Generalizing Constraint Models in Constraint Acquisition

Constraint Acquisition (CA) aims to widen the use of constraint programming by assisting users in the modeling process. However, most CA methods suffer from a significant drawback: they learn a single set of individual constraints for a specific problem instance, but cannot generalize these constraints to the parameterized constraint specifications of the problem. In this paper, we address this limitation by proposing GenCon, a novel approach to learn parameterized constraint models capable of modeling varying instances of the same problem. To achieve this generalization, we make use of statistical learning techniques at the level of individual constraints. Specifically, we propose to train a classifier to predict, for any possible constraint and parameterization, whether the constraint belongs to the problem. We then show how, for some classes of classifiers, we can extract decision rules to construct interpretable constraint specifications. This enables the generation of ground constraints for any parameter instantiation. Additionally, we present a generate-and-test approach that can be used with any classifier, to generate the ground constraints on the fly. Our empirical results demonstrate that our approach achieves high accuracy and is robust to noise in the input instances.

Learning to Learn in Interactive Constraint Acquisition

Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition (CA), the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g., asking whether a partial solution satisfies their (unspecified) constraints or not. While interac tive CA methods learn the constraints, the learning is related to symbolic concept learning, as the goal is to learn an exact representation. However, a large number of queries is still required to learn the model, which is a major limitation. In this paper, we aim to alleviate this limitation by tightening the connection of CA and Machine Learning (ML), by, for the first time in interactive CA, exploiting statistical ML methods. We propose to use probabilistic classification models to guide interactive CA to generate more promising queries. We discuss how to train classifiers to predict whether a candidate expression from the bias is a constraint of the problem or not, using both relation-based and scope-based features. We then show how the predictions can be used in all layers of interactive CA: the query generation, the scope finding, and the lowest-level constraint finding. We experimentally evaluate our proposed methods using different classifiers and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 72%.

Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities

Decision-focused learning (DFL) is an emerging paradigm in machine learning which trains a model to optimize decisions, integrating prediction and optimization in an end-to-end system. This paradigm holds the promise to revolutionize decision-making in many real-world applications which operate under uncertainty, where the estimation of unknown parameters within these decision models often becomes a substantial roadblock. This paper presents a comprehensive review of DFL. It provides an in-depth analysis of the various techniques devised to integrate machine learning and optimization models, introduces a taxonomy of DFL methods distinguished by their unique characteristics, and conducts an extensive empirical evaluation of these methods proposing suitable benchmark dataset and tasks for DFL. Finally, the study provides valuable insights into current and potential future avenues in DFL research.

Guided Bottom-Up Interactive Constraint Acquisition

Constraint Acquisition (CA) systems can be used to assist in the modeling of constraint satisfaction problems. In (inter)active CA, the system is given a set of candidate constraints and posts queries to the user with the goal of finding the right constraints among the candidates. Current interactive CA algorithms suffer from at least two major bottlenecks. First, in order to converge, they require a large number of queries to be asked to the user. Second, they cannot handle large sets of candidate constraints, since these lead to large waiting times for the user. For this reason, the user must have fairly precise knowledge about what constraints the system should consider. In this paper, we alleviate these bottlenecks by presenting two novel methods that improve the efficiency of CA. First, we introduce a bottom-up approach named GrowAcq that reduces the maximum waiting time for the user and allows the system to handle much larger sets of candidate constraints. It also reduces the total number of queries for problems in which the target constraint network is not sparse. Second, we propose a probability-based method to guide query generation and show that it can significantly reduce the number of queries required to converge. We also propose a new technique that allows the use of openly accessible CP solvers in query generation, removing the dependency of existing methods on less well-maintained custom solvers that are not publicly available. Experimental results show that our proposed methods outperform state-of-the-art CA methods, reducing the number of queries by up to 60%. Our methods work well even in cases where the set of candidate constraints is 50 times larger than the ones commonly used in the literature.

Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning

Many real-world optimization problems contain unknown parameters that must be predicted prior to solving. To train the predictive machine learning (ML) models involved, the commonly adopted approach focuses on maximizing predictive accuracy. However, this approach does not always lead to the minimization of the downstream task loss. Decision-focused learning (DFL) is a recently proposed paradigm whose goal is to train the ML model by directly minimizing the task loss. However, state-of-the-art DFL methods are limited by the assumptions they make about the structure of the optimization problem (e.g., that the problem is linear) and by the fact that can only predict parameters that appear in the objective function. In this work, we address these limitations by instead predicting \textit{distributions} over parameters and adopting score function gradient estimation (SFGE) to compute decision-focused updates to the predictive model, thereby widening the applicability of DFL. Our experiments show that by using SFGE we can: (1) deal with predictions that occur both in the objective function and in the constraints; and (2) effectively tackle two-stage stochastic optimization problems.