This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal-dual algorithm over a time-varying directed graph. Dynamic network regret and network cumulative constraint violation are leveraged to measure the performance of the algorithm. Based on the natural decreasing parameter sequences, we establish sublinear dynamic network regret and network cumulative constraint violation bounds. The theoretical results broaden the applicability of event-triggered online convex optimization to the regime with inequality constraints. Finally, a numerical simulation example is provided to verify the theoretical results.

翻译：本文研究带有随时间变化不等式约束的分布式在线凸优化问题，智能体网络中的每个智能体通过与其邻居协作，以最小化累积网络损失。为降低智能体间的通信开销，提出一种在时变有向图上运行的分布式事件触发在线原始-对偶算法。采用动态网络遗憾与网络累积约束违反量衡量算法性能。基于自然递减参数序列，建立了次线性动态网络遗憾与网络累积约束违反界。该理论结果将事件触发在线凸优化的适用范围扩展至含不等式约束的场景。最后通过数值仿真示例验证理论结果。