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Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for…

Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…

This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…

Weight averaging has become a standard technique for enhancing model performance. However, methods such as Stochastic Weight Averaging (SWA) and Latest Weight Averaging (LAWA) often require manually designed procedures to sample from the…

We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under…

Decisions under uncertainty or with multiple objectives usually require the decision maker to formulate a preference regarding risks or trade-offs. If this preference is known, the ordered weighted averaging (OWA) criterion can be applied…

Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative…

Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…

Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…

In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients.…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

While distributed training is often viewed as a solution to optimizing linear models on increasingly large datasets, inter-machine communication costs of popular distributed approaches can dominate as data dimensionality increases. Recent…

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, we extend the analysis of the orthogonal greedy algorithm…

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…

Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields…