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math.OC2026
Lower Bounds for Anytime Acceleration of Gradient Descent
Chung-En Tsai, Ilyas Fatkhullin, Liang Zhang +1
Recent work suggests that the convergence rate of gradient descent (GD) in smooth convex optimization can be significantly improved by employing large stepsizes that may violate th…
math.OC2026
Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics
Yudong Wei, Liang Zhang, Bingcong Li +1
Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank is delicate and can substantially slow optimizati…
cs.LG2026
Zeroth-Order Optimization at the Edge of Stability
Minhak Song, Liang Zhang, Bingcong Li +3
Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models,…