Online Learning for IoT Optimization: A Frank–Wolfe Adam-Based Algorithm

Many problems in the Internet of Things (IoT) can be regarded as online optimization problems. For this reason, an online-constrained problem in IoT is considered in this article, where the cost functions change over time. To solve this problem, many projected online optimization algorithms have been widely used. However, the projections of these algorithms become prohibitive in problems involving high-dimensional parameters and massive data. To address this issue, we propose a Frank–Wolfe Adam online learning algorithm called Frank–Wolfe Adam (FWAdam), which uses a Frank–Wolfe method to eschew costly projection operations. Furthermore, we first give the convergence analysis of the FWAdam algorithm, and prove its regret bound to <inline-formula> <tex-math notation="LaTeX">$O(T^{3/4})$ </tex-math></inline-formula> when cost functions are convex, where <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> is a time horizon. Finally, we present simulated experiments on two data sets to validate our theoretical results.