相关论文: New merit functions for multiobjective optimizatio…

Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

Approaches for appraising feature importance approximations, alternatively referred to as attribution methods, have been established across an extensive array of contexts. The development of resilient techniques for performance benchmarking…

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Understanding of the behavior of algorithms for resolving the optimization problem (hereafter shortened to OP) of optimizing a differentiable loss function (OP1), is enhanced by knowledge of the critical points of that loss function, i.e.…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio,…

This works aims at understanding further convergence properties of first order local search methods with complex geometries. We focus on the composite optimization model which unifies within a simple formalism many problems of this type. We…

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…

This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…

In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…