Game-theoretic solution concepts prescribe how rational parties should act, but to become operational the concepts need to be accompanied by algorithms. I will review the state of solving incomplete-information games. They encompass many practical problems such as auctions, negotiations, and security applications. I will discuss them in the context of how they have transformed computer poker. In short, game-theoretic reasoning now scales to many large problems, outperforms the alternatives on those problems, and in some games beats the best humans.

In this article, we survey a number of mechanisms created to elicit predictions, many newly proposed within the last decade. We focus on the engineering questions: How do they work and why? What factors and goals are most important in their design? The primary goal of a prediction mechanism is to obtain and aggregate dispersed information, which often exists in tacit forms as beliefs, opinions, or judgements of agents. Coalescing information is a necessary first step for decision making in almost all domains. For example, consider seasonal influenza, a significant cause of illness and death around the world. Although it recurs every year, the geographic location, timing, magnitude, and duration of outbreaks vary widely. Many people possess relevant pieces of the full information puzzle, including doctors who meet patients, clinical microbiologists who perform respiratory culture tests, pharmacists who fill prescriptions, people who have the flu, and people who know people who have the flu.

Indeed, game theory now serves as perhaps the main analytical framework in microeconomic theory, as evidenced by its prominent role in economics textbooks (for example, Mas-Colell, Whinston, and Green 1995) and by the many Nobel prizes in economic sciences awarded to prominent game theorists. Artificial intelligence got its start shortly after game theory (McCarthy et al. 1955), and indeed pioneers such as von Neumann and Simon made early contributions to both fields (see, for example, Findler [1988], Simon [1981]). Both game theory and AI draw (nonexclusively) on decision theory (von Neumann and Morgenstern 1947); for example, one prominent view defines artificial intelligence as "the study and construction of rational agents" (Russell and Norvig 2003), and hence takes a decision-theoretic approach when the world is stochastic. However, artificial intelligence spent most of its first 40 years focused on the design and analysis of agents that act in isolation, and hence had little need for game-theoretic analysis. Starting in the mid to late 1990s, game theory became a major topic of study for computer scientists, for at least two main reasons. First, economists began to be interested in systems whose computational properties posed serious barriers to practical use, and hence reached out to computer scientists; notably, this occurred around the study of combinatorial auctions (see, for example, Cramton, Shoham, and Steinberg 2006). Second, the rise of distributed computing in general and the Internet in particular made it increasingly necessary for computer scientists to study settings in which intelligent agents reason about and interact with other agents.

Software testing is an expensive process, which is vital in the industry. Construction of the test-data in software testing requires the major cost and to decide which method to use in order to generate the test data is important. This paper discusses the efficiency of search-based algorithms (preferably genetic algorithm) versus random testing, in soft- ware test-data generation. This study differs from all previous studies due to sample programs (SUTs) which are used. Since we want to in- crease the complexity of SUTs gradually, and the program generation is automatic as well, Grammatical Evolution is used to guide the program generation. SUTs are generated according to the grammar we provide, with different levels of complexity. SUTs will first undergo genetic al- gorithm and then random testing. Based on the test results, this paper recommends one method to use for automation of software testing.

When choosing a suitable technique for regression and classification with multivariate predictor variables, one is often faced with a tradeoff between interpretability and high predictive accuracy. To give a classical example, classification and regression trees are easy to understand and interpret. Tree ensembles like Random Forests provide usually more accurate predictions. Yet tree ensembles are also more difficult to analyze than single trees and are often criticized, perhaps unfairly, as `black box' predictors. Node harvest is trying to reconcile the two aims of interpretability and predictive accuracy by combining positive aspects of trees and tree ensembles. Results are very sparse and interpretable and predictive accuracy is extremely competitive, especially for low signal-to-noise data. The procedure is simple: an initial set of a few thousand nodes is generated randomly. If a new observation falls into just a single node, its prediction is the mean response of all training observation within this node, identical to a tree-like prediction. A new observation falls typically into several nodes and its prediction is then the weighted average of the mean responses across all these nodes. The only role of node harvest is to `pick' the right nodes from the initial large ensemble of nodes by choosing node weights, which amounts in the proposed algorithm to a quadratic programming problem with linear inequality constraints. The solution is sparse in the sense that only very few nodes are selected with a nonzero weight. This sparsity is not explicitly enforced. Maybe surprisingly, it is not necessary to select a tuning parameter for optimal predictive accuracy. Node harvest can handle mixed data and missing values and is shown to be simple to interpret and competitive in predictive accuracy on a variety of data sets.

The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welsh and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the non-negative matrix factorization (NMF) algorithm to improve the learned HMM parameters. Numerical examples are provided as well.

Markovian processes have long been used to model stochastic environments. Reinforcement learning has emerged as a framework to solve sequential planning and decision-making problems in such environments. In recent years, attempts were made to apply methods from reinforcement learning to construct decision support systems for action selection in Markovian environments. Although conventional methods in reinforcement learning have proved to be useful in problems concerning sequential decision-making, they cannot be applied in their current form to decision support systems, such as those in medical domains, as they suggest policies that are often highly prescriptive and leave little room for the user's input. Without the ability to provide flexible guidelines, it is unlikely that these methods can gain ground with users of such systems. This paper introduces the new concept of non-deterministic policies to allow more flexibility in the user's decision-making process, while constraining decisions to remain near optimal solutions. We provide two algorithms to compute non-deterministic policies in discrete domains. We study the output and running time of these method on a set of synthetic and real-world problems. In an experiment with human subjects, we show that humans assisted by hints based on non-deterministic policies outperform both human-only and computer-only agents in a web navigation task.

We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_{\theta}(x) of different parameters \theta in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is integrated out w.r.t \theta using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel \kappa. In that case, the kernel between x and x' is a a function of the Gram matrices produced by \kappa on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines.

We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer's average uncertainty in the source state vanishes exponentially fast and, as a consequence, an observer's average uncertainty in predicting future output converges exponentially fast to the source entropy rate.

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult case of strictly asymptotic synchronization is treated in a sequel. In both cases, we find that an observer, on average, will synchronize to the source state exponentially fast and that, as a result, the average accuracy in an observer's predictions of the source output approaches its optimal level exponentially fast as well. Additionally, we show here how to analytically calculate the synchronization rate for exact epsilon-machines and provide an efficient polynomial-time algorithm to test epsilon-machines for exactness.