Baiying Xin

Baiying Xin

Hi~
I am very much a beginner in the ocean of optimization and statistics.

And so we beat on …

Recent Updates

01 / notes

  1. Proximal three-point identity

    Added Proximal three-point identity to Short Notes, deriving the proximal three-point bound and its mirror descent and composite versions.

  2. Barrier PDLP algorithm slides

    Added Barrier PDLP to the new Linear Programming reading section, covering the logarithmic-barrier PDHG update, the perturbed KKT system, adaptive restarts, and barrier-stage updates.

  3. The bias-complexity tradeoff

    Added 05 - The Bias-Complexity Tradeoff to Understanding Machine Learning, covering the No-Free-Lunch theorem and its proof, why prior knowledge must enter through the choice of hypothesis class, and the decomposition of error into approximation and estimation terms.

02 / publications & preprints

  1. Optimal First-Order Methods for a Class of Structured Hölder-Smooth Problems

    Baiying Xin, Qi Deng

    2026 · arXiv:2610.21595 · Preprint

    For a class of Hölder-smooth problems arising from regularized ℓp\ell_p regression with 1<p<21<p<2, we develop a smoothing-based first-order method with an O(ε−1/p)\mathcal{O}(\varepsilon^{-1/p}) matrix–vector complexity and prove a matching Ω(ε−1/p)\Omega(\varepsilon^{-1/p}) lower bound for deterministic algorithms.