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Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

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…

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…

A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…

Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive…

In this paper, we propose a new Hessian inverse free Fully Single Loop Algorithm (FSLA) for bilevel optimization problems. Classic algorithms for bilevel optimization admit a double loop structure which is computationally expensive.…

Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or…

By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…

In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can be…

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we…