Dynamic Event-Triggered Distributed Online Optimization Subject to Long-Term Constraints

This paper investigates distributed online optimization with long-term constraints over time-varying unbalanced multi-agent networks under limited communication resources. To address network imbalance, communication overhead, and the computational burden of per-round constrained projections, a dynamic event-triggered distributed online optimization algorithm with long-term constraints is developed. The algorithm combines an auxiliary-variable-based weighting scheme for column-stochastic networks, a dynamic event-triggered communication protocol, and a long-term constraint mechanism that permits projection onto a simple superset of the original feasible set. We establish bounds on dynamic regret and cumulative absolute constraint violation, both of which explicitly depend on the time horizon and the path variation of the benchmark sequence. Under appropriate parameter choices and sufficiently slow-growing path variation, both bounds are sublinear. Numerical experiments on distributed online linear regression illustrate the theoretical properties of the proposed algorithm.