ABSTRACT Machine learning techniques are increasingly used for high‐stakes decision‐making, such as college admissions, loan attribution, or recidivism prediction. Thus, it is crucial to ensure that the models learnt can be audited or understood by human users, do not create or reproduce discrimination or bias and do not leak sensitive information regarding their training data. Indeed, interpretability, fairness, and privacy are key requirements for the development of responsible machine learning, and all three have been studied extensively during the last decade. However, they were mainly considered in isolation, while in practice they interplay with each other, either positively or negatively. In this survey paper, we review the literature on the interactions between these three desiderata. More precisely, for each pairwise interaction, we summarize the identified synergies and tensions. These findings highlight several fundamental theoretical and empirical conflicts, while also demonstrating that jointly considering these different requirements is challenging when one aims at preserving a high level of utility. To solve this issue, we also discuss possible conciliation mechanisms, showing that a careful design can enable to successfully handle these different concerns in practice.

The growing interest in explainable artificial intelligence(XAI) for critical decision making motivates the need for interpretable machine learning (ML) models. In fact, due to their structure (especially with small sizes), these models are inherently understandable by humans. Recently, several exact methods for computing such models are proposed to overcome weaknesses of traditional heuristic methods by providing more compact models or better prediction quality. Despite their compressed representation of Boolean functions, Binary decision diagrams (BDDs) did not gain enough interest as other interpretable ML models. In this paper, we first propose SAT-based models for learning optimal BDDs (in terms of the number of features) that classify all input examples. Then, we lift the encoding to a MaxSAT model to learn optimal BDDs in limited depths, that maximize the number of examples correctly classified. Finally, we tackle the fragmentation problem by introducing a method to merge compatible subtrees for the BDDs found via the MaxSAT model. Our empirical study shows clear benefits of the proposed approach in terms of prediction quality and interpretability (i.e., lighter size) compared to the state-of-the-art approaches.

FairCORELS is an open-source Python module for building fair rule lists. It is a multi-objective variant of CORELS, a branch-and-bound algorithm to learn certifiably optimal rule lists. FairCORELS supports six statistical fairness metrics, proposes several exploration parameters and leverages on the fairness constraints to prune the search space efficiently. It can easily generate sets of accuracy-fairness trade-offs. The models learnt are interpretable by design and a sparsity parameter can be used to control their length.

Recently, several exact methods to compute decision trees have been introduced. On the one hand, these approaches can find optimal trees for various objective functions including total size, depth or accuracy on the training set and therefore. On the other hand, these methods are not yet widely used in practice and classic heuristics are often still the methods of choice. In this paper we show how the SAT model proposed by [Narodytska et.al 2018] can be lifted to a MaxSAT approach, making it much more practically relevant. In particular, it scales to much larger data sets; the objective function can easily be adapted to take into account combinations of size, depth and accuracy on the training set; and the fine-grained control of the objective function it offers makes it particularly well suited for boosting. Our experiments show promising results. In particular, we show that the prediction quality of our approach often exceeds state of the art heuristics. We also show that the MaxSAT formulation is well adapted for boosting using the well-known AdaBoost Algorithm.

In this paper we describe a complex optimization application arising in maintenance scheduling, developed in close collaboration with an industrial partner. We have to plan and schedule preventive and corrective maintenance activities at customer sites by a group of traveling repair technicians. A specific property of the problem considered here is a mix of customers in both urban centers and rural areas. This means that travel times between customers must be considered when balancing overall workload for each agent. We discuss a problem decomposition compatible with current management practice, describe different solvers for the individual problem steps, and show results on real-world data from the industrial partner.

Stable Marriage (SM) is a well-known matching problem, where the aim is to match a set of men and women. The resulting matching must satisfy two properties: there is no unassigned person and there are no other assignments where two people of opposite gender prefer each other to their current assignments. We propose a new version of SM called as Robust Stable Marriage (RSM) by combining stability and robustness. We define robustness by introducing (a,b)-supermatches, which has been inspired by (a,b)-supermodels. An (a,b)-supermatch is a stable matching, where if at most a pairs want to break up, it is possible to find another stable matching by breaking at most b other pairs.

We study the problem of matching a set of applicants to a set of posts, where each applicant has an ordinal preference list, which may contain ties, ranking a subset of posts. A matching M is popular if there exists no matching M' where more applicants prefer M' to M . Several notions of optimality are studied in the literature for the case of strictly ordered preference lists. In this paper we address the case involving ties and propose novel algorithmic and complexity results for this variant. Next, we focus on the NP-hard case where additional copies of posts can be added in the preference lists, called Popular Matching with Copies. We define new dominance rules for this problem and present several novel graph properties characterising the posts that should be copied with priority. We present a comprehensive set of experiments for the popular matching problem with copies to evaluate our dominance rules as well as the different branching strategies. Our experimental study emphasizes the importance of the dominance rules and characterises the key aspects of a good branching strategy.

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.

We propose a constraint programming approach to the popular matching problem. We show that one can use the Global Cardinality Constraint to encode the problem even in cases that involve ties in the ordinal preferences of the applicants.