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math.OC2026
A short proof of near-linear convergence of adaptive gradient descent under fourth-order growth and convexity
Damek Davis, Dmitriy Drusvyatskiy
Davis, Drusvyatskiy, and Jiang showed that gradient descent with an adaptive stepsize converges locally at a nearly-linear rate for smooth functions that grow at least quartically…
math.OC2025
Gradient descent with adaptive stepsize converges (nearly) linearly under fourth-order growth
Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In th…