We consider constraint-based methods for causal structure learning, such as the PC algorithm or any PC-derived algorithms whose first step consists in pruning a complete graph to obtain an undirected graph skeleton, which is subsequently oriented. All constraint-based methods perform this first step of removing dispensable edges, iteratively, whenever a separating set and corresponding conditional independence can be found. Yet, constraint-based methods lack robustness over sampling noise and are prone to uncover spurious conditional independences in finite datasets. In particular, there is no guarantee that the separating sets identified during the iterative pruning step remain consistent with the final graph. In this paper, we propose a simple modification of PC and PC-derived algorithms so as to ensure that all separating sets identified to remove dispensable edges are consistent with the final graph,thus enhancing the explainability of constraint-basedmethods. It is achieved by repeating the constraint-based causal structure learning scheme, iteratively, while searching for separating sets that are consistent with the graph obtained at the previous iteration.

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to the Polyak-Lojasiewicz and Mangasarian-Fromowitz conditions. In particular, when a first-order solver is used for the inner iterates, we prove that iALM finds a first-order stationary point with $\tilde{\mathcal{O}}(1/\epsilon 3)$ calls to the first-order oracle. These complexity results match the known theoretical results in the literature. We also provide strong numerical evidence on large-scale machine learning problems, including the Burer-Monteiro factorization of semidefinite programs, and a novel nonconvex relaxation of the standard basis pursuit template.

We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to account for a fine-grained timing. More precisely, we exemplarily show how the hybrid ASP system clingo[DL] can be used to tackle demanding planning-and-scheduling problems. In particular, we investigate how to boost performance by combining distinct ASP solving techniques, such as approximations and heuristics, with preprocessing and encoding techniques for tackling large-scale, real-world train scheduling instances.

Agile satellites are the new generation of Earth observation satellites (EOSs) with stronger attitude maneuvering capability. Since optical remote sensing instruments equipped on satellites cannot see through the cloud, the cloud coverage has a significant influence on the satellite observation missions. We are the first to address multiple agile EOSs scheduling problem under cloud coverage uncertainty where the objective aims to maximize the entire observation profit. The chance constraint programming model is adopted to describe the uncertainty initially, and the observation profit under cloud coverage uncertainty is then calculated via sample approximation method. Subsequently, an improved simulated annealing based heuristic combining a fast insertion strategy is proposed for large-scale observation missions. The experimental results show that the improved simulated annealing heuristic outperforms other algorithms for the multiple AEOSs scheduling problem under cloud coverage uncertainty, which verifies the efficiency and effectiveness of the proposed algorithm.

Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, we learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm, called QUACQ, that, given a negative example, focuses onto a constraint of the target network in a number of queries logarithmic in the size of the example. The whole constraint network can then be learned with a polynomial number of partial queries. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases.

Agile satellites with advanced attitude maneuvering capability are the new generation of Earth observation satellites (EOSs). The continuous improvement in satellite technology and decrease in launch cost have boosted the development of agile EOSs (AEOSs). To efficiently employ the increasing orbiting AEOSs, the AEOS scheduling problem (AEOSSP) aiming to maximize the entire observation profit while satisfying all complex operational constraints, has received much attention over the past 20 years. The objectives of this paper are thus to summarize current research on AEOSSP, identify main accomplishments and highlight potential future research directions. To this end, general definitions of AEOSSP with operational constraints are described initially, followed by its three typical variations including different definitions of observation profit, multi-objective function and autonomous model. A detailed literature review from 1997 up to 2019 is then presented in line with four different solution methods, i.e., exact method, heuristic, metaheuristic and machine learning. Finally, we discuss a number of topics worth pursuing in the future.

We introduce the exactCover global constraint dedicated to the exact cover problem, the goal of which is to select subsets such that each element of a given set belongs to exactly one selected subset. This NP-complete problem occurs in many applications, and we more particularly focus on a conceptual clustering application. We introduce three propagation algorithms for exactCover, called Basic, DL, and DL+: Basic ensures the same level of consistency as arc consistency on a classical decomposition of exactCover into binary constraints, without using any specific data structure; DL ensures the same level of consistency as Basic but uses Dancing Links to efficiently maintain the relation between elements and subsets; and DL+ is a stronger propagator which exploits an extra property to filter more values than DL. We also consider the case where the number of selected subsets is constrained to be equal to a given integer variable k, and we show that this may be achieved either by combining exactCover with existing constraints, or by designing a specific propagator that integrates algorithms designed for the NValues constraint. These different propagators are experimentally evaluated on conceptual clustering problems, and they are compared with state-of-the-art declarative approaches. In particular, we show that our global constraint is competitive with recent ILP and CP models for mono-criterion problems, and it has better scale-up properties for multi-criteria problems.

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.

We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNF-formulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to those of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors.

Monocular 3D object detection is an essential component in autonomous driving while challenging to solve, especially for those occluded samples which are only partially visible. Most detectors consider each 3D object as an independent training target, inevitably resulting in a lack of useful information for occluded samples. To this end, we propose a novel method to improve the monocular 3D object detection by considering the relationship of paired samples. This allows us to encode spatial constraints for partially-occluded objects from their adjacent neighbors. Specifically, the proposed detector computes uncertainty-aware predictions for object locations and 3D distances for the adjacent object pairs, which are subsequently jointly optimized by nonlinear least squares. Finally, the one-stage uncertainty-aware prediction structure and the post-optimization module are dedicatedly integrated for ensuring the run-time efficiency. Experiments demonstrate that our method yields the best performance on KITTI 3D detection benchmark, by outperforming state-of-the-art competitors by wide margins, especially for the hard samples.