Publications associées à Condition de Hölder

Dynamic Voxels Based on Ego-Conditioned Prediction: An Integrated Spatio-Temporal Framework for Motion Planning

Prediction is a vital component of motion planning for autonomous vehicles (AVs). By reasoning about the possible behavior of other target agents, the ego vehicle (EV) can navigate safely, efficiently, and politely. However, most of the existing work overl ...

IEEE Institute of Electrical and Electronics Engineers2024

Stability of Image-Reconstruction Algorithms

Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

The statistical complexity of early-stopped mirror descent

Tomas Vaskevicius, Varun Kanade

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrain ...

Oxford Univ Press2023

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

Volkan Cevher, Grigorios Chrysos, Zhenyu Zhu, Fabian Ricardo Latorre Gomez

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coup ...

2022

Predicting in Uncertain Environments: Methods for Robust Machine Learning

Paul Thierry Yves Rolland

One of the main goal of Artificial Intelligence is to develop models capable of providing valuable predictions in real-world environments. In particular, Machine Learning (ML) seeks to design such models by learning from examples coming from this same envi ...

EPFL2022

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

Microtome Publishing2022

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Volkan Cevher, Fanghui Liu, Luca Viano

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that fa ...

2022

Learning Lipschitz-Controlled Activation Functions in Neural Networks for Plug-and-Play Image Reconstruction Methods

Michaël Unser, Dimitris Perdios, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sébastien Alexandre Emery

Ill-posed linear inverse problems are frequently encountered in image reconstruction tasks. Image reconstruction methods that combine the Plug-and-Play (PnP) priors framework with convolutional neural network (CNN) based denoisers have shown impressive per ...

2021

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021