SDYNA is a general framework designed to address large stochastic reinforcement learning problems. Unlike previous model based methods in FMDPs, it incrementally learns the structure and the parameters of a RL problem using supervised learning techniques. Then, it integrates decision-theoric planning algorithms based on FMDPs to compute its policy. SPITI is an instanciation of SDYNA that exploits ITI, an incremental decision tree algorithm, to learn the reward function and the Dynamic Bayesian Networks with local structures representing the transition function of the problem. These representations are used by an incremental version of the Structured Value Iteration algorithm. In order to learn the structure, SPITI uses Chi-Square tests to detect the independence between two probability distributions. Thus, we study the relation between the threshold used in the Chi-Square test, the size of the model built and the relative error of the value function of the induced policy with respect to the optimal value. We show that, on stochastic problems, one can tune the threshold so as to generate both a compact model and an efficient policy. Then, we show that SPITI, while keeping its model compact, uses the generalization property of its learning method to perform better than a stochastic classical tabular algorithm in large RL problem with an unknown structure. We also introduce a new measure based on Chi-Square to qualify the accuracy of the model learned by SPITI. We qualitatively show that the generalization property in SPITI within the FMDP framework may prevent an exponential growth of the time required to learn the structure of large stochastic RL problems.

This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal relationships. We first review Pearl's work on this topic [Pearl, 1995], in which several useful graphical criteria are presented. Then we present a complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem. By exploiting the completeness of this algorithm, we prove that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities.

Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into classes that predict the kinds of probabilistic dependencies they participate in. Here we capture this form of prior knowledge in a hierarchical Bayesian framework, and exploit it to enable structure learning and type discovery from small datasets. Specifically, we present a nonparametric generative model for directed acyclic graphs as a prior for Bayes net structure learning. Our model assumes that variables come in one or more classes and that the prior probability of an edge existing between two variables is a function only of their classes. We derive an MCMC algorithm for simultaneous inference of the number of classes, the class assignments of variables, and the Bayes net structure over variables. For several realistic, sparse datasets, we show that the bias towards systematicity of connections provided by our model yields more accurate learned networks than a traditional, uniform prior approach, and that the classes found by our model are appropriate.

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the problem are discussed. It is shown that the algorithm runs in polynomial-time if the underlying graph of the model has bounded tree-width, and that it provides guarantees to the lower and upper bounds obtained within a fixed amount of computational resources. Experiments with both real and synthetic generated models highlight its main characteristics and show that it compares favorably against Park and Darwiche's systematic search, particularly in the case of problems with many MAP variables and moderate tree-width.

The National Airspace System (NAS) is a large and complex system with thousands of interrelated components: administration, control centers, airports, airlines, aircraft, passengers, etc. The complexity of the NAS creates many difficulties in management and control. One of the most pressing problems is flight delay. Delay creates high cost to airlines, complaints from passengers, and difficulties for airport operations. As demand on the system increases, the delay problem becomes more and more prominent. For this reason, it is essential for the Federal Aviation Administration to understand the causes of delay and to find ways to reduce delay. Major contributing factors to delay are congestion at the origin airport, weather, increasing demand, and air traffic management (ATM) decisions such as the Ground Delay Programs (GDP). Delay is an inherently stochastic phenomenon. Even if all known causal factors could be accounted for, macro-level national airspace system (NAS) delays could not be predicted with certainty from micro-level aircraft information. This paper presents a stochastic model that uses Bayesian Networks (BNs) to model the relationships among different components of aircraft delay and the causal factors that affect delays. A case study on delays of departure flights from Chicago O'Hare international airport (ORD) to Hartsfield-Jackson Atlanta International Airport (ATL) reveals how local and system level environmental and human-caused factors combine to affect components of delay, and how these components contribute to the final arrival delay at the destination airport.

We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and then returning the least cost output uncovered during the search. This framework can be instantiated for a wide range of search spaces and search procedures, and easily incorporates arbitrary structured-prediction loss functions. In this paper, we make two main technical contributions. First, we define the limited-discrepancy search space over structured outputs, which is able to leverage powerful classification learning algorithms to improve the search space quality. Second, we give a generic cost function learning approach, where the key idea is to learn a cost function that attempts to mimic the behavior of conducting searches guided by the true loss function. Our experiments on six benchmark domains demonstrate that using our framework with only a small amount of search is sufficient for significantly improving on state-of-the-art structured-prediction performance.

In this paper we introduce a framework for option model composition. Option models are temporal abstractions that, like macro-operators in classical planning, jump directly from a start state to an end state. Prior work has focused on constructing option models from primitive actions, by intra-option model learning; or on using option models to construct a value function, by inter-option planning. We present a unified view of intra- and inter-option model learning, based on a major generalisation of the Bellman equation. Our fundamental operation is the recursive composition of option models into other option models. This key idea enables compositional planning over many levels of abstraction. We illustrate our framework using a dynamic programming algorithm that simultaneously constructs optimal option models for multiple subgoals, and also searches over those option models to provide rapid progress towards other subgoals.

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of variables increases. Nevertheless, in this paper we show that it is possible to learn the best Bayesian network structure with over 30 variables, which covers many practically interesting cases. Our algorithm is less complicated and more efficient than the techniques presented earlier. It can be easily parallelized, and offers a possibility for efficient exploration of the best networks consistent with different variable orderings. In the experimental part of the paper we compare the performance of the algorithm to the previous state-of-the-art algorithm. Free source-code and an online-demo can be found at http://b-course.hiit.fi/bene.

A central task in many applications is reasoning about processes that change in a continuous time. The mathematical framework of Continuous Time Markov Processes provides the basic foundations for modeling such systems. Recently, Nodelman et al introduced continuous time Bayesian networks (CTBNs), which allow a compact representation of continuous-time processes over a factored state space. In this paper, we introduce continuous time Markov networks (CTMNs), an alternative representation language that represents a different type of continuous-time dynamics. In many real life processes, such as biological and chemical systems, the dynamics of the process can be naturally described as an interplay between two forces - the tendency of each entity to change its state, and the overall fitness or energy function of the entire system. In our model, the first force is described by a continuous-time proposal process that suggests possible local changes to the state of the system at different rates. The second force is represented by a Markov network that encodes the fitness, or desirability, of different states; a proposed local change is then accepted with a probability that is a function of the change in the fitness distribution. We show that the fitness distribution is also the stationary distribution of the Markov process, so that this representation provides a characterization of a temporal process whose stationary distribution has a compact graphical representation. This allows us to naturally capture a different type of structure in complex dynamical processes, such as evolving biological sequences. We describe the semantics of the representation, its basic properties, and how it compares to CTBNs. We also provide algorithms for learning such models from data, and discuss its applicability to biological sequence evolution.

We consider apprenticeship learning, i.e., having an agent learn a task by observing an expert demonstrating the task in a partially observable environment when the model of the environment is uncertain. This setting is useful in applications where the explicit modeling of the environment is difficult, such as a dialogue system. We show that we can extract information about the environment model by inferring action selection process behind the demonstration, under the assumption that the expert is choosing optimal actions based on knowledge of the true model of the target environment. Proposed algorithms can achieve more accurate estimates of POMDP parameters and better policies from a short demonstration, compared to methods that learns only from the reaction from the environment.