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Recently, we developed the Survey Descent iteration that is a multipoint generalization of gradient decent for nonsmooth optimization. Specifically, for smooth, strongly convex objectives, classic theory guarantee the linear* convergence of gradient descent. An analogous guarantee for nonsmooth objectives is challenging: While traditional remedies such as subgradient and bundle methods are empirically successful, guarantees of their convergence have generally remained sublinear. We prove that Survey Descent achieves linear convergence when the nonsmooth objective possesses a “max-of-smooth” structure, while our experiments suggest a more general phenomenon.
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Archives, Access and Artificial IntelligenceDigital Humanities Researchpp.29-60, (2022)
International Conference on Learning Representations (ICLR) (2022)
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#Papers: 7
#Citation: 498
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Sociability: 3
Diversity: 1
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