APPENDIX A Further Related Work Additional related Work and discussions

Additional related Work and discussions. Several attempts have been made to formalize and study stateful online learning models. In this section, we provide the proofs missing from Section 3. Proof of Proposition 3.1. Given the aforementioned choice of notation, the transformation of an OJS instance to a DRACC instance should now be straightforward. Corollary C.1 is derived from the regret bound of OJS problem (see Corollary C.3). Lemma C.2.