Related papers: Robust high dimensional learning for Lipschitz and…
We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance…
Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized…
Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…
We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when…
Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…
Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss…
Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significantly expanded the class of problems for which optimal…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
Distributionally robust optimization (DRO) has attracted attention in machine learning due to its connections to regularization, generalization, and robustness. Existing work has considered uncertainty sets based on phi-divergences and…
We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…
We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning…
Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically…
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving,…
This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial…
We consider the problem of linear classification under general loss functions in the limited-data setting. Overfitting is a common problem here. The standard approaches to prevent overfitting are dimensionality reduction and regularization.…