We consider conditions that allow us to find an optimal strategy for sequential decisions from a given data situation. For the case where all interventions are unconditional (atomic), identifiability has been discussed by Pearl & Robins (1995). We argue here that an optimal strategy must be conditional, i.e. take the information available at each decision point into account. We show that the identification of an optimal sequential decision strategy is more restrictive, in the sense that conditional interventions might not always be identified when atomic interventions are. We further demonstrate that a simple graphical criterion for the identifiability of an optimal strategy can be given.

Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also inefficient for large count values and requires averaging over many samples to reduce variance. On the other hand, variational Bayesian inference is efficient and accurate for large count values but suffers from bias for small counts. We propose a hybrid algorithm that combines the best of both worlds: it samples very small counts and applies variational updates to large counts. This hybridization is shown to significantly improve testset perplexity relative to variational inference at no computational cost.

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an upper and lower bound for it. We give necessary conditions for the Gaussian fractional Bethe free energies to be bounded from below. It turns out that the bounding condition is the same as the pairwise normalizability condition derived by Malioutov et al. (2006) as a sufficient condition for the convergence of the message passing algorithm. By giving a counterexample, we disprove the conjecture in Welling and Teh (2001): even when the Bethe free energy is not bounded from below, it can possess a local minimum to which the minimization algorithms can converge.

An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of such models is a well-studied problem. However, existing methods have significant limitations. Methods based on conditional independencies (Spirtes et al. 1993; Pearl 2000) cannot distinguish between independence-equivalent models, whereas approaches purely based on Independent Component Analysis (Shimizu et al. 2006) are inapplicable to data which is partially Gaussian. In this paper, we generalize and combine the two approaches, to yield a method able to learn the model structure in many cases for which the previous methods provide answers that are either incorrect or are not as informative as possible. We give exact graphical conditions for when two distinct models represent the same family of distributions, and empirically demonstrate the power of our method through thorough simulations.

The need to economize limited resources, such as fuel or money, is aubiquitous feature of planning problems. If the resources cannot bereplenished, the planner must make do with the initial supply. It isthen of paramount importance how constrained the problem is,i.e., whether and to which extent the initial resource supply exceedsthe minimum need. While there is a large body of literature on numericplanning and planning with resources, such resource constrainednesshas only been scantily investigated. We herein start to address thisin more detail. We generalize the previous notion of resourceconstrainedness, characterized through a numeric problem feature C≥1 , to the case of multiple resources. We implement an extendedbenchmark suite controlling C . We conduct a large-scale study of thecurrent state of the art as a function of C , highlighting whichtechniques contribute to success. We introduce two new techniques ontop of a recent Monte Carlo Random Walk method, resulting in a plannerthat, in these benchmarks, outperforms previous planners whenresources are scarce ( C close to 1 ). We investigate the parametersinfluencing the performance of that planner, and we show that one ofthe two new techniques works well also on the regular IPC benchmarks.

Optimal plans of delete-free planning tasks are interesting both in domains that have no delete effects and as the relaxation heuristic h+ in general planning. Many heuristics for optimal and satisficing planning approximate the h+ heuristic, which is well-informed and admissible but intractable to compute. In this work, branch-and-bound and IDA* search are used in a search space tailored to delete-free planning together with an incrementally computed version of the LM-cut heuristic. The resulting algorithm for optimal delete-free planning exceeds the performance of A* with the LM-cut heuristic in the state-of-the-art planner Fast Downward.

Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has addressed this via the well-known notion of bisimulation. When aggregating only bisimilar states -- essentially, states whose behavior is identical under every planning operator -- M&S yields a perfect heuristic. However, bisimulations are typically exponentially large. Thus we must relax the bisimulation criterion, so that it applies to more state pairs, and yields smaller abstractions. We herein devise a fine-grained method for doing so. We restrict the bisimulation criterion to consider only a subset K of the planning operators. We show that, if K is chosen appropriately, then M&S still yields a perfect heuristic, while abstraction size may decrease exponentially. Designing practical approximations for K, we obtain M&S heuristics that are competitive with the state of the art.

Engineering companies working with machine tools will often be required to calibrate those machines to international standards. The calibration process requires various errors in the machine to be measured by a skilled expert. In addition to conducting the tests, the engineer must also plan the order in which the tests should take place, and also which instruments should be used to perform each test. It is critical to find as short a calibration plan as possible so that the machine is not out of service for too long. In this work, automated planning is applied to the problem of generating machine tool calibration plans. Given a description of a machine, and its various axes, we produce a calibration plan that minimises the time taken to measure all of the errors of a machine. We also consider the case when there is not enough time to test all errors of the machine, and the calibration plan must maximise the importance of the set of errors tested in the limited time available.

The Liner Shipping Fleet Repositioning Problem (LSFRP) poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between services in a liner shipping network. The LSFRP is characterized by chains of interacting activities, many of which have costs that are a function of their duration; for example, sailing slowly between two ports is cheaper than sailing quickly. Despite its great industrial importance, the LSFRP has received little attention in the literature. We show how the LSFRP can be solved sub-optimally using the planner POPF and optimally with a mixed-integer program (MIP) and a novel method called Temporal Optimization Planning (TOP). We evaluate the performance of each of these techniques on a dataset of real-world instances from our industrial collaborator, and show that automated planning scales to the size of problems faced by industry.

Portfolio planners and parameter tuning are two ideas that have recently attracted significant attention in the domain-independent planning community. We combine these two ideas and present a portfolio planner that runs automatically configured planners. We let the automatic parameter tuning framework ParamILS find fast configurations of the Fast Downward planning system for a number of planning domains. Afterwards we learn a portfolio of those planner configurations. Evaluation of our portfolio planner on the IPC 2011 domains shows that it has a significantly higher IPC score than the winner of the sequential satisficing track.