arXiv:2606. 00431v1 Announce Type: new Abstract: We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits.
arXiv:2502. 08870v2 Announce Type: replace Abstract: We provide an approach for the analysis of randomised exploration algorithms like Thompson sampling that does not rely on forced optimism or posterior inflation.
arXiv:2602. 08026v2 Announce Type: replace Abstract: We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits.
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:2607. 12389v1 Announce Type: cross Abstract: We consider Bayesian bandit models and prove that Thompson sampling makes at most twice the expected number of mistakes (selections of a suboptimal arm) as any other policy.
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:2608. 16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization.
arXiv:2606. 28616v1 Announce Type: new Abstract: In stochastic linear bandits, the canonical Upper Confidence Bound (UCB) algorithm admits a simple frequentist regret analysis but can be computationally demanding, while Thompson Sampling (TS) is computationally attractive yet typically harder to analyze due to its non-optimistic nature.
arXiv:2609. 01999v1 Announce Type: cross Abstract: We study a variant of the Thompson Sampling (TS) algorithm, called $\alpha$-TS, for solving stochastic generalized linear bandit problems.
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: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:2601. 02022v2 Announce Type: replace Abstract: We prove that Thompson sampling exhibits $\tilde{O}(\sigma d \sqrt{T} + d r \sqrt{\mathrm{Tr}(\Sigma_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(\mu_0, \Sigma_0)$ prior distribution on the coefficients, where $d$ is the dimension, $T$ is the time horizon, $r$ is the maximum $\ell_2$ norm of the actions, and $\sigma^2$ is the noise variance.
arXiv:2609.26213v1 Announce Type: cross Abstract: We study the multiplayer multi-armed bandit problem with information asymmetry under Bernoulli rewards, for three information structures: asymmetry i...