Convergence of adaptive algorithms for weakly convex constrained optimization

Ahmet Alacaoglu; Yura Malitsky; Volkan Cevher

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arXiv · 2006.06650

Convergence of adaptive algorithms for weakly convex constrained optimization

Ahmet Alacaoglu·Yura Malitsky·Volkan Cevher

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Abstract

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the $\mathcal{\tilde O}(t^{-1/4})$ rate of convergence for the norm of the gradient of Moreau envelope, which is the standard stationarity measure for this class of problems. It matches the known rates that adaptive algorithms enjoy for the specific case of unconstrained smooth stochastic optimization. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly unbounded optimization domains. Finally, we illustrate the applications and extensions of our results to specific problems and algorithms.

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Ahmet Alacaoglu, Yura Malitsky, Volkan Cevher. 2020-06-11. Convergence of adaptive algorithms for weakly convex constrained optimization. https://arxiv.org/abs/2006.06650

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