arXiv Machine Learning
Sep 3

Improved Gradient Descent Lower Bounds Beyond Nesterov

The paper investigates the limits of accelerating gradient descent (GD) using predetermined step sizes in smooth convex optimization. It establishes new lower bounds: an ≥·n−1.6342 non‑anytime bound and an ≥·n−1.2408 anytime bound, surpassing previous results. These findings also demonstrate a strict separation between convergence exponents achievable in non‑anytime versus anytime settings.

By Yuhan Ye, Kaizhao Liu
arXiv Machine Learning
Sep 21

Single-Loop Stochastic Projected Damped Extragradient Methods for Stochastic Nonconvex--(Strongly) Concave Minimax Optimization

The paper introduces single-loop stochastic projected damped extragradient (SPDE) and its variance-reduced variant (VR-SPDE) for stochastic nonconvex–(strongly) concave minimax problems. It provides SFO complexity bounds for achieving game stationarity and optimization stationarity, improving upon previous multi-loop methods while maintaining a single-loop structure. The results claim the best-known SFO complexities for these stationarity criteria among single-loop stochastic first‑order methods.

By Huiling Zhang, Minhao Zhang, Zi Xu