Transposition tables are a powerful tool in search domains for avoiding duplicate effort and for ... more Transposition tables are a powerful tool in search domains for avoiding duplicate effort and for guiding node expansions. Traditionally, however, they have only been applicable when the current state is exactly the same as a previously explored state. We consider a generalized transposition table, whereby a similarity metric that exploits local structure is used to compare the current state with a neighbourhood of previously seen states. We illustrate this concept and forward pruning based on function approximation in the domain of Skat, and show that we can achieve speedups of 16+ over standard methods. 1
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '07, 2007
Most contemporary processors offer some version of Single Instruction Multiple Data (SIMD) machin... more Most contemporary processors offer some version of Single Instruction Multiple Data (SIMD) machinery -vector registers and instructions to manipulate data stored in such registers. The central idea of this paper is to use these SIMD resources to improve the performance of the tail of recursive sorting algorithms. When the number of elements to be sorted reaches a set threshold, data is loaded into the vector registers, manipulated in-register, and the result stored back to memory. Three implementations of sorting with two different SIMD machineries -x86-64's SSE2 and G5's AltiVec -demonstrate that this idea delivers significant speed improvements. The improvements provided are orthogonal to the gains obtained through empirical search for a suitable sorting algorithm . When integrated with the Dynamically Tuned Sorting Library (DTSL) this new code generation strategy reduces the time spent by DTSL up to 22% for moderately-sized arrays, with greater relative reductions for small arrays. Wall-clock performance of d-heaps is improved by up to 39% using a similar technique.
Real-time strategy (RTS) games are complex decision domains which require quick reactions as well... more Real-time strategy (RTS) games are complex decision domains which require quick reactions as well as strate- gic planning. In this paper we describe the first RTS game AI tournament, which was held in June 2006, and the programs that participated.
Amazons is a perfect information board game with simple rules and large branching factors. Two pl... more Amazons is a perfect information board game with simple rules and large branching factors. Two play- ers alternately move chess queen-like pieces and block squares on a 10 10 playing eld. The player who makes the last move wins. Ama- zons endgames usually decompose into indepen- dent subgames. Therefore, the game is a nat- ural testbed for combinatorial game theory. It was known that determining the winner of simple generalized Amazons endgames is NP-equivalent. This paper presents two proofs for the PSPACE- completeness of the generalized version of the full game.
The genre of real-time strategy (RTS) video games is very popular and poses numerous challenges t... more The genre of real-time strategy (RTS) video games is very popular and poses numerous challenges to AI researchers who want to create systems that play autonomously or aid human players. One obstacle for AI progress in this area is closed commercial software which restricts game access to inflexible graphical user interfaces. In this article we describe the current state of the free RTS game engine ORTS which allows users to define RTS games in form of scripts and to connect arbitrary game client software — ranging from 3d GUIs to distributed AI systems. This flexibility opens up new venues for RTS game competitions and AI research, of which some are discussed here as well.
Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect info... more Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect information games that are too large to be optimally solved. Although PIMC search has been criticized in the past for its theoretical deficiencies, in practice it has often produced strong results in a variety of domains. In this paper, we set out to resolve this discrepancy. The contributions of the paper are twofold. First, we use synthetic game trees to identify game properties that result in strong or weak performance for PIMC search as compared to an optimal player. Second, we show how these properties can be detected in real games, and demonstrate that they do indeed appear to be good predictors of the strength of PIMC search. Thus, using the tools established in this paper, it should be possible to decide a priori whether PIMC search will be an effective approach to new and unexplored games.
Skat is Germany's national card game played by millions of players around the world. In this ... more Skat is Germany's national card game played by millions of players around the world. In this paper, we present the world's first computer skat player that plays at the level of human experts. This per- formance is achieved by improving state evalua- tions using game data produced by human players and by using these state evaluations to perform in- ference on the unobserved hands of opposing play- ers. Our results demonstrate the gains from adding inference to an imperfect information game player and show that training on data from average human players can result in expert-level playing strength.
This article motivates AI research in the area of real–time strategy (RTS) games and de-scribes t... more This article motivates AI research in the area of real–time strategy (RTS) games and de-scribes the road–map and the current status of the ORTS project whose goals are to imple-ment an RTS game programming environment and to build AI systems that eventually can outperform human experts in this popular and challenging domain.
This article 1 motivates AI research in the area of real-time strategy (RTS) games and describes ... more This article 1 motivates AI research in the area of real-time strategy (RTS) games and describes the current status of the ORTS project whose goals are to implement an RTS game programming environment and to build AI systems that eventually can outperform human experts in this popular and challenging domain.
Alpha-Beta is the most common game tree search algorithm, due to its high-performance and straigh... more Alpha-Beta is the most common game tree search algorithm, due to its high-performance and straightforward implementation. In practice one must find the best trade-off between heuristic eval- uation time and bringing the subset of nodes ex- plored closer to a minimum proof graph. In this paper we present a series of structural properties of minimum proof graphs that help us to prove that finding such graphs is NP-hard for arbitrary DAG inputs, but can be done in linear time for trees. We then introduce the class of fastest-cut-first search heuristics that aim to approximate minimum proof graphs by sorting moves based on approximations of sub-DAG values and sizes. To explore how var- ious aspects of the game tree (such as branching factor and distribution of move values) affect the performance of Alpha-Beta we introduce the class of "Prefix Value Game Trees" that allows us to la- bel interior nodes with true minimax values on the fly without search. Using these trees we show...
Transposition tables are a powerful tool in search domains for avoiding duplicate effort and for ... more Transposition tables are a powerful tool in search domains for avoiding duplicate effort and for guiding node expansions. Traditionally, however, they have only been applicable when the current state is exactly the same as a previously explored state. We consider a generalized transposition table, whereby a similarity metric that exploits local structure is used to compare the current state with a neighbourhood of previously seen states. We illustrate this concept and forward pruning based on function approximation in the domain of Skat, and show that we can achieve speedups of 16+ over standard methods. 1
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '07, 2007
Most contemporary processors offer some version of Single Instruction Multiple Data (SIMD) machin... more Most contemporary processors offer some version of Single Instruction Multiple Data (SIMD) machinery -vector registers and instructions to manipulate data stored in such registers. The central idea of this paper is to use these SIMD resources to improve the performance of the tail of recursive sorting algorithms. When the number of elements to be sorted reaches a set threshold, data is loaded into the vector registers, manipulated in-register, and the result stored back to memory. Three implementations of sorting with two different SIMD machineries -x86-64's SSE2 and G5's AltiVec -demonstrate that this idea delivers significant speed improvements. The improvements provided are orthogonal to the gains obtained through empirical search for a suitable sorting algorithm . When integrated with the Dynamically Tuned Sorting Library (DTSL) this new code generation strategy reduces the time spent by DTSL up to 22% for moderately-sized arrays, with greater relative reductions for small arrays. Wall-clock performance of d-heaps is improved by up to 39% using a similar technique.
Real-time strategy (RTS) games are complex decision domains which require quick reactions as well... more Real-time strategy (RTS) games are complex decision domains which require quick reactions as well as strate- gic planning. In this paper we describe the first RTS game AI tournament, which was held in June 2006, and the programs that participated.
Amazons is a perfect information board game with simple rules and large branching factors. Two pl... more Amazons is a perfect information board game with simple rules and large branching factors. Two play- ers alternately move chess queen-like pieces and block squares on a 10 10 playing eld. The player who makes the last move wins. Ama- zons endgames usually decompose into indepen- dent subgames. Therefore, the game is a nat- ural testbed for combinatorial game theory. It was known that determining the winner of simple generalized Amazons endgames is NP-equivalent. This paper presents two proofs for the PSPACE- completeness of the generalized version of the full game.
The genre of real-time strategy (RTS) video games is very popular and poses numerous challenges t... more The genre of real-time strategy (RTS) video games is very popular and poses numerous challenges to AI researchers who want to create systems that play autonomously or aid human players. One obstacle for AI progress in this area is closed commercial software which restricts game access to inflexible graphical user interfaces. In this article we describe the current state of the free RTS game engine ORTS which allows users to define RTS games in form of scripts and to connect arbitrary game client software — ranging from 3d GUIs to distributed AI systems. This flexibility opens up new venues for RTS game competitions and AI research, of which some are discussed here as well.
Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect info... more Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect information games that are too large to be optimally solved. Although PIMC search has been criticized in the past for its theoretical deficiencies, in practice it has often produced strong results in a variety of domains. In this paper, we set out to resolve this discrepancy. The contributions of the paper are twofold. First, we use synthetic game trees to identify game properties that result in strong or weak performance for PIMC search as compared to an optimal player. Second, we show how these properties can be detected in real games, and demonstrate that they do indeed appear to be good predictors of the strength of PIMC search. Thus, using the tools established in this paper, it should be possible to decide a priori whether PIMC search will be an effective approach to new and unexplored games.
Skat is Germany's national card game played by millions of players around the world. In this ... more Skat is Germany's national card game played by millions of players around the world. In this paper, we present the world's first computer skat player that plays at the level of human experts. This per- formance is achieved by improving state evalua- tions using game data produced by human players and by using these state evaluations to perform in- ference on the unobserved hands of opposing play- ers. Our results demonstrate the gains from adding inference to an imperfect information game player and show that training on data from average human players can result in expert-level playing strength.
This article motivates AI research in the area of real–time strategy (RTS) games and de-scribes t... more This article motivates AI research in the area of real–time strategy (RTS) games and de-scribes the road–map and the current status of the ORTS project whose goals are to imple-ment an RTS game programming environment and to build AI systems that eventually can outperform human experts in this popular and challenging domain.
This article 1 motivates AI research in the area of real-time strategy (RTS) games and describes ... more This article 1 motivates AI research in the area of real-time strategy (RTS) games and describes the current status of the ORTS project whose goals are to implement an RTS game programming environment and to build AI systems that eventually can outperform human experts in this popular and challenging domain.
Alpha-Beta is the most common game tree search algorithm, due to its high-performance and straigh... more Alpha-Beta is the most common game tree search algorithm, due to its high-performance and straightforward implementation. In practice one must find the best trade-off between heuristic eval- uation time and bringing the subset of nodes ex- plored closer to a minimum proof graph. In this paper we present a series of structural properties of minimum proof graphs that help us to prove that finding such graphs is NP-hard for arbitrary DAG inputs, but can be done in linear time for trees. We then introduce the class of fastest-cut-first search heuristics that aim to approximate minimum proof graphs by sorting moves based on approximations of sub-DAG values and sizes. To explore how var- ious aspects of the game tree (such as branching factor and distribution of move values) affect the performance of Alpha-Beta we introduce the class of "Prefix Value Game Trees" that allows us to la- bel interior nodes with true minimax values on the fly without search. Using these trees we show...
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Papers by Timothy Furtak