Computational implementation of exact-posterior Thompson sampling

Develop a computational method for implementing exact-posterior Thompson sampling for arbitrary convex, non-monotone convex ridge losses while preserving the stated Bayesian regret setting.

Background

The result is statistical rather than computational: it establishes a regret guarantee for the canonical exact-posterior Thompson-sampling rule under arbitrary priors and fixed measurable minimizer selections. The paper does not provide an efficient procedure for representing the posterior, sampling exactly from it, or computing the selected minimizers.

The authors explicitly identify computation as an unresolved issue within the scope of their result, separate from the unresolved question of the dimension dependence.