Event-triggered distributed online convex optimization with delayed bandit feedback.

• Two bandit algorithms are designed based on the non-Euclidean framework. The Bregman divergence is used as the distance measure in the projection step. • In our algorithms, the potential time delay existing in the feedback process and the limited network resources are taken into account. • The static regret bounds are provided for the ET-DOCO algorithms with delayed bandit feedback. The obtained results show that the two algorithms can ensure a sublinear regret bound if the triggering threshold tends to zero. This paper is concerned with an online distributed convex-constrained optimization problem over a multi-agent network, where the limited network bandwidth and potential feedback delay caused by network communication are considered. To cope with the limited network bandwidth, an event-triggered communication scheme is introduced in information exchange. Then, based on the delayed (i.e., single-point and two-point) bandit feedback, two event-triggered distributed online convex optimization algorithms are developed by utilizing the Bregman divergence in the projection step. Meanwhile, the convergence of the two developed algorithms is analyzed according to the provided static regret bounds achieved by the algorithm. The obtained results show that a sublinear static regret with respect to the time horizon T can be ensured if the triggering threshold gradually approaches zero. In this case, the corresponding order of the regret bounds is also determined by choosing suitable triggering thresholds. Finally, a distributed online regularized linear regression problem is provided as an example to illustrate the effectiveness of the proposed two algorithms. [ABSTRACT FROM AUTHOR]