Related papers: Dual Lagrangian Learning for Conic Optimization
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Domain-Incremental Learning (DIL) involves the progressive adaptation of a model to new concepts across different domains. While recent advances in pre-trained models provide a solid foundation for DIL, learning new concepts often results…
In this work we consider a possibility to use the conception of $(\delta, L)$-model of a function for optimization tasks, whereby solving a primal problem there is a necessity to recover a solution of a dual problem. The conception of…
Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline significantly increases the overall training time. In this paper, we develop a…
In recent years, deep dictionary learning (DDL)has attracted a great amount of attention due to its effectiveness for representation learning and visual recognition.~However, most existing methods focus on unsupervised deep dictionary…
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of…
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A…
When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a…
Federated learning (FL), as a distributed collaborative machine learning (ML) framework under privacy-preserving constraints, has garnered increasing research attention in cross-organizational data collaboration scenarios. This paper…
Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…
Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented…
We consider the problem of two active particles in 2D complex flows with the multi-objective goals of minimizing both the dispersion rate and the energy consumption of the pair. We approach the problem by means of Multi Objective…
For deep ordinal classification, learning a well-structured feature space specific to ordinal classification is helpful to properly capture the ordinal nature among classes. Intuitively, when Euclidean distance metric is used, an ideal…
The widespread application of large language models (LLMs) raises increasing demands on ensuring safety or imposing constraints, such as reducing harmful content and adhering to predefined rules. While there have been several works studying…
High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far,…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…
Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…