In recent years, multi-classifier learning is of significant interest in industrial and economic fields. Moreover, neural network is a popular approach in multi-classifier learning. However, the accuracies of neural networks are often limited by their loss functions. For this reason, we design a novel cross entropy loss function, named MPCE, which based on the maximum probability in predictive results. In this paper, we first analyze the difference of gradients between MPCE and the cross entropy loss function. Then, we propose the gradient update algorithm based on MPCE. In the experimental part of this paper, we utilize four groups of experiments to verify the performance of the proposed algorithm on six public datasets. The first group of experimental results show that the proposed algorithm converge faster than the algorithms based on other loss functions. Moreover, the results of the second group show that the proposed algorithm obtains the highest training and test accuracy on the six datasets, and the proposed algorithm perform better than others when class number changing on the sensor dataset. Furthermore, we use the model of convolutional neural network to implement the compared methods on the mnist dataset in the fourth group of experiments. The results show that the proposed algorithm has the highest accuracy among all executed methods.

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.