aiqbench analysis
This paper is primarily about machine learning algorithms for risk-averse bandits, specifically addressing the theoretical optimality of Thompson Sampling under sub-Gaussian reward distributions. However, the work has been withdrawn by the author due to a critical counterexample that invalidates the core regret bounds and assumptions presented in the analysis. For researchers in reinforcement learning and algorithmic optimization, this serves as a significant cautionary note regarding the robustness of nonparametric Thompson Sampling methods when applied to complex risk functionals like the Sharpe ratio.
Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards
arXiv:2606.09191v2 Announce Type: replace 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. Both this result and its bounded-support counterpart require only continuity of $\rho$: 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.
This paper has been withdrawn by Joel Q. L. Chang
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. Both this result and its bounded-support counterpart require only continuity of $\rho$: 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.
Withdrawn due to a counterexample identified after posting that invalidates a key step in the risk-averse regret bounds. The result does not hold as stated under the assumptions given. We are revising the analysis and will resubmit if the fix can be established rigorously
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2606.09191 [cs.LG]
(or arXiv:2606.09191v2 [cs.LG] for this version)
From: Joel Q. L. Chang [view email] [v1] Mon, 8 Jun 2026 08:26:37 UTC (1,985 KB) [v2] Sat, 22 Aug 2026 14:52:12 UTC (1 KB) (withdrawn)
Full text under the publisher's open licence · 272 words
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