  Projection operations are a typical computation bottleneck in online
learning. In this paper, we enable projection-free online learning within the
framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures
how the history of decisions affects the current outcome by allowing the online
learning loss functions to depend on both current and past decisions.
Particularly, we introduce the first projection-free meta-base learning
algorithm with memory that minimizes dynamic regret, i.e., that minimizes the
suboptimality against any sequence of time-varying decisions. We are motivated
by artificial intelligence applications where autonomous agents need to adapt
to time-varying environments in real-time, accounting for how past decisions
affect the present. Examples of such applications are: online control of
dynamical systems; statistical arbitrage; and time series prediction. The
algorithm builds on the Online Frank-Wolfe (OFW) and Hedge algorithms. We
demonstrate how our algorithm can be applied to the online control of linear
time-varying systems in the presence of unpredictable process noise. To this
end, we develop a controller with memory and bounded dynamic regret against any
optimal time-varying linear feedback control policy. We validate our algorithm
in simulated scenarios of online control of linear time-invariant systems.
