Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards
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 co...
| Authors | Joel Q. L. Chang |
|---|---|
| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 22 August 2026 |
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