The paper revisits the Successive Rejects (SR) algorithm for best‑arm identification, showing that although SR appears non‑adaptive due to fixed phase lengths, it achieves an optimal worst‑instance error exponent for Gaussian arms with common variance. The authors formulate an optimization problem to design a phase schedule that maximizes the normalized error exponent, leading to a new variant called H1‑balanced Successive Rejects (H1‑SR). H1‑SR attains at least 11/12 of the optimal normalized rate for all K ≥ 2, approaching the optimum as K grows, and experiments demonstrate significant performance gains over the original SR while highlighting trade‑offs in early elimination strategies.
arXiv:2607. 11635v1 Announce Type: new Abstract: In fixed-budget best-arm identification, also known as ranking and selection, an algorithm has a sampling budget to distribute across $K$ arms.
arXiv:2506. 24007v5 Announce Type: replace-cross Abstract: This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification.
arXiv:2603. 10346v2 Announce Type: replace Abstract: We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits.
arXiv:2610.02771v1 Announce Type: cross Abstract: We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set,...
arXiv:2610. 10488v1 Announce Type: cross Abstract: We study the best arm identification problem in a stochastic environment with a novel form of adversarial perturbations, which we coin Shifting Means.
The paper investigates Bayesian fixed‑confidence best‑arm identification where a learner may abstain from a final recommendation. It introduces the Screen‑and‑Confirm (S&C) algorithm, analyzes its expected stopping time, and derives lower bounds for any algorithm under error probability δ and abstention budget α constraints. For Gaussian priors, the authors provide matching upper and lower bounds, characterize exact constants for practical regimes, and show that S&C achieves optimal α–dependent rates, improving on previous results when abstention is disallowed.
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:2607. 06879v1 Announce Type: new Abstract: Best-arm identification is a canonical model for data-driven decision-making, but in many applications each reward observation is costly.
arXiv:2609. 13954v1 Announce Type: new Abstract: Ensemble sampling offers a practical approach to randomized exploration by maintaining a collection of models, but how small an ensemble can be while retaining strong regret guarantees remains unresolved.
arXiv:2606. 29203v1 Announce Type: new Abstract: We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation.
arXiv:2609.37932v1 Announce Type: new Abstract: Systems operating in dynamic environments require timely updates to sustain performance. For resource-intensive systems such as machine learning models...
arXiv:2610.16840v1 Announce Type: cross Abstract: Real-world systems often serve many objectives but can deploy only a few options, whose performance must be learned from noisy feedback. Modeling eac...