Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associated with a Gaussian Markov Random Field (GMRF), the Ising model and the Potts model, by extending previous work on $l_1$ regularized neighborhood estimation to include the elastic net $l_1+l_2$ penalty. Additionally, we show numerical evidence that the edge density plays a role in the graph recovery process. Finally, we introduce a novel method for augmenting neighborhood estimation by leveraging pair-wise neighborhood union estimates.

An example is a Mars rover: The major problem with applying POMDP approaches to thanks to low-level control and obstacle avoidance, rovers realistic planning problems like the Mars rovers is the sheer can be expected to reach their destinations reliably, and can size of the problems. Using point-based approximations and collect and communicate data, but they do not know in advance structured representations similar to those used in classical which science targets are interesting and hence will planning (Poupart 2005), problems with tens of millions provide valuable data. Similarly, robots performing tasks of states can be solved approximately, but even that corresponds such as security or cognitive assistance are generally able to to a classical planning problem with only 25 binary navigate reliably, but use unreliable vision algorithms to detect variables, which is a quite small problem by the standards the people and objects with which they are supposed of classical deterministic planning. The alternative we propose to interact. Following Besse and Chaib-draa (2009), we in this paper is to construct a series of classical deterministic will refer to problems with deterministic actions but stochastic planning problems from the quasi-deterministic observations as quasi-deterministic problems, which differ problem. By solving each of these deterministic problems from Deterministic-POMDPs (DET-POMDPS) (Bonet we construct a contingent plan--one that contains branches 2009) by taking into account of uncertainty from observation to be chosen between at run-time.

In this paper, we address the problem of computing the policy of an autonomous agent, taking human recommendations into account which could be appropriate for mixed initiative, or adjustable autonomy. For this purpose, we present Goal Biased Markov Decision Process (GBMDP) which assume two kinds of recommendation. The human recommends to the agent to avoid some situations (represented by undesirable states), or he recommends favorable situations represented by desirable states. The agent takes those recommendations into account by updating its policy (only updating the states concerned by the recommendations, not the whole policy). We show that GBMDP is efficient and it improves the human's intervention by reducing its time of attention paid to the agent. Moreover, GBMDP optimizes robot's computation time by updating only the necessary states. We also show how GBMDP can consider more than one recommendation. Finally, our experiments show how we update policies which are intractable by standard approaches.

Context-aware recommender systems (CARS) generate more relevant recommendations by adapting them to the specific contextual situation of the user. This article explores how contextual information can be used to create more intelligent and useful recommender systems. It provides an overview of the multifaceted notion of context, discusses several approaches for incorporating contextual information in recommendation process, and illustrates the usage of such approaches in several application areas where different types of contexts are exploited. The article concludes by discussing the challenges and future research directions for context-aware recommender systems.

Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs, and novel reduction techniques to keep the representation small. Second, the paper shows how FODDs can be used to develop solutions for RMDPs, where reasoning is performed at the abstract level and the resulting optimal policy is independent of domain size (number of objects) or instantiation. In particular, a variant of the value iteration algorithm is developed by using special operations over FODDs, and the algorithm is shown to converge to the optimal policy.

Multi-agent planning in stochastic environments can be framed formally as a decentralized Markov decision problem. Many real-life distributed problems that arise in manufacturing, multi-robot coordination and information gathering scenarios can be formalized using this framework. However, finding the optimal solution in the general case is hard, limiting the applicability of recently developed algorithms. This paper provides a practical approach for solving decentralized control problems when communication among the decision makers is possible, but costly. We develop the notion of communication-based mechanism that allows us to decompose a decentralized MDP into multiple single-agent problems. In this framework, referred to as decentralized semi-Markov decision process with direct communication (Dec-SMDP-Com), agents operate separately between communications. We show that finding an optimal mechanism is equivalent to solving optimally a Dec-SMDP-Com. We also provide a heuristic search algorithm that converges on the optimal decomposition. Restricting the decomposition to some specific types of local behaviors reduces significantly the complexity of planning. In particular, we present a polynomial-time algorithm for the case in which individual agents perform goal-oriented behaviors between communications. The paper concludes with an additional tractable algorithm that enables the introduction of human knowledge, thereby reducing the overall problem to finding the best time to communicate. Empirical results show that these approaches provide good approximate solutions.

Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.

This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters of the proposal mechanism automatically to ensure efficient mixing of the Markov chains.

Value iteration is a powerful yet inefficient algorithm for Markov decision processes (MDPs) because it puts the majority of its effort into backing up the entire state space, which turns out to be unnecessary in many cases. In order to overcome this problem, many approaches have been proposed. Among them, ILAO* and variants of RTDP are state-of-the-art ones. These methods use reachability analysis and heuristic search to avoid some unnecessary backups. However, none of these approaches build the graphical structure of the state transitions in a pre-processing step or use the structural information to systematically decompose a problem, whereby generating an intelligent backup sequence of the state space. In this paper, we present two optimal MDP algorithms. The first algorithm, topological value iteration (TVI), detects the structure of MDPs and backs up states based on topological sequences. It (1) divides an MDP into strongly-connected components (SCCs), and (2) solves these components sequentially. TVI outperforms VI and other state-of-the-art algorithms vastly when an MDP has multiple, close-to-equal-sized SCCs. The second algorithm, focused topological value iteration (FTVI), is an extension of TVI. FTVI restricts its attention to connected components that are relevant for solving the MDP. Specifically, it uses a small amount of heuristic search to eliminate provably sub-optimal actions; this pruning allows FTVI to find smaller connected components, thus running faster. We demonstrate that FTVI outperforms TVI by an order of magnitude, averaged across several domains. Surprisingly, FTVI also significantly outperforms popular `heuristically-informed' MDP algorithms such as ILAO*, LRTDP, BRTDP and Bayesian-RTDP in many domains, sometimes by as much as two orders of magnitude. Finally, we characterize the type of domains where FTVI excels --- suggesting a way to an informed choice of solver.

Allocating scarce resources among agents to maximize global utility is, in general, computationally challenging. We focus on problems where resources enable agents to execute actions in stochastic environments, modeled as Markov decision processes (MDPs), such that the value of a resource bundle is defined as the expected value of the optimal MDP policy realizable given these resources. We present an algorithm that simultaneously solves the resource-allocation and the policy-optimization problems. This allows us to avoid explicitly representing utilities over exponentially many resource bundles, leading to drastic (often exponential) reductions in computational complexity. We then use this algorithm in the context of self-interested agents to design a combinatorial auction for allocating resources. We empirically demonstrate the effectiveness of our approach by showing that it can, in minutes, optimally solve problems for which a straightforward combinatorial resource-allocation technique would require the agents to enumerate up to 2^100 resource bundles and the auctioneer to solve an NP-complete problem with an input of that size.