On Fixed Convex Combinations of No-Regret Learners

No-regret algorithms are powerful tools for learning in online convex problems that have received increased attention in recent years. Considering affine and external regret, we investigate what happens when a set of no-regret learners (voters) merge their respective strategies in each learning iteration to a single, common one in form of a convex combination. We show that an agent who executes this merged decision in each iteration of the online learning process and each time feeds back a reward function to the voters that is a correspondingly weighted version of its own reward, incurs sublinear regret itself. As a by-product, we obtain a simple method that allows us to construct new no-regret algorithms out of known ones.