difficulty originates from the fact that all the statistical learning guarantees for offline regression with a general ${{\mathcal{F}}}$ require one to take an expectation over contexts. In other words, context-dependent statistical guarantees are generally impossible for an offline regression oracle.

**Statistical hurdle associated with analyzing dependent actions.** [@foster2020beyond] propose an optimal and efficient contextual bandit algorithm assuming access to an online regression oracle, which is quite different from an offline regression oracle. Statistically, the difference between offline and online regression oracles is that, offline regression oracles only assume statistical guarantees for an i.i.d. data sequence (see §\[sec:extension\] for our definition of a general offline regression oracle), while online regression oracles assume statistical guarantees for an arbitrary data sequence possibly generated by an adaptive adversary. Evidently, access to an online regression oracle is a stronger assumption than access to an offline regression oracle. As [@foster2020beyond] mention, their algorithm requires an online regression oracle because “the analysis critically uses that the regret bound (of the online regression oracle) holds when the actions $a_1,\dots,a_T$ are chosen adaptively, since actions selected in early rounds are used by `SquareCB` to determine the action distribution at later rounds”. That is, the technical hurdle of using an 