arXiv:2604. 03218v2 Announce Type: replace-cross Abstract: We study power-one sequential testing for an i.
arXiv:2504. 19952v2 Announce Type: replace-cross Abstract: We present two general lower bounds for stopping times of sequential tests between arbitrary composite nulls $\mathcal P$ and alternatives $\mathcal Q$.
arXiv:2609.23163v1 Announce Type: cross Abstract: Comparing probability measures in machine learning trades transport geometry against computational cost: Wasserstein distances encode the geometry of...
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
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...
The paper investigates quantile distributional policy evaluation by approximating the return distribution under a policy with a quantile Bellman fixed point. It constructs an estimator from an empirical Markov decision process and derives non‑asymptotic error bounds in Wasserstein distances, achieving root‑n rates that are independent of the quantile resolution for a wide range of Wasserstein orders. The authors also characterize the exact local asymptotic minimax risk and show that their estimator attains this optimal rate, while examining how the risk depends on resolution in simple state‑space examples.
arXiv:2610. 29898v1 Announce Type: new Abstract: Haussler's covering lemma (JCTA 1995) gives the sharp $(C/\delta)^d$ metric-entropy bound for binary VC classes under normalized $\ell_1$ distance.
arXiv:2607. 10751v1 Announce Type: new Abstract: Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$).
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
arXiv:2609. 27765v1 Announce Type: cross Abstract: In safe hypothesis testing with test supermartingales, Ville's inequality provides anytime-valid type-I error guarantees for every significance level $\alpha\in(0,1]$, if one rejects the null hypothesis whenever the wealth process first exceeds $1/\alpha$.
arXiv:2605. 03823v3 Announce Type: replace Abstract: We study strong universal Bayes-consistency in the realizable setting for learning with general metric losses, extending classical characterizations beyond $0$-$1$ classification (Bousquet et al.
arXiv:2603. 17925v2 Announce Type: replace-cross Abstract: We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms.
arXiv:2608. 03353v1 Announce Type: cross Abstract: For a Markov kernel $T$ with an invariant probability measure $\pi$, we give a self-contained proof of the Markov chain convergence theorem via a criterion called asymptotic equivalence with the target.