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Adaptive Proximal Gradient Method for Convex Optimization
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In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].
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Cited by 2 Pith papers
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Adaptive Stepsize Selection in Decentralized Convex Optimization
A fully local adaptive step-size scheme achieves linear (strongly convex) and sublinear (convex) convergence rates, matching tuned nonadaptive decentralized methods.
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A Parameter-free Decentralized Algorithm for Composite Convex Optimization
A local backtracking rule for stepsizes in decentralized composite convex optimization is shown to preserve robust convergence without global network information.
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