Related papers: On Optimal Regularization Parameters via Bilevel L…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…
We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased…
In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…
When working with textual data, a natural application of disentangled representations is fair classification where the goal is to make predictions without being biased (or influenced) by sensitive attributes that may be present in the data…
Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…
Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity…
We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
Learning to optimize is an approach that leverages training data to accelerate the solution of optimization problems. Many approaches use unrolling to parametrize the update step and learn optimal parameters. Although L2O has shown…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…