相关论文: Logarithmic convexity of fixed points of stochasti…

In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…

In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\mathcal{H}_\gamma (\mathbb{D})$ over the unit disc $\mathbb{D}$. We provide a complete classification in terms…

We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the…

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…

Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…

We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty fixed point set converges geometrically for any starting point. We also show that positivity is crucial for this result to hold, and the concept of…

We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach's contraction property. As an application, we demonstrate the existence of Nash equilibrium in a…

In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the…

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP…

Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…

We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres (Duke Math. J., 166(10):1789--1858, 2017) for Dirichlet and Robin boundary conditions. This proves the rigidity of the Airy-$\beta$ point…

In the paper we consider one point and two point multiarmed bamdit problems. In other words we consider the online stochastic convex optimization problems with oracle that return the value (realization) of the function at one point or at…

Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We show a sharp quantitative stability of these estimates with the optimal norm and the exponent and an…

This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in reward allocation is the core, which is the set of stable allocations where…

Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We…