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.
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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.
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).
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.
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: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: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.