Distributed online optimization subject to long-term constraints and time-varying topology: An event-triggered and bandit feedback approach

This paper considers the distributed online optimization problem (DOO) with long-term constraints (LTC) and bandit feedback under a time-varying communication network, where the cost functions are time-varying and only two specific values are disclosed to agents subsequent to their decision-making process. In order to alleviate computation and communication burdens, long-term constraints is considered, and an event-triggered strategy is established for scheduling network communication. Based on this, an event-triggered distributed online algorithm is proposed with two-point bandit feedback for the DOO-LTC through B-strongly connected communication. Two cases of general convex and strongly convex cost functions are taken into consideration. The derived upper bounds for the regret and cumulative absolute constraint violation (CACV) are O(Tmax{c,1−c}) and O(T1−c2) for a general convex cost function, and O(logT) and O(TlogT) for a strongly convex cost function, respectively. Finally, a numerical example of distributed online regularization linear regression is provided to show the effectiveness of the proposed algorithm.