We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus performing poorly in the setting considered. In contrast, using the 0-1 loss or a suitable non-convex approximation results in robust … Read more
Binarized neural networks are an important class of neural network in deep learning due to their computational efficiency. This paper contributes towards a better understanding of the structure of binarized neural networks, specifically, ideal convex representations of the activation functions used. We describe the convex hull of the graph of the signum activation function associated … Read more
We consider a general multi-period repositioning problem in vehicle-sharing networks such as bicycle-sharing systems, free-float car-sharing systems, and autonomous mobility-on-demand systems. This problem is subject to uncertainties along multiple dimensions – including demand, travel time, and repositioning duration – and faces several operational constraints such as the service level and cost budget. We propose a … Read more
Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems. Specific examples are game-theoretic settings like the bimatrix game or energy market models like for electricity or natural gas. While optimization under uncertainties is rather well-developed, the field of equilibrium models represented by complementarity problems under uncertainty … Read more
We use Markov risk measures to formulate a risk averse version of a total cost problem on a controlled Markov process in infinite horizon. The one step costs are in $L^1$ but not necessarily bounded. We derive the conditions for the existence of the optimal strategies and present the robust dynamic programming equations. We illustrate … Read more
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns. Bittorf, Recht, R\’e and Tropp (`Factoring nonnegative matrices with linear programs’, NIPS 2012) proposed a linear programming … Read more
Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is separable (that is, there exists a cone spanned by a small subset of the columns containing all columns). Since then, several algorithms have been designed to … Read more
This article explains, again, why radius of stability models, such as info-gap’s robustness model, are models of local robustness and why they are therefore unsuitable for the treatment of severe uncertainty. CitationWorking Paper SM-12-2, Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, Australia.ArticleDownload View PDF
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We … Read more
The routing of the rolling stock depends strongly on the rolling stock assignment to di erent opera- tions and the shunting schedule. Therefore, the integration of these decision making is justi ed and is appropriate to introduce robustness in the model. We propose a new approach to obtain better circula- tions of the rolling stock material, solving … Read more