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Decision trees, owing to their interpretability, are attractive as control policies for (dynamical) systems. Unfortunately, constructing, or synthesising, such policies is a challenging task. Previous approaches do so by imitating a…

We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…

Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…

We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs…

We propose an approach for learning optimal tree-based prescription policies directly from data, combining methods for counterfactual estimation from the causal inference literature with recent advances in training globally-optimal decision…

Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our…

In several applications of automatic diagnosis and active learning a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the…

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…

In this paper we introduce an evolutionary algorithm for the solution of linear integer programs. The strategy is based on the separation of the variables into the integer subset and the continuous subset; the integer variables are fixed by…

Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…

We report on work towards flexible algorithms for solving decision problems represented as influence diagrams. An algorithm is given to construct a tree structure for each decision node in an influence diagram. Each tree represents a…

We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk…

Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…