Related papers: Regularized Learning Schemes in Feature Banach Spa…
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…
In this paper, we introduce a unified framework, inspired by classical regularization theory, for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares…
Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…
A crucial aspect in reliable machine learning is to design a deployable system in generalizing new related but unobserved environments. Domain generalization aims to alleviate such a prediction gap between the observed and unseen…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
This paper reviews the topological groundwork for the study of reinforcement learning (RL) by focusing on the structure of state, action, and policy spaces. We begin by recalling key mathematical concepts such as complete metric spaces,…
Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific…
Several applications of Reinforcement Learning suffer from instability due to high variance. This is especially prevalent in high dimensional domains. Regularization is a commonly used technique in machine learning to reduce variance, at…
This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…
This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…
We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting…
We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of…
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…
While recent model-free Reinforcement Learning (RL) methods have demonstrated human-level effectiveness in gaming environments, their success in everyday tasks like visual navigation has been limited, particularly under significant…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…