Electronic Companion to Adaptivity and Confounding in Multi-Armed Bandit Experiments

Chao Qin, Daniel Russo

Abstract: This paper provides an electronic companion to Qin and Russo [2022]. It contains the proof of a proposition regarding the asymptotic behavior of deconfounded Thompson sampling. The proof is omitted from that paper, since it is closely related to analyses in Russo [2020], Qin et al. [2017], and Shang et al. [2020]. While the analysis here is quite technical, we have tried to give a relatively clear proof template that could be useful in future work.