相关论文: A new characterization of the convergence factor o…

Multi-Task Learning is a learning paradigm that uses correlated tasks to improve performance generalization. A common way to learn multiple tasks is through the hard parameter sharing approach, in which a single architecture is used to…

We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…

Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…

In many neural models, new features as polynomial functions of existing ones are used to augment representations. Using the natural language inference task as an example, we investigate the use of scaled polynomials of degree 2 and above as…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…

We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower…

Text alignment finds application in tasks such as citation recommendation and plagiarism detection. Existing alignment methods operate at a single, predefined level and cannot learn to align texts at, for example, sentence and document…

In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…

We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…

Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems…

This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results…

We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…

Exploiting label correlations is important to multi-label classification. Previous methods capture the high-order label correlations mainly by transforming the label matrix to a latent label space with low-rank matrix factorization.…

The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…