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arXiv · 1906.03056

Polyak Steps for Adaptive Fast Gradient Method

Mathieu Barré·Alexandre d'Aspremont
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Abstract

Accelerated algorithms for minimizing smooth strongly convex functions usually require knowledge of the strong convexity parameter $μ$. In the case of an unknown $μ$, current adaptive techniques are based on restart schemes. When the optimal value $f^*$ is known, these strategies recover the accelerated linear convergence bound without additional grid search. In this paper we propose a new approach that has the same bound without any restart, using an online estimation of strong convexity parameter. We show the robustness of the Fast Gradient Method when using a sequence of upper bounds on $μ$. We also present a good candidate for this estimate sequence and detail consistent empirical results.

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Mathieu Barré, Alexandre d'Aspremont. 2019-06-07. Polyak Steps for Adaptive Fast Gradient Method. https://arxiv.org/abs/1906.03056

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