Before revision:  (Recently, Wager and Xu (arXiv:2101.09855) independently proposed this regime and developed similar SDE and random ODE approximations  .) Our weak convergence theory covers both the classical multi-armed and linear bandit settings,  and can be used, for instance, to obtain insight about the characteristics of the regret distribution when there is information sharing among arms, as well as the effects of variance estimation, model mis-specification and batched updates in bandit learning. Our theory is developed from first-principles and can also be adapted to analyze other sampling-based bandit algorithms .
After revision:  (Recently, Wager and Xu (arXiv:2101.09855) independently proposed this regime and developed similar SDE and random ODE approximations .) Our weak convergence theory covers both the classical multi-armed and linear bandit settings, and can be directly adapted to analyze other sampling-based bandit algorithms .