The paper studies upper confidence bound (UCB) algorithms for large‑scale pure exploration problems where the performance distributions may be heavy‑tailed and not sub‑Gaussian. It introduces a meta‑UCB framework that selects the alternative with the largest sample size as the best upon stopping, and derives a distribution‑free lower bound on the probability of correct selection. Using this bound, the authors show that the meta‑UCB algorithm achieves sample optimality in both indifference‑zone and non‑indifference‑zone settings under a uniform variance bound, and provide numerical experiments that illustrate the behavior of UCB algorithms beyond the meta‑UCB framework.
arXiv:2409. 18909v2 Announce Type: replace Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret.
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.
arXiv:2607. 08979v1 Announce Type: new Abstract: We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons.
arXiv:2607. 29460v1 Announce Type: new Abstract: Heavy-tailed distributions arise naturally in sequential decision-making problems such as financial investment, online advertising, and network management, where rare but extreme outcomes can dominate performance.
arXiv:2506. 24007v5 Announce Type: replace-cross Abstract: This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification.
The paper introduces SELECT, an algorithmic framework for satisficing regret minimization in bandit problems, achieving constant expected satisficing regret when a satisficing arm exists. A variant, SELECT‑LITE, further ensures a light‑tailed satisficing regret distribution while maintaining constant expected regret in the realizable case and sub‑linear standard regret otherwise. Experiments on synthetic data and a real‑world dynamic pricing scenario demonstrate the practical effectiveness of both algorithms.
arXiv:2602. 03972v3 Announce Type: replace-cross Abstract: The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC).
arXiv:2604. 00531v2 Announce Type: replace Abstract: Multi-task representation learning exploits the shared structure among related tasks by learning a common latent representation, thereby improving sample efficiency.
arXiv:2603. 09276v2 Announce Type: replace-cross Abstract: We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP.
arXiv:2603. 21180v4 Announce Type: replace Abstract: Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation.
arXiv:2603.21716v2 Announce Type: replace-cross Abstract: Efficient selection among multiple generative models is increasingly important in modern generative AI, where sampling from suboptimal models...