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:2512. 09850v2 Announce Type: replace Abstract: We introduce Conformal Bandits, a novel framework integrating Conformal Prediction (CP) into bandit problems, a classic paradigm for sequential decision-making under uncertainty.
By Simone Cuonzo, Nina Deliu
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:2307. 03587v4 Announce Type: replace Abstract: In non-stationary linear contextual bandits, existing efficient algorithms typically rely on the Weighted Regularized Least-Squares (WRLS) estimator.
By Nicklas Werge, Yi-Shan Wu, Abdullah Akg\"ul, Melih Kandemir
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:2609.13564v1 Announce Type: new
Abstract: We study KL-regularized contextual bandits under both reward and preference feedback. We show that greedy sampling can achieve logarithmic regret witho...
By Zichen Wang, Haoyang Hong, Huazheng Wang
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.
By Shion Takeno, Shogo Iwazaki
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: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.
By Prateek Jaiswal, Debdeep Pati, Anirban Bhattacharya, Bani K. Mallick
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.
By Marc Abeille, David Janz, Ciara Pike-Burke
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:2606. 00431v1 Announce Type: new Abstract: We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits.
By Tom Perneczky, Marc Abeille, David Janz