We present three results on the complexity of MINIMAX APPROVAL VOTING. First, we study MINIMAX APPROVAL VOTING parameterized by the Hamming distance d from the solution to the votes. We show MINIMAX APPROVAL VOTING admits no algorithm running in time O ⋆ (2 o ( d log d ) , unless the Exponential Time Hypothesis (ETH) fails. This means that the O ⋆ ( d 2 d ) algorithm of Misra et al. (AAMAS 2015) is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O ⋆ ((3/ε) 2 d ), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs in time n O(1/ε2·log(1/ε)) · poly( m ), almost matching the running time of the fastest known PTAS for CLOSEST STRING due to Ma and Sun (SIAM J. Comp. 2009).

We present a complete algorithm for finding an epsilon-Nash equilibrium, for arbitrarily small epsilon, in games with more than two players. The method improves the best-known upper bound with respect to the number of players n, and it is the first implemented algorithm, to our knowledge, that manages to solve all instances. The main components of our tree-search-based method are a node-selection strategy, an exclusion oracle, and a subdivision scheme. The node-selection strategy determines the next region (of the strategy profile probability vector space) to be explored — based on the region's size and an estimate of whether the region contains an equilibrium. The exclusion oracle provides a provably correct sufficient condition for there not to exist an equilibrium in the region. The subdivision scheme determines how the region is split if it cannot be excluded. Unlike the well-known incomplete methods, our method does not need to proceed locally, which avoids it getting stuck in a local minimum---in the space of players' regrets — that may be far from any actual equilibrium. The run time grows rapidly with the game size; this reflects the dimensionality of this difficult problem. That suggests a hybrid scheme where one of the relatively fast prior incomplete algorithms is run, and if it fails to find an equilibrium, then our method is used.

We show that the HyperPlay technique, which maintains a bag of updatable models for sampling an imperfect-information game, is more efficient than taking random samples of play sequences. Also, we demonstrate that random sampling may become impossible under the practical constraints of a game. We show the HyperPlay sample can become biased and not uniformly distributed across an information set and present a remedy for this bias, showing the impact on game results for biased and unbiased samples. We extrapolate the use of the technique beyond General Game Playing and in particular for enhanced security games with in-game percepts to facilitate a flexible defense response.

In this paper, we investigate the profit-driven team grouping problem in social networks. We consider a setting in which people possess different skills and compatibility among these individuals is captured by a social network. Here, we assume a collection of tasks, where each task requires a specific set of skills, and yields a different profit upon completion. Active and qualified individuals may collaborate with each other in the form of teams to accomplish a set of tasks. Our goal is to find a grouping method that maximizes the total profit of the tasks that these teams can complete. Any feasible grouping must satisfy the following three conditions: (i) each team possesses all skills required by the task, (ii) individuals within the same team are social compatible, and (iii) each individual is not overloaded. We refer to this as the Team Grouping problem. Our work presents a detailed analysis of the computational complexity of the problem, and propose a LP-based approximation algorithm to tackle it and its variants. Although we focus on team grouping in this paper, our results apply to a broad range of optimization problems that can be formulated as a cover decomposition problem.

This paper deals with the constrained DAG shortest path problem (CDSP), which finds the shortest path on a given directed acyclic graph (DAG) under any logical constraints posed on taken edges. There exists a previous work that uses binary decision diagrams (BDDs) to represent the logical constraints, and traverses the input DAG and the BDD simultaneously. The time complexity of this BDD-based method is derived from BDD size, and tends to be fast only when BDDs are small. However, since it does not prioritize the search order, there is considerable room for improvement, particularly for large BDDs. We combine the well-known A* search with the BDD-based method synergistically, and implement several novel heuristic functions. The key insight here is that the ‘shortest path’ in the BDD is a solution of a relaxed problem, just as the shortest path in the DAG is. Experiments, particularly practical machine learning applications, show that the proposed method deceases search time by up to 2 orders of magnitude, with the specific result that it is 2,000 times faster than a commercial solver.

We present the Utility Maximizing Design (UMD) model for optimally redesigning stochastic environments to achieve maximized performance. This model suits well contemporary applications that involve the design of environments where robots and humans co-exist an co-operate, e.g., vacuum cleaning robot. We discuss two special cases of the UMD model. The first is the equi-reward UMD (ER-UMD) in which the agents and the system share a utility function, such as for the vacuum cleaning robot. The second is the goal recognition design (GRD) setting, discussed in the literature, in which system and agent utilities are independent. To find the set of optimal modifications to apply to a UMD model, we present a generic method, based on heuristic search. After specifying the conditions for optimality in the general case, we present an admissible heuristic for the ER-UMD case. We also present a novel compilation that embeds the redesign process into a planning problem, allowing use of any off-the-shelf solver to find the best way to modify an environment when a design budget is specified. Our evaluation shows the feasibility of the approach using standard benchmarks from the probabilistic planning competition.

Learning approximate payoff functions is important to understand the dynamics in multi-player interactions. In general repeat games, each player's payoff can be represented as a combination of all other players' action choices using normal forms, which grow exponentially as the number of action choices increases. Graphical games, however, provide a compact representation to specify the inter-relations where one player's action choice is influenced by its neighbourhood. In this paper, we present how to learn players' approximate payoff functions from normal-form representations, yet also learn a compact graphical game representation of the inter-relations among the players. In this normal form representation, we explore the structural connections of mutual influence between players' action choices in game playing. We formally describe the problem of learning a player influence network and give a novel reward structure-learning algorithm for multiagent graphical games, called the Multi-Descendent Regression Learning Structure Algorithm (MDRLSA). We evaluate MDRLSA on random graphical games generated in GAMUT. Experiments show that MDRLSA can efficiently identify the independence among players and extract the influence graph accurately. The running time of MDRLSA increases linearly with the number of strategy profiles of a game. Compared with state-of-the-art graphical game model learning methods, MDRLSA shows efficiency in terms of time and accuracy.

This paper presents a demonstration of how AI can be useful in the game design and development process of a modern board game. By using an artificial intelligence algorithm to play a substantial amount of matches of the Ticket to Ride board game and collecting data, we can analyze several features of the gameplay as well as of the game board. Results revealed loopholes in the game's rules and pointed towards trends in how the game is played. We are then led to the conclusion that large scale simulation utilizing artificial intelligence can offer valuable information regarding modern board games and their designs that would ordinarily be prohibitively expensive or time-consuming to discover manually.

Symmetry-breaking is a technique for efficiently solving SAT instances that contain high degrees of symmetry among the variables of the instance. When satisfiability problems are represented as a relational schema, symmetries between objects in the domain can be detected directly from evidence, that is, variables known to have a particular setting prior to solving. These symmetries between domain objects are called term symmetries. In this work, we present two novel extensions to the technique of term equivalent symmetry breaking which allow the detection and exploitation of conditional or hidden symmetries, those relationships between domain objects that are obscured until the instance is partially solved. We give promising preliminary experimental results for this technique, and discuss how the techniques could be extended for use in probabilistic domains.

The problem of ordering documents in a large collection into a sequence that is efficient for learning (both human and machine) is of high practical significance, but has not yet been well-formulated. We formulate this problem as mining a maximally informative simple sequence of documents. The mined sequence should be maximally informative in the sense that the reader learns quickly by reading only a few documents, and it should be simple so that the reader is not overwhelmed while trying to learn the content. The task can be posed as: Given that a reader wishes to read (at most) k documents, which documents should be selected from the repository and in what order, so as to provide maximum information. We present the WikiSeq algorithm for this purpose. We also design a metric based on information-gain to help objectively evaluate WikiSeq, and conduct experiments to compare with indicative baselines. Finally, we provide case-studies to subjectively illustrate WikiSeq’s merits.