学术报告：A Correlation-induced Finite Difference Estimator

报告时间：4月2日（星期四）下午14:30-15:30

报告地点：沙河校区，二教107

主持人：张少钦教授

报告人：张琨，中国人民大学，讲师

报告摘要：Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. The optimal FD estimator is constructed assuming known optimal perturbation, which is rarely the case in practice. This paper establishes a novel sample-driven method that leverages Lepski’s rule and regression techniques to estimate the optimal perturbation based on all simulated samples. We then normalize and transform these samples according to the estimated optimal perturbation, leading to correlated samples. Using these correlated samples, we propose an efficient FD estimator. Theoretical analyses of both the perturbation estimator and the FD estimator reveal that, surprisingly, the correlation enables the proposed FD estimator to achieve a reduction in variance, implying the robustness of our method. Numerical results demonstrate that our method performs robustly across a variety of black-box environments.

报告人简介：张琨，男，中国人民大学信息学院讲师。他于2018年获得香港城市大学商学院管理科学系运筹专业哲学博士学位，此前获得北京师范大学数学科学学院数学与应用数学专业理学学士学位、概率论与数理统计专业理学硕士学位。2018年至2019年在香港城市大学商学院任博士后研究员，2019年8月至2025年8月任教于中国人民大学统计与大数据研究院。研究兴趣：随机优化，机器学习，金融工程与风险管理，商业分析。论文发表于Operations Research, INFORMS Journal on Computing, Naval Research Logistics, European Journal of Operational Research, IEEE Transactions on Neural Networks and Learning Systems等期刊。

撰稿人：刘洁

审稿人：邓露