Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits
Abstract
Combinatorial Thompson sampling (CTS) draws independent posterior samples for every arm, so its exploration dynamics ignore any relation among arms. We study a minimal change to those dynamics: an LLM is queried once for a partition of the arms, the partition becomes a positive-definite correlation matrix Σ through an RBF kernel on cluster ranks, and the per-round posterior sample is drawn with covariance Σ while the Beta posteriors are updated from real rewards only, so the LLM shapes how the sampler moves, not what it believes. We give a self-contained Bayesian regret bound for the idealized Gaussian sampler whose information gain splits into a Klog T term from the K-cluster structure and a ridge term that grows to dlog T: the √(d/K) improvement over independent sampling is a finite-horizon transient, exact only as the within-cluster correlation tends to one. The correlated sampler reduces regret by 19% over CTS on 16 synthetic Bernoulli families at T=2,500 (6-7% at T=25,000 with data-adaptive kernels) and by 41% on the Microsoft MIND-small news benchmark (d=200 real articles), while pseudo-observation warm starts give nothing. An LLM-free ablation with a simulated oracle of controlled quality shows that on unstructured instances the gain is a property of the kernel shape (a random partition, or a plain tempering of the sampling noise, reproduces it), while belief injection at matched oracle quality never helps.
Related
- Sharp Normalized Covariance Bounds and Constant-Stretch Correlated Sampling on the Hypersimplex
- When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity
- Thompson Sampling for Learning in Zero-Sum Games
- High-Probability Regret Bounds for Feel-Good Thompson Sampling
- Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization
BibTeX
@misc{kakaria2026structure,
title = {{Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits}},
author = {Vikram Kakaria and Anish Kataria and Anany Kotawala},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07470},
eprint = {2610.07470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07470},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits
AU - Vikram Kakaria
AU - Anish Kataria
AU - Anany Kotawala
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07470
UR - https://arxiv.org/abs/2610.07470
AB - Combinatorial Thompson sampling (CTS) draws independent posterior samples for every arm, so its exploration dynamics ignore any relation among arms. We study a minimal change to those dynamics: an LLM is queried once for a partition of the arms, the partition becomes a positive-definite correlation matrix Σ through an RBF kernel on cluster ranks, and the per-round posterior sample is drawn with covariance Σ while the Beta posteriors are updated from real rewards only, so the LLM shapes how the sampler moves, not what it believes. We give a self-contained Bayesian regret bound for the idealized Gaussian sampler whose information gain splits into a Klog T term from the K-cluster structure and a ridge term that grows to dlog T: the √(d/K) improvement over independent sampling is a finite-horizon transient, exact only as the within-cluster correlation tends to one. The correlated sampler reduces regret by 19% over CTS on 16 synthetic Bernoulli families at T=2,500 (6-7% at T=25,000 with data-adaptive kernels) and by 41% on the Microsoft MIND-small news benchmark (d=200 real articles), while pseudo-observation warm starts give nothing. An LLM-free ablation with a simulated oracle of controlled quality shows that on unstructured instances the gain is a property of the kernel shape (a random partition, or a plain tempering of the sampling noise, reproduces it), while belief injection at matched oracle quality never helps.
ER -