  High-velocity streams of high-dimensional data pose significant "big data"
analysis challenges across a range of applications and settings. Online
learning and online convex programming play a significant role in the rapid
recovery of important or anomalous information from these large datastreams.
While recent advances in online learning have led to novel and rapidly
converging algorithms, these methods are unable to adapt to nonstationary
environments arising in real-world problems. This paper describes a dynamic
mirror descent framework which addresses this challenge, yielding low
theoretical regret bounds and accurate, adaptive, and computationally efficient
algorithms which are applicable to broad classes of problems. The methods are
capable of learning and adapting to an underlying and possibly time-varying
dynamical model. Empirical results in the context of dynamic texture analysis,
solar flare detection, sequential compressed sensing of a dynamic scene,
traffic surveillance,tracking self-exciting point processes and network
behavior in the Enron email corpus support the core theoretical findings.
