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A fundamental challenge in imperfect-information games is that states do not have well-defined values. As a result, depth-limited search algorithms used in single-agent settings and perfect-information games do not apply. This paper…
Skat is a fascinating combinatorial card game, show-casing many of the intrinsic challenges for modern AI systems such as cooperative and adversarial behaviors (among the players), randomness (in the deal), and partial knowledge (due to…
We present two recursive strategy improvement algorithms for solving simple stochastic games. First we present an algorithm for solving SSGs of degree $d$ that uses at most $O\left(\left\lfloor(d+1)^2/2\right\rfloor^{n/2}\right)$…
This paper aims to solve the optimal strategy against a well-known adaptive algorithm, the Hedge algorithm, in a finitely repeated $2\times 2$ zero-sum game. In the literature, related theoretical results are very rare. To this end, we make…
{\alpha}{\mu} is an anytime heuristic search algorithm for incomplete information games that assumes perfect information for the opponents. {\alpha}{\mu} addresses the strategy fusion and non-locality problems encountered by Perfect…
This paper presents an analysis of complexity of double dummy bridge. Values of both, a state-space (search-space) complexity and a game tree complexity have been estimated. ----- Oszacowanie z{\l}o\.zono\'sci problemu rozgrywki w otwarte…
Recent advances in deep reinforcement learning (RL) have led to considerable progress in many 2-player zero-sum games, such as Go, Poker and Starcraft. The purely adversarial nature of such games allows for conceptually simple and…
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…
Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less…
A model checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that…
The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the…
Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…
Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no…
The goal of reinforcement learning algorithms is to estimate and/or optimise the value function. However, unlike supervised learning, no teacher or oracle is available to provide the true value function. Instead, the majority of…
In imperfect information games, the evaluation of a game state not only depends on the observable world but also relies on hidden parts of the environment. As accessing the obstructed information trivialises state evaluations, one approach…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a…
Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement…
Game solving is a similar, yet more difficult task than mastering a game. Solving a game typically means to find the game-theoretic value (outcome given optimal play), and optionally a full strategy to follow in order to achieve that…
Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. {\em Optimization} is one form of analysis. We argue that in many cases it may be better to replace the optimization…