学术报告报告题目: Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization
报 告人: Lingjiong Zhu副教授(佛罗里达州立大学)
报告时间: 2022年4月13日（星期三）上午10:00-11:00
报告地点: Zoom会议，会议链接: https://fsu.zoom.us/j/7339556904
邀 请人: 何志坚 教授
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数学学院
2022年4月11日
报告摘要：Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradient with momentum where a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates towards a global minimum. Many works reported its empirical success in practice for solving stochastic non-convex optimization problems, in particular it has been observed to outperform overdamped Langevin Monte Carlo-based methods such as stochastic gradient Langevin dynamics (SGLD) in many applications. We provide finite-time performance bounds for the global convergence of both SGHMC variants for solving stochastic non-convex optimization problems with explicit constants. Our results lead to non-asymptotic guarantees for both population and empirical risk minimization problems. For a fixed target accuracy level, on a class of non-convex problems, we obtain complexity bounds for SGHMC that can be tighter than those for SGLD. These results show that acceleration with momentum is possible in the context of global non-convex optimization.
报告人简介：Lingjiong Zhu got his BA from University of Cambridge in 2008 and PhD from New York University in 2013. He worked at Morgan Stanley and University of Minnesota before joining the faculty at Florida State University in 2015. His research interests include applied probability, data science, financial engineering and operations research. His works have been published in many leading conferences and journals including Annals of Applied Probability, Finance and Stochastics, ICML, INFORMS Journal on Computing, Journal of Machine Learning Research, NeurIPS, Production and Operations Management, SIAM Journal on Financial Mathematics and Operations Research.