The present paper deals with online convex optimization involving both time-varying loss functions, and time-varying constraints. The loss functions are not fully accessible to the learner, and instead only the function values (a.k.a. bandit feedback) are revealed at queried points. The constraints are revealed after making decisions, and can be instantaneously violated, yet they must be satisfied in the long term. This setting fits nicely the emerging online network tasks such as fog computing in the Internet-of-Things (IoT), where online decisions must flexibly adapt to the changing user preferences (loss functions), and the temporally unpredictable availability of resources (constraints). Tailored for such human-in-the-loop systems where the loss functions are hard to model, a family of bandit online saddle-point (BanSaP) schemes are developed, which adaptively adjust the online operations based on (possibly multiple) bandit feedback of the loss functions, and the changing environment. Performance here is assessed by: i) dynamic regret that generalizes the widely used static regret; and, ii) fit that captures the accumulated amount of constraint violations. Specifically, BanSaP is proved to simultaneously yield sub-linear dynamic regret and fit, provided that the best dynamic solutions vary slowly over time. Numerical tests in fog computation offloading tasks corroborate that our proposed BanSaP approach offers competitive performance relative to existing approaches that are based on gradient feedback.

针对在线凸优化中的时间变化的损失函数和约束条件进行分析，提出了一种 bandit online saddle-point（BanSaP）算法，该算法可适应不断变化的损失函数和环境，同时进行优化，在雾计算下的实验表明相对于已有的基于梯度反馈的算法，提出的方法提供了竞争性的性能。

基于Bandit凸优化的可扩展和动态IoT管理