SPEAKER: 张琨，助理教授，中国人民大学

TIME/DATE: 2024.10.31  2:00pm

CLASSROOM: 同济大厦A楼401教室

讲座摘要:

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 bootstrap 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 and, in some cases, a decrease in bias compared to the optimal FD estimator. Numerical results confirm the efficiency of our estimators and align well with the theory presented, especially in scenarios with small sample sizes. Finally, we apply the estimator to solve derivative-free optimization (DFO) problems, and numerical studies show that DFO problems with 100 dimensions can be effectively addressed.

演讲嘉宾简介:

张琨，现为中国人民大学统计与大数据研究院助理教授、博士生导师。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年秋至今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等国际期刊。