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.
By Prakhar Singhvi (Abstract Math Institute), Yi Zou (Abstract Math Institute), Abhishek Bhattacharjee (Abstract Math Institute)
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.
By Shunxing Yan, Han Zhong
arXiv:2608. 18863v1 Announce Type: cross Abstract: We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model.
By Matthias Mandl, Hanne Kekkonen
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.
By Junwen Yang, Vincent Y. F. Tan, Tianyuan Jin
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.
By Joel Q. L. Chang
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:2607. 10936v1 Announce Type: new Abstract: We study the bandit-feedback version of online principal component analysis (Bandit PCA): in each round $t = 1,\dots,T$, the adversary selects a $d \times d$ symmetric gain matrix $G_t$ with spectrum in $[0,1]$ and rank at most $r$; the learner simultaneously selects a unit vector $w_t \in S^{d-1}$ and receives the reward $w_t^\top G_t w_t$.
By Mo\"ise Blanchard, Dmitrii Ostrovskii, Aadirupa Saha
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@$k$.
By Bingkui Tong, Junpei Komiyama, Soichiro Nishimori, Paavo Parmas
arXiv:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.
By Jack Sandberg, Morteza Haghir Chehreghani
arXiv:2510.10730v3 Announce Type: replace
Abstract: We provide a unified algorithmic framework for ensemble sampling in nonlinear contextual bandits and develop corresponding regret bounds for two mo...
By Jiazheng Sun, Weixin Wang, Pan Xu
arXiv:2606. 09802v1 Announce Type: cross Abstract: We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time.
By Udvas Das, Waris Radji, Debabrota Basu, Odalric-Ambrym Maillard
arXiv:2506. 24007v5 Announce Type: replace-cross Abstract: This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification.
By Masahiro Kato