  This paper considers online distributed convex constrained optimization over
a time-varying multi-agent network. Agents in this network cooperate to
minimize the global objective function through information exchange with their
neighbors and local computation. Since the capacity or bandwidth of
communication channels often is limited, a random quantizer is introduced to
reduce the transmission bits. Through incorporating this quantizer, we develop
a quantized distributed online projection-free optimization algorithm, which
can achieve the saving of communication resources and computational costs. For
different parameter settings of the quantizer, we establish the corresponding
dynamic regret upper bounds of the proposed algorithm and reveal the trade-off
between the convergence performance and the quantization effect. Finally, the
theoretical results are illustrated by the simulation of distributed online
linear regression problem.
