Decentralized multi-agent optimization usually relies on information exchange between neighboring agents, which can incur unaffordable communication overhead in practice. To reduce the communication cost, we apply event-triggering technique to the decentralized multi-agent online convex optimization problem, where each agent is associated with a time-varying local loss function and the goal is to minimize the accumulated total loss (the sum of all local loss functions) by choosing appropriate actions sequentially. We first develop an event-triggered decentralized online subgradient descent algorithm for the full information case, where the local loss function is fully revealed to each agent at each time. We establish an upper bound for the regret of each agent in terms of the event-triggering thresholds. It is shown that the regret is sublinear provided that the event-triggering thresholds converge to zero as time goes to infinity. The algorithm and analysis are further extended to the scenario of bandit feedback, where only the values of the local loss function at two random points close to the current action are disclosed to each agent. We show that the two-point bandit feedback does not degrade the performance of the proposed algorithm in order sense and a regret bound similar to the full information case can be established. Finally, numerical results on the problem of decentralized online least squares are presented to validate the proposed algorithms.

中文翻译：

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具有事件触发通信的分散式在线凸优化

分散式多智能体优化通常依赖于相邻智能体之间的信息交换，这在实践中会产生难以承受的通信开销。为了降低通信成本，我们将事件触发技术应用于分散的多智能体在线凸优化问题，其中每个智能体都与一个随时间变化的局部损失函数相关联，目标是最小化累积总损失（所有局部损失函数）通过​​依次选择适当的动作。我们首先为全信息情况开发了一个事件触发的去中心化在线次梯度下降算法，其中每次都向每个代理完全揭示局部损失函数。我们根据事件触发阈值为每个代理的遗憾建立了上限。结果表明，如果事件触发阈值随着时间趋于无穷大而收敛到零，则遗憾是次线性的。该算法和分析进一步扩展到老虎机反馈的场景，其中仅向每个代理公开靠近当前动作的两个随机点的局部损失函数值。我们表明，两点老虎机反馈不会在顺序意义上降低所提出算法的性能，并且可以建立类似于完整信息情况的遗憾界限。最后，给出了关于分散在线最小二乘问题的数值结果以验证所提出的算法。其中只有接近当前动作的两个随机点的局部损失函数值才会向每个代理公开。我们表明，两点老虎机反馈不会在顺序意义上降低所提出算法的性能，并且可以建立类似于完整信息情况的遗憾界限。最后，给出了关于分散在线最小二乘问题的数值结果以验证所提出的算法。其中只有接近当前动作的两个随机点的局部损失函数的值才会向每个代理公开。我们表明，两点老虎机反馈不会在顺序意义上降低所提出算法的性能，并且可以建立类似于完整信息情况的遗憾界限。最后，给出了关于分散在线最小二乘问题的数值结果以验证所提出的算法。