Jannis Kurtz In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to develop models which are robust against small perturbations in the training data. We … Read more
Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks with binary activation functions and continuous or integer weights (BDNN). We show that the BDNN can be reformulated as a … Read more
In this work we investigate the min-max-min robust optimization problem applied to combinatorial problems with uncertain cost-vectors which are contained in a convex uncertainty set. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions would … Read more
We study deep neural networks with binary activation functions (BDNN), i.e. the activation function only has two states. We show that the BDNN can be reformulated as a mixed-integer linear program which can be solved to global optimality by classical integer programming solvers. Additionally, a heuristic solution algorithm is presented and we study the model … Read more
In this work we study binary two-stage robust optimization problems with objective uncertainty. The concept of two-stage robustness is tailored for problems under uncertainty which have two different kinds of decision variables, first-stage decisions which have to be made here-and-now and second-stage decisions which can be determined each time after an uncertain scenario occured. We … Read more
In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be group-sparse in the sense that its support is contained in the union … Read more
In this survey, we discuss the state-of-the-art of robust combinatorial optimization under uncertain cost functions. We summarize complexity results presented in the literature for various underlying problems, with the aim of pointing out the connections between the different results and approaches, and with a special emphasis on the role of the chosen uncertainty sets. Moreover, … Read more
In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we … Read more
We investigate a robust approach for solving the Capacitated Vehicle Routing Problem (CVRP) with uncertain travel times. It is based on the concept of K-adaptability, which allows to calculate a set of k feasible solutions in a preprocessing phase before the scenario is revealed. Once a scenario occurs, the corresponding best solution may be picked … Read more
We consider combinatorial optimization problems with uncertain objective functions. In the min-max-min robust optimization approach, a fixed number k of feasible solutions is computed such that the respective best of them is optimal in the worst case. The idea is to calculate a set of candidate solutions in a potentially expensive preprocessing and then select … Read more