题目：Langevin dynamics-based algorithm e-THεO POULA for stochastic optimization with discontinuous stochastic gradient

摘要：We introduce a new Langevin dynamics-based algorithm, called e-THεO POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-THεO POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-THεO POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Two key applications in finance are provided, namely, multi-period portfolio optimization and transfer learning in multi-period portfolio optimization, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-THεO POULA compared to SGLD, ADAM, and AMSGrad in terms of model accuracy.

报告人：张莹 香港科技大学（广州）

报告时间：2024年6月6日 下午 14:30-15:40

报告地点：数理楼235教室

报告人简介：张莹博士，现任香港科技大学（广州）社会枢纽金融科技学域助理教授。她于2020年获得爱丁堡大学的数学博士学位，并在2020-2023年担任新加坡南洋理工大学博士后研究员。主要研究领域为非线性随机系统的数值算法与其收敛性分析及各领域的应用。典型例子包括SDE的数值算法、MCMC、解决（包含神经网络的）最优化问题的随机数值算法等。研究成果发表在IMA Journal of Numerical Analysis、Bernoulli、Applied Mathematics & Optimization、SIAM Journal on Mathematics of Data Science等国际知名刊物。