Related papers: Optimal Rates for Vector-Valued Spectral Regulariz…

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…

Safety in reinforcement learning (RL) is a key property in both training and execution in many domains such as autonomous driving or finance. In this paper, we formalize it with a constrained RL formulation in the distributional RL setting.…

Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

We study the problem of learning vector-valued linear predictors: these are prediction rules parameterized by a matrix that maps an $m$-dimensional feature vector to a $k$-dimensional target. We focus on the fundamental case with a convex…

We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as…

We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…

This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Value function approximation is important in modern reinforcement learning (RL) problems especially when the state space is (infinitely) large. Despite the importance and wide applicability of value function approximation, its theoretical…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…

In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the…

We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper…

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new…

Utilizing a generative regime switching framework, we perform Monte-Carlo simulations of asset returns for Value at Risk threshold estimation. Using equity markets and long term bonds as test assets in the global, US, Euro area and UK…

This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…