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This paper revisits the Polyak step size schedule for convex optimization problems, proving that a simple variant of it simultaneously attains near optimal convergence rates for the gradient descent algorithm, for all ranges of strong convexity, smoothness, and Lipschitz parameters, without a-priory knowledge of these parameters.
A method of solving a convex programming problem with convergence rate o ( 1 / k 2 ) o(1/k^{2})
Yurii Nesterov · 1983
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A stochastic approximation method
Herbert Robbins and Sutton Monro · 1985
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Introduction to optimization
Boris T. Polyak · 1987
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Mark Schmidt, Nicolas Le Roux, and Francis Bach · 2017
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