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A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…

Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered…

Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex…

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

We present an optimization-based approach to stochastic control problems with nonclassical information structures. We cast these problems equivalently as optimization prob- lems on joint distributions. The resulting problems are necessarily…

Variational regularization has remained one of the most successful approaches for reconstruction in imaging inverse problems for several decades. With the emergence and astonishing success of deep learning in recent years, a considerable…

This paper proposes a new optimizer for deep learning, named d-AmsGrad. In the real-world data, noise and outliers cannot be excluded from dataset to be used for learning robot skills. This problem is especially striking for robots that…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…

Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…

Recurrent Neural Networks (RNNs) are rich models for the processing of sequential data. Recent work on advancing the state of the art has been focused on the optimization or modelling of RNNs, mostly motivated by adressing the problems of…

We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…

Inverse Reinforcement Learning (IRL) aims to facilitate a learner's ability to imitate expert behavior by acquiring reward functions that explain the expert's decisions. Regularized IRL applies strongly convex regularizers to the learner's…

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…