepts. In this paper we look at the technology behind today's chess programs, its current status and ho...

A new domain-independent pruning method is described that guarantees returning a correct game value. Even though alpha-beta-based chess programs are already searching close to the minimal tree, there is still scope for improvement. Our idea hinges on the recognition that the game tree has two types of node, those where cutoffs occur and those that...

Reinforcement learning methods are not yet widely used in computer games, at least not for demanding online learning tasks. This is in part because such methods often require excessive number of training samples before converging. This can be particularly troublesome in mobile game devices where both storage and CPU are limited and valuable resourc...

The contestants. 2003 saw a Hex tournament take place at the Computer Games Olympiad for the first time since 2000, when Vadim Anshelevich's Hexy (gold) defeated Jack van Rijswijck's Queenbee (silver) and Emanuel Brasa's KillerBee (bronze) [1]. programs incorporate the key ideas behind Hexy [2], finding virtual connections via H-search (which uses...

As computer game worlds get more elaborate the more visible pathnding performance bottlenecks become. The heuristic functions typically used for guiding A - based pathnding are too simplistic to provide the search with the necessary guidance in such large and complex game worlds. This may result in A -search exploring the entire game map in order t...