Supplementary Material for " Online Convex Optimization Over Erd os-Rényi Random Networks "

Let Assumptions 1 and 2 hold. By substituting (A.5) into (A.3) and using Assumption 2, we derive Hence by (A.7), we obtain (A.2). Jensen's inequality for conditional expectations, we obtain that Enull nulle Suppose Assumptions 1, and 2, hold. By combing (2) with (A.14) and (A.8), there holds x Note by the Jensen's inequality that Then from (A.13) it follows that E null Then the theorem is proved. This combined with (A.19) proves the theorem.