Job Description

In recent decades, we have witnessed significant progresses in the convergence and complexity theory of the first-order optimization methods, with gradient global Lipschitz continuity (GGLC) assumption playing a central role, in many classical results. However, a large class of important problems arising in modern optimization and machine learning do not satisfy this assumption. As a result, there remains a substantial gap between the theory and practical behavior of many widely used algorithms.

This project, led by Dr. Zhang, aims to strengthen the theoretical foundation of relative smooth optimization, an emerging framework developed to go beyond the classical GGLC setting. In particular, the project will study first-order methods under relative smoothness, with a focus on nonconvex problems, more appropriate optimality measures, and new non-Euclidean Lipschitz tools that better capture the underlying problem geometry. The goal is to establish sharper convergence and complexity results, clarify several widely adopted but potentially misleading arguments in the current literature, and develop a more reliable and powerful new analysis framework for the relative smooth problem class.

Job Requirements

Interested applicants are required to possess a BSc. in 2026. He/she should have a good understanding in

1. convergence and complexity analysis for (nonconvex) optimization algorithms
2. stochastic process and stochastic approximation methods

In particular, as this is a research assistant position for only 1 year. The applicant should be experienced in MATLAB and Python coding. In particular, he/she should have the ability to adapt base codes of PyTorch to implement new algorithms instead of calling built-in functions.

As we plan to apply our methodologies to the training and tuning of language models, it will be an advantage if the applicant has related experience.