Related papers: On the Robustness of Regularized Pairwise Learning…

In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…

Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. This problem has gained increasing attention in recent years, and efforts to improve it have grown substantially. To aid RL researchers and production…

This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide…

In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

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…

In online continual learning, a neural network incrementally learns from a non-i.i.d. data stream. Nearly all online continual learning methods employ experience replay to simultaneously prevent catastrophic forgetting and underfitting on…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…

We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…

This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…

In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…

This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that…

This paper presents a novel learning economic model predictive control scheme for uncertain nonlinear systems subject to input and state constraints and unknown dynamics. We design a fast and accurate Lipschitz regression method using input…