  Distributed online optimization and game have been increasingly researched in
the last decade, mostly motivated by its wide applications in sensor networks,
robotics (e.g., distributed target tracking and formation control), smart
grids, deep learning, and so forth. In these problems, there is a network of
agents who may be cooperative (i.e., distributed online optimization) or
noncooperative (i.e., online game) through local information exchanges. And the
local cost function of each agent is often time-varying in dynamic and even
adversarial environments. At each time, a decision must be made by each agent
based on historical information at hand without knowing future information on
cost functions. For these problems, a comprehensive survey is still lacking.
This paper aims to provide a thorough overview of distributed online
optimization and game from the perspective of problem settings, communication,
computation, algorithms, and performances. In addition, some potential future
directions are also discussed.
