An Accelerated DFO Algorithm for Finite-sum Convex Functions

• URL: http://arxiv.org/abs/2007.03311v2
• Date: Mon, 3 Aug 2020 03:55:59 GMT
• Title: An Accelerated DFO Algorithm for Finite-sum Convex Functions
• Authors: Yuwen Chen (1), Antonio Orvieto (1), Aurelien Lucchi (1) ((1) ETH Zurich)
• Abstract summary: Derivative-free optimizationDFO) has recently gained a lot momentum in machine learning. In this paper, we exploit the finite-sum objective functions in order to design accessible DFO algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given to the concept of acceleration in the DFO literature, existing stochastic algorithms for objective functions with a finite-sum structure have not been shown theoretically to achieve an accelerated rate of convergence. Algorithms that use acceleration in such a setting are prone to instabilities, making it difficult to reach convergence. In this work, we exploit the finite-sum structure of the objective in order to design a variance-reduced DFO algorithm that provably yields acceleration. We prove rates of convergence for both smooth convex and strongly-convex finite-sum objective functions. Finally, we validate our theoretical results empirically on several tasks and datasets.

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