The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions
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Abstract (arXiv)
In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an L-smooth function. We establish a new convergence rate, and show that the bound may be exact in some cases, in particular when all step lengths lie in the interval (0,1/L]. In addition, we derive an optimal step length with respect to the new bound.
Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Apr 2021.
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Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 0; 2026: 1.
4 papers.
- 2024Provable Complexity Improvement of AdaGrad over SGD: Upper and Lower Bounds in Stochastic Non-Convex Optimizationcited by 16
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Pythoncited by 11
- 2026A lower bound for stepsize-based acceleration of gradient descentcited by 4
- 2023Differentiable Arbitrating in Zero-sum Markov Gamescited by 1
- 2026A lower bound for stepsize-based acceleration of gradient descent11 Aug 2026
- 2024Provable Complexity Improvement of AdaGrad over SGD: Upper and Lower Bounds in Stochastic Non-Convex Optimization7 Jun 2024
- 2023Differentiable Arbitrating in Zero-sum Markov Games20 Feb 2023
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python11 Jan 2022