Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimization

• URL: http://arxiv.org/abs/2111.15645v1
• Date: Tue, 30 Nov 2021 18:28:17 GMT
• Title: Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimization
• Authors: X.Y. Han and Adrian S. Lewis
• Abstract summary: We propose a generalization of the gradient descent iteration for local optimization. We prove linear convergence when the objective is itself max-of-smooth, and experiments suggest a more general phenomenon.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging: even when the objective is smooth at every iterate, the corresponding local models are unstable, and traditional remedies need unpredictably many cutting planes. We instead propose a multipoint generalization of the gradient descent iteration for local optimization. While designed with general objectives in mind, we are motivated by a "max-of-smooth" model that captures subdifferential dimension at optimality. We prove linear convergence when the objective is itself max-of-smooth, and experiments suggest a more general phenomenon.

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