The paper introduces "confidence horizons", a new class of statistical tools that provide sharper large‑sample anytime‑valid inference when a finite time horizon is imposed. These objects function as large‑sample confidence sequences limited to a bounded number of interim looks, analogous to group sequential repeated confidence intervals. The authors connect confidence horizons to classic group sequential boundaries (Pocock, O’Brien–Fleming, Wang–Tsiatis), derive closed‑form distribution functions for certain statistics, and demonstrate their application to treatment effect estimation in sequentially randomized experiments with adaptive Neyman allocation.
arXiv:2606. 00913v1 Announce Type: cross Abstract: Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge.
arXiv:2607. 14604v1 Announce Type: new Abstract: Online controlled experiments are the gold standard for hypothesis testing in online platforms.
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
arXiv:2508.10336v3 Announce Type: replace-cross Abstract: In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of Gibbs and Cand\`es (2021). For any given poi...
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: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:2608. 13209v1 Announce Type: cross Abstract: Many operational decisions are sequences of interventions under a cumulative resource limit, such as a maintenance schedule within a crew-hour budget.
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.
The paper studies distributionally robust ranking and selection (DRR&S), where the goal is to identify the best alternative under input uncertainty by considering multiple plausible input distributions. It introduces the concept of sequential additivity, showing that efficient sampling should focus on a small, additive set of critical scenarios rather than a multiplicative number. The authors prove an algorithm‑independent lower bound on sampling, design an additive allocation (AA) procedure that meets this bound and achieves exponentially decreasing error probability, and extend the approach to a general additive allocation (GAA) framework that incorporates traditional R&S sampling rules.
Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n succ...
arXiv:2606. 20820v2 Announce Type: replace Abstract: Can we trust evaluation scores to capture an LLM's true real-world performance?
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.