In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when the models are complex like deep networks. In this paper, we investigate reasons for such overfitting by studying a weakly supervised problem called learning with complementary labels. We argue the quality of gradient estimation matters more in risk minimization. Theoretically, we show that a URE gives an unbiased gradient estimator(UGE). Practically, however, UGEs may suffer from huge variance, which causes empirical gradients to be usually far away from true gradients during minimization. To this end, we propose a novel surrogate complementary loss(SCL) framework that trades zero bias with reduced variance and makes empirical gradients more aligned with true gradients in the direction. Thanks to this characteristic, SCL successfully mitigates the overfitting issue and improves URE-based methods.

There is no doubt that cloud computing provides a simple but efficient way to share computational resources we have for an information system. Developing a highly effective method for solving the workflow scheduling problem (WSP) is one critical issue for enhancing the performance of such a system that requires to minimize the execution time, rent costs of resources, and transmission costs of data in a cloud workflow management system. This paper presents an efficient search algorithm, which is an extended version of search economics (SE), to solve WSP in a cloud computing environment, called search economics for workflow scheduling algorithm (SEWSA). The proposed algorithm inherits the distinguishing features of SE that uses not only the objective value to make a decision for the later search directions but also the potential of the subsolution space. The experimental results show that the proposed algorithm can find a better scheduling strategy to optimize the makespan time and to reduce the total cost than other metaheuristic algorithms.