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: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.
By Joel Q. L. Chang
arXiv:2605.07107v4 Announce Type: replace-cross
Abstract: It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and con...
By Leighton P. Barnes, Alex Dytso
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.
By Qianqian Lei, Soham Bonnerjee, Yuefeng Han, Wei Biao Wu
arXiv:2609.27766v1 Announce Type: cross
Abstract: In safe hypothesis testing with test supermartingals, Ville's inequality provides anytime-valid type-I error guarantees for every significance level...
By Patrick Forr\'e
arXiv:2607. 22971v1 Announce Type: cross Abstract: Let $X = (X_1, \ldots, X_n)$ be a random vector from any Borel probability law on $\mathbb{R}_+^n$.
By George Bissias, Erik Learned-Miller
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.
By Aleksandr Storozhenko
The paper establishes a bounded‑differences inequality for functions of non‑isotropic Gaussian vectors, showing that the concentration bound depends on the condition number of the covariance matrix. It applies this result to demonstrate the subgaussianity of sign‑quantized linear maps, addressing a question posed by Simone Bombari. The authors also correct attribution to earlier work by Barber and Kolar and highlight the role of AI assistance in the discovery process.
By Guangyi Zou, Roman Vershynin
arXiv:2609.37787v1 Announce Type: new
Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
By Ruinan Jin, Difei Cheng, Ling Chen, Jun Luo, Hao Zhou, Youzhi Zhang
arXiv:2608. 19643v1 Announce Type: new Abstract: Self-normalized concentration inequalities are standard tools in bandit and reinforcement-learning analyses.
By Yi-Shan Wu
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.
By Huiming Zhang, Binghan Li, Wan Tian, Qiang Sun