Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits

arXiv:2610.07470v1 Announce Type: cross 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 $\Sigma$ through an RBF kernel on cluster ranks, and the per-round posterior sample is drawn with covariance $\Sigma$ while the Beta posteriors are updated from real rewards only, so the LLM shapes how the sampler moves, not what it believes.

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