What question did this study set out to answer?

The aim is to improve gradient descent methods by developing new stepsize schedules with better convergence properties.

Accelerated Gradient Descent by Concatenation of Stepsize Schedules

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This work introduces new stepsize schedules for gradient descent, improving convergence rates for smooth convex objectives.

The aim is to improve gradient descent methods by developing new stepsize schedules with better convergence properties.
Proposed a unified technique to construct stepsizes through concatenation of existing schedules.
Introduced two new families of stepsize schedules applicable for an arbitrary number of iterations.
Derived analytical bounds for the performance of the newly constructed schedules.
Achieved a convergence rate of O(n^{- ext{log}_2( ext{ extsqrt{2}+1}}) with state-of-the-art constants.
New schedules either match or exceed the performance of the best previously computed schedules for objective value and gradient norm.

Zhang et al. (2026) studied this question.

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