Event-Based Broadcasting for Stochastic Subgradient Algorithms

Stochastic subgradient algorithms (SSAs) are widely studied owing to their applications in distributed and online learning. However, in a distributed setting, their sub-linear convergence rates tend to attract a large number of information exchanges that raise the overall communication burden. In order to reduce this burden, in this paper, we design two static stochastic event-based broadcasting protocols that operate in conjunction with SSAs to address a set-constrained distributed optimization problem (DOP). We address two notions of stochastic convergence, namely, almost sure and mean convergence; for each of these notions we design event-based broadcasting protocols, specifically, the stochastic event-Thresholds. Subsequently, we illustrate the design via a numerical example and provide comparisons to evaluate its performance against the existing event-based protocols.