Related papers: Robust learning and complexity dependent bounds fo…

This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…

In many estimation problems, e.g. linear and logistic regression, we wish to minimize an unknown objective given only unbiased samples of the objective function. Furthermore, we aim to achieve this using as few samples as possible. In the…

We study the problem of regression with interval targets, where only upper and lower bounds on target values are available in the form of intervals. This problem arises when the exact target label is expensive or impossible to obtain, due…

In the realm of reinforcement learning (RL), accounting for risk is crucial for making decisions under uncertainty, particularly in applications where safety and reliability are paramount. In this paper, we introduce a general framework on…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

Convex risk measures play a foundational role in the area of stochastic optimization. However, in contrast to risk neutral models, their applications are still limited due to the lack of efficient solution methods. In particular, the mean…

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…

We study over-parameterized classifiers where Empirical Risk Minimization (ERM) for learning leads to zero training error. In these over-parameterized settings there are many global minima with zero training error, some of which generalize…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover,…

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…

We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…

A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed…

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for…