Projection-Free Methods for Online Distributed Quantized Optimization With Strongly Pseudoconvex Cost Functions

This paper investigates online distributed optimization within multi-agent systems under inequality constraints. Agents are allowed to exchange local data with their immediate neighbors through a time-varying digraph and perform computations, aiming to minimize a collective objective function. Considering that the communication capacity of multi-agent systems is often limited in practical applications, a random quantizer is introduced to reduce the transmission bits when agents exchange information over the network. In this study, we specifically consider the scenario where the cost function is strongly pseudoconvex. To handle these problems, a quantized distributed online projection-free optimization algorithm is developed for the strongly pseudoconvex problem with an inequality constraint set. The performance of the algorithm is evaluated using the expectation of dynamic regret. Provided that the graph satisfies certain mild conditions, it has been demonstrated that the bound for each dynamic regret function increases at a sublinear rate. A simulation example is presented to illustrate the validity of our theoretical results.