Monte Carlo Tree Search (MCTS) has improved the performance of game engines in domains such as Go, Hex, and general game playing. MCTS has been shown to outperform classic alpha-beta search in games where good heuristic evaluations are difficult to obtain. In recent years, combining ideas from traditional minimax search in MCTS has been shown to be advantageous in some domains, such as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new way to use heuristic evaluations to guide the MCTS search by storing the two sources of information, estimated win rates and heuristic evaluations, separately. Rather than using the heuristic evaluations to replace the playouts, our technique backs them up implicitly during the MCTS simulations. These minimax values are then used to guide future simulations. We show that using implicit minimax backups leads to stronger play performance in Kalah, Breakthrough, and Lines of Action.

Attacker-Defender Stackelberg security games (SSGs) have emerged as an important research area in multi-agent systems. However, existing SSGs models yield fixed, static, schedules which fail in dynamic domains where defenders face execution uncertainty, i.e., in domains where defenders may face unanticipated disruptions of their schedules. A concrete example is an application involving checking fares on trains, where a defender's schedule is frequently interrupted by fare evaders, making static schedules useless. To address this shortcoming, this paper provides four main contributions. First, we present a novel general Bayesian Stackelberg game model for security resource allocation in dynamic uncertain domains. In this new model, execution uncertainty is handled by using a Markov decision process (MDP) for generating defender policies. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem structure to reduce it to a polynomial-sized optimization problem. Shifting to evaluation, our third contribution shows, in simulation, that our MDP-based policies overcome the failures of previous SSG algorithms. In so doing, we can now build a complete system, that enables handling of schedule interruptions and, consequently, to conduct some of the first controlled experiments on SSGs in the field.

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances to each element in that set. We propose two original algorithms to compute Wasserstein barycenters that build upon the subgradient method. A direct implementation of these algorithms is, however, too costly because it would require the repeated resolution of large primal and dual optimal transport problems to compute subgradients. Extending the work of Cuturi (2013), we propose to smooth the Wasserstein distance used in the definition of Wasserstein barycenters with an entropic regularizer and recover in doing so a strictly convex objective whose gradients can be computed for a considerably cheaper computational cost using matrix scaling algorithms. We use these algorithms to visualize a large family of images and to solve a constrained clustering problem.

Noname manuscript No. (will be inserted by the editor) Abstract Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics. Keywords Graphical models · Quantum graphical models · Conditional independence · Quantum conditional independence · Commuting Hamiltonian · Quantum Markov network 1 Introduction In 1988, Pearl devised belief propagation algorithm to solve marginalization and other inference problems.

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness of Bayesian optimization. Although Gaussian processes provide a flexible prior over functions which can be queried efficiently, there are various classes of functions that remain difficult to model. One of the most frequently occurring of these is the class of non-stationary functions. The optimization of the hyperparameters of machine learning algorithms is a problem domain in which parameters are often manually transformed a priori, for example by optimizing in "log-space," to mitigate the effects of spatially-varying length scale. We develop a methodology for automatically learning a wide family of bijective transformations or warpings of the input space using the Beta cumulative distribution function. We further extend the warping framework to multi-task Bayesian optimization so that multiple tasks can be warped into a jointly stationary space. On a set of challenging benchmark optimization tasks, we observe that the inclusion of warping greatly improves on the state-of-the-art, producing better results faster and more reliably.

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.

We introduce a novel algorithmic approach to content recommendation based on adaptive clustering of exploration-exploitation ("bandit") strategies. We provide a sharp regret analysis of this algorithm in a standard stochastic noise setting, demonstrate its scalability properties, and prove its effectiveness on a number of artificial and real-world datasets. Our experiments show a significant increase in prediction performance over state-of-the-art methods for bandit problems.

Many applications, ranging from video games to dynamic robotics, require solving single-agent, deterministic search problems in partially known environments under very tight time constraints. Real-Time Heuristic Search (RTHS) algorithms are specifically designed for those applications. As a subroutine, most of them invoke a standard, but bounded, search algorithm that searches for the goal. In this paper we present FRIT, a simple approach for single-agent deterministic search problems under tight constraints and partially known environments that unlike traditional RTHS does not search for the goal but rather searches for a path that connects the current state with a so-called ideal tree T . When the agent observes that an arc in the tree cannot be traversed in the actual environment, it removes such an arc from T and then carries out a reconnection search whose objective is to find a path between the current state and any node in T . The reconnection search is done using an algorithm that is passed as a parameter to FRIT. If such a parameter is an RTHS algorithm, then the resulting algorithm can be an RTHS algorithm. We show, in addition, that FRIT may be fed with a (bounded) complete blind-search algorithm. We evaluate our approach over grid pathfinding benchmarks including game maps and mazes. Our results show that FRIT, used with RTAA*, a standard RTHS algorithm, outperforms RTAA* significantly; by one order of magnitude under tight time constraints. In addition, FRIT(daRTAA*) substantially outperforms daRTAA*, a state-of-the-art RTHS algorithm, usually obtaining solutions 50% cheaper on average when performing the same search effort. Finally, FRIT(BFS), i.e., FRIT using breadth-first-search, obtains best-quality solutions when time is limited compared to Adaptive A* and Repeated A*. Finally we show that Bug2, a pathfinding-specific navigation algorithm, outperforms FRIT(BFS) when planning time is extremely limited, but when given more time, the situation reverses.

Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior. The model and this inference network are trained jointly by maximizing a variational lower bound on the log-likelihood. Although the naive estimator of the inference network gradient is too high-variance to be useful, we make it practical by applying several straightforward modelindependent variance reduction techniques. Applying our approach to training sigmoid belief networks and deep autoregressive networks, we show that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset.