Structure, Not Belief: Correlated Thompson Sampling from LLM-Derived Covariance in Combinatorial Semi-Bandits
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 $K\log T$ term from the $K$-cluster st...
| Authors | Vikram Kakaria, Anish Kataria, Anany Kotawala |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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