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. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...
Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...
It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and—in asynchronous implementations—on the gradient staleness. Especially, it has been observed that the spe ...
We propose an incentive mechanism for the sponsored content provider (CP) market in which the communication of users can be represented by a graph, and the private information of the users is assumed to have a continuous distribution function. The CP stipu ...
We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a soluti ...
Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...
Many important problems in contemporary machine learning involve solving highly non- convex problems in sampling, optimization, or games. The absence of convexity poses significant challenges to convergence analysis of most training algorithms, and in some ...
We study in this thesis the asymptotic behavior of optimal paths on a random graph model, the configuration model, for which we assign continuous random positive weights on its edges.
We start by describing the asymptotic behavior of the diameter and the f ...
The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By consid ...
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, an ...
