Quantizer-based distributed mirror descent for multi-agent convex optimization

This paper is concerned with the constrained distributed multi-agent convex optimization problem over a time-varying network. We assume that the bit rate of the considered communication is limited, such that a uniform quantizer is applied in the process of exchanging information over the multi-agent network. Then a quantizer-based distributed mirror descent (QDMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is developed for such optimization problem. The convergence result of the developed algorithm is also analyzed. By choosing the iteration step-size
$\eta_{t}=\lambda/\sqrt{t}$
and quantization interval
$v_{t}=\lambda/t$
with a prescribed parameter
$\lambda$
, it is shown that the convergence rate of the QDMD algorithm can achieve
$\mathcal{O}(1/\sqrt{T})$
, where
$T$
is the number of iterations.