SupplementaryMaterialfor" OnlineConvex OptimizationOverErd os-RényiRandomNetworks "

Neural Information Processing Systems 

A.1 PreliminaryLemmas In this subsection, we present some preliminary lemmas that will be used in the subsequent for provingtheregretbounds. Suppose Assumptions 1, and 2, hold. Let the local estimates{xi,t}Tt=1 for each node i V begeneratedbyAlgorithm1. Thenthefollowingholdwith xt = 1N