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We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

In offline reinforcement learning, in-sample learning methods have been widely used to prevent performance degradation caused by evaluating out-of-distribution actions from the dataset. Extreme Q-learning (XQL) employs a loss function based…

Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the…

We study the generalization properties of unregularized gradient methods applied to separable linear classification -- a setting that has received considerable attention since the pioneering work of Soudry et al. (2018). We establish tight…

This paper proposes a scoring-rule-based method for ranking predictive distributions in the Fr\'echet domain that is able to distinguish between different tail indices. The approach is built on normalized order statistics and exploits…

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…

Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…

Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interesting aspects of stochastic optimizers by using heavy-tailed…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through…

In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal works of Mendelson [Men15, Men18] on the analysis of ERM with…

Deriving generalization bounds for stable algorithms is a classical question in learning theory taking its roots in the early works by Vapnik and Chervonenkis (1974) and Rogers and Wagner (1978). In a series of recent breakthrough papers by…

We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…

The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…

This paper introduces ergodic-risk criteria, which capture long-term cumulative risks associated with controlled Markov chains through probabilistic limit theorems--in contrast to existing methods that require assumptions of either finite…

The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…

Prior work (Klochkov $\&$ Zhivotovskiy, 2021) establishes at most $O\left(\log (n)/n\right)$ excess risk bounds via algorithmic stability for strongly-convex learners with high probability. We show that under the similar common assumptions…