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.
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:2309. 06349v2 Announce Type: replace-cross Abstract: Thompson sampling (TS) is one of the most popular and earliest algorithms to solve stochastic multi-armed bandit problems.
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.
arXiv:2603. 10346v2 Announce Type: replace Abstract: We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits.
arXiv:2608. 15365v1 Announce Type: new Abstract: Regret minimization (RM) and best-arm identification (BAI) are two fundamental objectives in multi-armed bandits.
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.
arXiv:2605.20854v3 Announce Type: replace Abstract: We provide the first regret analysis of ReMax in stochastic multi-armed bandits. Originally introduced for reinforcement learning, ReMax is motivat...
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:2609.10529v1 Announce Type: cross Abstract: We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and...
The paper addresses an online resource allocation problem where a budget must be distributed among multiple arms under censored feedback. Each arm yields a reward only if it is activated by an unknown Bernoulli process and the allocated budget exceeds a random threshold from an unknown parametric distribution. The authors establish a worst‑case regret lower bound of Σ(√T), propose the RA‑UCB algorithm achieving near‑optimal regret when the budget is known, and introduce MG‑UCB for unknown, round‑dependent budgets, validating both approaches experimentally.
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 presents the first high‑probability regret bounds for both cumulative and current‑step variants of Feel‑Good Thompson Sampling (FGTS) in contextual bandits with general realizable function approximation. The bounds rely on decoupling coefficients and prior mass near the true reward function, and in the linear setting they achieve ≠d√T log(2T)+√T log(1/δ) regret with probability at least 1‑δ. This matches the dimension and horizon dependence of upper‑confidence‑bound algorithms up to logarithmic factors, while the high‑probability cost adds only linear dependence on log(1/δ).