Related papers: Variational properties of value functions

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex…

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…

Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…

Inverse reinforcement learning methods aim to retrieve the reward function of a Markov decision process based on a dataset of expert demonstrations. The commonplace scarcity and heterogeneous sources of such demonstrations can lead to the…

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

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…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…

Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This…

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

Bootstrapping is behind much of the successes of Deep Reinforcement Learning. However, learning the value function via bootstrapping often leads to unstable training due to fast-changing target values. Target Networks are employed to…

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…

Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…