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Online mirror descent (OMD) and dual averaging (DA) -- two fundamentalalgorithms for online convex optimization -- are known to have very similar(and sometimes identical) performance guarantees when used with a fixedlearning rate. Under dynamic learning rates, however, OMD is provably inferiorto DA and suffers a linear regret, even in common settings such as predictionwith expert advice. We modify the OMD algorithm through a simple technique thatwe call stabilization. We give essentially the same abstract regret bound forOMD with stabilization and for DA by modifying the classical OMD convergenceanalysis in a careful and modular way that allows for straightforward andflexible proofs. Simple corollaries of these bounds show that OMD withstabilization and DA enjoy the same performance guarantees in many applications-- even under dynamic learning rates. We also shed light on the similaritiesbetween OMD and DA and show simple conditions under which stabilized-OMD and DAgenerate the same iterates.

Online mirror descent and dual averaging: keeping pace in the dynamic case