arXiv:2609. 09152v2 Announce Type: replace-cross Abstract: We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization.
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arXiv:2609.09152v1 Announce Type: cross Abstract: We study how far gradient descent (GD) can be accelerated by predetermined nonnegative stepsizes in smooth convex optimization. Writing $p_{\mathrm{s...
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.
arXiv:2610. 33381v2 Announce Type: new Abstract: Training is often stopped at a data-dependent time, so guarantees for the last iterate must hold at all times simultaneously.
arXiv:2608. 10418v1 Announce Type: cross Abstract: Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications.
arXiv:2609.08537v1 Announce Type: cross Abstract: We study the time-uniform convergence of the raw iterate of standard stochastic gradient descent (SGD) for unconstrained smooth convex objectives. We...
arXiv:2610.07814v1 Announce Type: cross Abstract: How far can stochastic gradient descent ascent (SGDA) go by tuning its timescale ratio and step sizes in nonconvex min-max games? We answer this ques...