Related papers: Addendum on data driven regularization by projecti…
In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common…
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…
The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process,…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
Data augmentation is used in machine learning to make the classifier invariant to label-preserving transformations. Usually this invariance is only encouraged implicitly by including a single augmented input during training. However,…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two…
Inverse problems are often ill-posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is…
The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…
We present an approach to compute stabilizing controllers for continuous-time linear time-invariant systems directly from an input-output trajectory affected by process and measurement noise. The proposed output-feedback design combines (i)…
This paper presents a linear-programming based algorithm to perform data-driven stabilizing control of linear positive systems. A set of state-input-transition observations is collected up to magnitude-bounded noise. A state feedback…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
We study the problem of learning the objective functions or constraints of a multiobjective decision making model, based on a set of sequentially arrived decisions. In particular, these decisions might not be exact and possibly carry…
Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
We discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal…