Related papers: Applying Set Optimization to Weak Efficiency

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak…

In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the…

A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…

Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…

When samples have internal structure, we often see a mismatch between the objective optimized during training and the model's goal during inference. For example, in sequence-to-sequence modeling we are interested in high-quality translated…

Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods…

Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…

It is generally accepted that one of the critical parts of current vision algorithms based on deep learning and convolutional neural networks is the annotation of a sufficient number of images to achieve competitive performance. This is…

We present a new alternative theorems for sequences of functions. As applications, we extend recent results in the literature related to first-order necessary conditions for optimality problems. Our contributions involve extending…