题　目：Proximal Oracles for Optimization and Sampling

嘉　宾：梁家铭，University of Rochester, Assistant Professor

主持人：葛冬冬，金沙威尼斯欢乐娱人城教授

时　间：2024年6月4日（周二）14:00-15:30

地　点：金沙威尼斯欢乐娱人城B207

内容简介: 

We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is either Hölder continuous or in composite form as the finite sum of Hölder continuous components. To overcome the challenges caused by non-smoothness, our algorithms employ two powerful proximal frameworks in optimization and sampling: the proximal point framework for optimization and the alternating sampling framework (ASF) that uses Gibbs sampling on an augmented distribution. A key component of both optimization and sampling algorithms is the efficient implementation of the proximal map by the regularized cutting-plane method. We establish the iteration-complexity of the proximal map in both Hölder continuous and composite settings. We further propose an adaptive proximal bundle method for non-smooth optimization. The proposed method is universal since it does not need any problem parameters as input. Additionally, we develop a proximal sampling oracle that resembles the proximal map in optimization and establish its complexity using a novel technique (a modified Gaussian integral). Finally, we combine this proximal sampling oracle and ASF to obtain a Markov chain Monte Carlo method with non-asymptotic complexity bounds for sampling in Hölder continuous and composite settings.

演讲人简介：

Jiaming Liang is an assistant professor in the Goergen Institute for Data Science and the Department of Computer Science at the University of Rochester. He was a postdoctoral researcher in Computer Science at Yale University. Jiaming obtained PhD in Operations Research from Georgia Institute of Technology. He received his bachelor’s degree in Ocean Engineering and Applied Math from Shanghai Jiao Tong University. Jiaming's primary research goal is to design, analyze, and implement fast algorithms for solving a general class of problems in data science. His research interests broadly include topics in optimization, sampling, differential privacy, and market equilibrium and design.

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