The paper introduces Halve-Then-Greedy (HTG), an adaptive sampling strategy for fixed-budget experimentation that maximizes the probability of obtaining sufficient posterior evidence that a recommended design’s mean performance exceeds a target. HTG combines an initial balanced allocation, successive halving, and posterior-greedy sampling, and the authors prove instance-dependent, finite-budget exponential bounds on posterior-failure probability. They also establish that HTG matches an asymptotic sample-complexity lower bound up to a logarithmic factor and demonstrate, through analysis and simulations, that HTG outperforms uniform sampling and sequential halving in terms of sample efficiency.
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...
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:2506. 24007v5 Announce Type: replace-cross Abstract: This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification.
arXiv:2608. 01545v1 Announce Type: cross Abstract: We study the problem of identifying the dominant arm in multi-armed bandits, where the objective is to find the action with the highest probability of exceeding the realized rewards of all other actions.
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 analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
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:2605. 20854v2 Announce Type: replace Abstract: We study a stochastic bandit algorithm motivated by retry-aware objectives that value the best outcome among multiple attempts, such as pass@$k$ and max@$k$.
arXiv:2602. 06014v2 Announce Type: replace-cross Abstract: Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle.
arXiv:2606. 01655v1 Announce Type: cross Abstract: The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints.
arXiv:2402. 07391v3 Announce Type: replace-cross Abstract: We consider a replicable stochastic multi-armed bandit algorithm that ensures, with high probability, that the algorithm's sequence of actions is not affected by the randomness inherent in the dataset.
arXiv:2609.30321v1 Announce Type: new Abstract: Adaptive arm selection changes the distribution of the observations collected by a bandit algorithm, but it need not change their limiting empirical sp...