Related papers: Convergence in Models with Bounded Expected Relati…

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…

An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…

As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased,…

Sequential learning -- where complex tasks are broken down into simpler, hierarchical components -- has emerged as a paradigm in AI. This paper views sequential learning through the lens of low-rank linear regression, focusing specifically…

Recently, there has been a surge in interest in safe and robust techniques within reinforcement learning (RL). Current notions of risk in RL fail to capture the potential for systemic failures such as abrupt stoppages from system failures…

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and…

Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…

Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of…

This paper investigates the stability and convergence properties of asynchronous stochastic approximation (SA) algorithms, with a focus on extensions relevant to average-reward reinforcement learning. We first extend a stability proof…

Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…

Cr\'epey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit…

This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly-played, positive-utility, finite strategic-form games. Prior work in this class of…

We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…

Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…

A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the…

Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…