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 paper, where the cost functions change over time. To solve this problem, many projected online optimization algorithms have been wildly 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 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 O(T3/4) when cost functions are convex, where T is a time horizon. Finally, we present simulated experiments on two datasets to validate our theoretical results.

Computing offloading of mobile devices (MDs) through cloud is a greatly effective way to solve the problem of local resource constraints. However, cloud servers are usually located far away from MDs leading to a long response time. To this end, edge cloud servers (ECSs) provide a shorter response time due to being closer to MDs. In this paper, we propose a computing offloading game for MDs and ECSs. We prove the existence of a Stackelberg equilibrium in the game. In addition, we propose two algorithms, F‐SGA and C‐SGA, for delay‐sensitive and compute‐intensive applications, respectively. Moreover, the response time is reduced by F‐SGA, which makes decisions quickly. An optimal decision is obtained by C‐SGA, which achieves the equilibrium. Both algorithms above proposed can adjust the computing resource and utility of system users according to parameters control in computing offloading. The simulation results show that the game significantly saves the computing resources and response time of both the MD and the ECSs during the computing offloading process.

Adaptive gradient algorithms have recently become extremely popular because they have been applied successfully in training deep neural networks, such as Adam, AMSGrad, and AdaBound. Despite their success, however, the distributed variant of the adaptive method, which is expected to possess a rapid training speed at the beginning and a good generalization capacity at the end, is rarely studied. To fill the gap, a distributed adaptive subgradient algorithm is presented, called D-AdaBound, where the learning rates are dynamically bounded by clipping the learning rates. Moreover, we obtain the regret bound of D-AdaBound, in which the objective functions are convex. Finally, we confirm the effectiveness of D-AdaBound by simulation experiments on different datasets. The results show the performance improvement of D-AdaBound relative to existing distributed online learning algorithms.