Related papers: Inexact Derivative-Free Optimization for Bilevel L…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…
Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…
Data rebalancing techniques, including oversampling and undersampling, are a common approach to addressing the challenges of imbalanced data. To tackle unresolved problems related to both oversampling and undersampling, we propose a new…
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
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…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…
When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…