Select a Bayesian prior encoding mean-discrepancy information

Determine how to choose a Bayesian prior that encodes the side-information constraint \(|\mu_k-\mu'_k|<L_k\) when prior observations are generated by an unknown adaptive policy and may remain asymptotically influential.

Background

The paper notes that Bayesian bandit methods could in principle incorporate source information through a prior distribution. However, the relevant side information is a constraint on the difference between source and target means, rather than a conventional prior over a fixed target distribution.

Moreover, the number of source observations may scale with the horizon, so the side information need not become asymptotically negligible. The paper therefore leaves unresolved how a Bayesian prior should represent the mean-discrepancy constraint while preserving meaningful asymptotic guarantees.

References

It is not clear how to choose the prior to encode the prior distribution \hat \nu'_k with our condition on the mean | \mu_k - \mu'_k| < L_k and in our setting this side information can remain influential in the regret as T\to\infty whenever N'_k itself scales with T while in the current analysis of Bayesian approach it is used that the prior become asymptotically negligible.

— Transfer Learning in Bandits from Unknown Adaptive Policies: Problem-Dependent Lower and Upper Bounds  (2610.21582 - Prevost et al., 15 Oct 2026) in Section 2, paragraph “Bayesian approaches to bandits”