Related papers: Implicit Bias of Mirror Flow on Separable Data
Learning-to-optimize is an emerging framework that leverages training data to speed up the solution of certain optimization problems. One such approach is based on the classical mirror descent algorithm, where the mirror map is modelled…
Motivated by understanding the behavior of the Alternating Mirror Descent (AMD) algorithm for bilinear zero-sum games, we study the discretization of continuous-time Hamiltonian flow via the symplectic Euler method. We provide a framework…
We consider determining the $\R$-minimizing solution of ill-posed problem $A x = y$ for a bounded linear operator $A: X \to Y$ from a Banach space $X$ to a Hilbert space $Y$, where $\R: X \to (-\infty, \infty]$ is a strongly convex…
This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with…
Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…
We study properties of ridge functions $f(x)=g(a\cdot x)$ in high dimensions $d$ from the viewpoint of approximation theory. The considered function classes consist of ridge functions such that the profile $g$ is a member of a univariate…
Steady incompressible potential flows of an inviscid or viscous fluid are considered in infinite N-dimensional cylinders with tangential boundary conditions. We show that such flows, if away from stagnation, are constant and parallel to the…
Stochastic flows generated by reflected SDEs in a half-plane with an additive diffusion term are considered. A derivative in the initial data is represented a.s. as an infinite product of matrices. We use this representation and construct…
This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with…
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…
We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the…
We estimate from above the rate at which a solution to the rescaled mean curvature flow on a closed hypersurface may converge to a limit self-similar solution, i.e. a shrinker. Our main result implies that any solution which converges to a…
We introduce the generalized notion of semicontinuity of a function defined on a topological space and derive the useful classification of the so-called Lipschitz derivatives of functions defined on a metric space. Secondly, we investigate…
In the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open…