Related papers: Scaling the Convex Barrier with Sparse Dual Algori…

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…

In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Remarkable achievements have been attained by deep neural networks in various applications. However, the increasing depth and width of such models also lead to explosive growth in both storage and computation, which has restricted the…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

Neural Networks are used today in numerous security- and safety-relevant domains and are, as such, a popular target of attacks that subvert their classification capabilities, by manipulating the network parameters. Prior work has introduced…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce…

We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality…

Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…

Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network…

The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a…

Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…

Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…

Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One…