Biblio

Privacy protection is becoming more and more important in the era of big data. Differential privacy is a rigorous and provable privacy protection method that can protect privacy for a single piece of data. But existing differential privacy online learning methods have great limitations in the scope of application and accuracy. Aiming at this problem, we propose a more general and accurate algorithm, named DPOL-CT, for differential privacy online learning. We first distinguish the difference in differential privacy protection between offline learning and online learning. Then we prove that the DPOL-CT algorithm achieves (∊, δ)-differential privacy for online learning under the Gaussian, the Laplace and the Staircase mechanisms and enjoys a sublinear expected regret bound. We further discuss the trade-off between the differential privacy level and the regret bound. Theoretical analysis and experimental results show that the DPOL-CT algorithm has good performance guarantees.

Interval uncertainty can cause uncontrollable variations in the objective and constraint values, which could seriously deteriorate the performance or even change the feasibility of the optimal solutions. Robust optimization is to obtain solutions that are optimal and minimally sensitive to uncertainty. In this paper, a sequential multi-objective robust optimization (MORO) approach based on support vector machines (SVM) is proposed. Firstly, a sequential optimization structure is adopted to ease the computational burden. Secondly, SVM is used to construct a classification model to classify design alternatives into feasible or infeasible. The proposed approach is tested on a numerical example and an engineering case. Results illustrate that the proposed approach can reasonably approximate solutions obtained from the existing sequential MORO approach (SMORO), while the computational costs are significantly reduced compared with those of SMORO.