Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards

• URL: http://arxiv.org/abs/2606.09191v1
• Date: Mon, 08 Jun 2026 08:26:37 GMT
• Title: Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards
• Abstract summary: $text-mathrmNPTS_mathrmSG$ is an anchor-free nonparametric Thompson Sampling algorithm for risk-averse bandits.<n>We prove that $text-mathrmNPTS_mathrmSG$ achieves regret matching the instance-dependent lower bound to leading order in $log n$.
• Score: 1.370633147306388
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. The bounded-support case is developed first as a stepping stone sharing the same proof structure. The key technical contributions are a discretisation lemma (bounded support) and a truncated discretisation lemma (sub-Gaussian tails), each projecting the growing-alphabet Dirichlet posterior onto a fixed grid via the Dirichlet aggregation property, holding all polynomial prefactors at fixed degree independent of sample size and breaking the super-exponential barrier that blocked prior proofs.

Related papers

• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Continuous K-Max Bandits [54.21533414838677]
  We study the $K$-Max multi-armed bandits problem with continuous outcome distributions and weak value-index feedback.<n>This setting captures critical applications in recommendation systems, distributed computing, server scheduling, etc.<n>Our key contribution is the computationally efficient algorithm DCK-UCB, which combines adaptive discretization with bias-corrected confidence bounds.
  arXiv  Detail & Related papers  (2025-02-19T06:37:37Z)
• Towards a Sharp Analysis of Offline Policy Learning for $f$-Divergence-Regularized Contextual Bandits [49.96531901205305]
  We analyze $f$-divergence-regularized offline policy learning.<n>For reverse Kullback-Leibler (KL) divergence, we give the first $tildeO(epsilon-1)$ sample complexity under single-policy concentrability.<n>We extend our analysis to dueling bandits, and we believe these results take a significant step toward a comprehensive understanding of $f$-divergence-regularized policy learning.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• Multi-Agent Bayesian Optimization with Coupled Black-Box and Affine Constraints [21.38692458445459]
  We study the problem of distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints. A primal-dual distributed algorithm is proposed that achieves similar regret/violation bounds as those in the single-agent case.
  arXiv  Detail & Related papers  (2023-10-02T08:07:36Z)
• Finite-Time Regret of Thompson Sampling Algorithms for Exponential Family Multi-Armed Bandits [88.21288104408556]
  We study the regret of Thompson sampling (TS) algorithms for exponential family bandits, where the reward distribution is from a one-dimensional exponential family. We propose a Thompson sampling, termed Expulli, which uses a novel sampling distribution to avoid the under-estimation of the optimal arm.
  arXiv  Detail & Related papers  (2022-06-07T18:08:21Z)
• A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits [91.3755431537592]
  This paper unifies the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem. Using the contraction principle in the theory of large deviations, we prove novel concentration bounds for continuous risk functionals. We show that a wide class of risk functionals as well as "nice" functions of them satisfy the continuity condition.
  arXiv  Detail & Related papers  (2021-08-25T17:09:01Z)
• ROOT-SGD: Sharp Nonasymptotics and Near-Optimal Asymptotics in a Single Algorithm [71.13558000599839]
  We study the problem of solving strongly convex and smooth unconstrained optimization problems using first-order algorithms. We devise a novel, referred to as Recursive One-Over-T SGD, based on an easily implementable, averaging of past gradients. We prove that it simultaneously achieves state-of-the-art performance in both a finite-sample, nonasymptotic sense and an sense.
  arXiv  Detail & Related papers  (2020-08-28T14:46:56Z)
• Regret and Belief Complexity Trade-off in Gaussian Process Bandits via Information Thresholding [42.669970064867556]
  We show how to characterize the trade-off between regret bounds of GP bandit algorithms and complexity of the posterior distributions. We observe state of the art accuracy and complexity trade-offs for GP bandit algorithms applied to global optimization.
  arXiv  Detail & Related papers  (2020-03-23T21:05:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.