Related papers: A ranking approach to global optimization
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
Bipartite ranking, which aims to learn a scoring function that ranks positive individuals higher than negative ones from labeled data, is widely adopted in various applications where sample prioritization is needed. Recently, there have…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected…
This paper considers the minimization of a general objective function $f(X)$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To reduce the computational burden, we factorize the variable $X$ into a product of…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking…
Unsupervised aggregation of independently built univariate predictors is explored as an alternative regularization approach for noisy, sparse datasets. Bipartite ranking algorithm Smooth Rank implementing this approach is introduced. The…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
We formulate the local ranking problem in the framework of bipartite ranking where the goal is to focus on the best instances. We propose a methodology based on the construction of real-valued scoring functions. We study empirical risk…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting…
Algorithmic fairness has been a serious concern and received lots of interest in machine learning community. In this paper, we focus on the bipartite ranking scenario, where the instances come from either the positive or negative class and…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…
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…
Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their…