We show that the proposed algorithms converge to the (regularized) global optimal solution, andmoreover,theirratesofconvergence areofpolynomial orderinthe online setting and exponential order inthe finite sample setting, respectively.

Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics.

One of the fundamental problems in learning neural networks is parameter recovery, where we assume the data are generated from a "teacher" network, and the task is to estimate the groundtruth parameters of the teacher network based on the generated data.

Usingalgebraic geometry,weestablish that UPCA is a well-defined algebraic problem in the sense that the only matrices of minimal rank that agree with the given data are row-permutations of the ground-truth matrix, arising as the unique solutions of a polynomial system of equations.

Pre-trained large language models (LLMs) based on Transformer have demonstrated striking in-context learning (ICL) abilities.

Fair machine learning.Generally, fair machine learning methods fall into three categories: preprocessing, in-processing, and post-processing [44, 7]. In this paper, we focus on in-processing methods thatmodify learning algorithms toremovediscrimination during thetraining process. All of those works are for indistribution fairness, and we investigate out-of-distribution fairness in this paper. Weuse LAFTR [42],anadversarial learning method that showsadvanced performance onfairness [47],tolearn a fair model in the source domain and adapt it to the target domain. We also test CFair[72] in our experiments.