arXiv:2606. 06855v1 Announce Type: cross Abstract: While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses.
arXiv:2604. 10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed.
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
arXiv:2602. 20971v3 Announce Type: replace-cross Abstract: Bubeck and Selke (2021) propose the connection between the Law of Robustness and robust generalization error as an open problem.
arXiv:2606. 00520v1 Announce Type: cross Abstract: Many stochastic gradient methods are believed not to converge when the noise in stochastic gradients has only a finite $p$-th moment for $p\in\left(1,2\right)$, a setting known as the heavy-tailed noise assumption.
arXiv:2605. 26000v2 Announce Type: replace-cross Abstract: Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization.
arXiv:2608. 08662v1 Announce Type: cross Abstract: The single-selection prophet inequality is a canonical Bayesian online selection problem in which independent nonnegative values arrive sequentially and the decision-maker must irrevocably select at most one.
We prove that $ρ\text{-}\mathrm{NPTS}_{\mathrm{SG}}$, an anchor-free nonparametric Thompson Sampling algorithm for risk-averse bandits, achieves regret matching the instance-dependent lower bound to leading order in $\log n$, establishing it as asymptotically optimal for any continuous risk functional $ρ$ (CVaR, mean-variance, Sharpe ratio, distortion risk measures, and more) on the class of distributions with bounded density and sub-Gaussian tails, including Gaussian arms. Both this result and its bounded-support counterpart require only continuity of $ρ$: strictly weaker than the dominance condition of prior parametric Thompson Sampling results, and strictly weaker than the Lipschitz condition of UCB-type algorithms, yielding the first instance-optimal guarantees for non-Lipschitz functionals such as the Sharpe ratio without parametric reward assumptions.
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
arXiv:2608. 06182v1 Announce Type: cross Abstract: We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set.
arXiv:2505. 16713v3 Announce Type: replace-cross Abstract: We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument.
arXiv:2606. 09191v1 Announce Type: new Abstract: We prove that $\rho\text{-}\mathrm{NPTS}_{\mathrm{SG}}$, an anchor-free nonparametric Thompson Sampling algorithm for risk-averse bandits, achieves regret matching the instance-dependent lower bound to leading order in $\log n$, establishing it as asymptotically optimal for any continuous risk functional $\rho$ (CVaR, mean-variance, Sharpe ratio, distortion risk measures, and more) on the class of distributions with bounded density and sub-Gaussian tails, including Gaussian arms.
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.