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• W2788590923 abstract "Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient computation at each step, both of which can be prohibitively expensive for large-scale applications. At the same time, there is a growing trend of non-convex optimization in machine learning community and a need for online methods. Continuous DR-submodular functions, which exhibit a natural diminishing returns condition, have recently been proposed as a broad class of non-convex functions which may be efficiently optimized. Although online methods have been introduced, they suffer from similar problems. In this work, we propose Meta-Frank-Wolfe, the first online projection-free algorithm that uses stochastic gradient estimates. The algorithm relies on a careful sampling of gradients in each round and achieves the optimal $O( sqrt{T})$ adversarial regret bounds for convex and continuous submodular optimization. We also propose One-Shot Frank-Wolfe, a simpler algorithm which requires only a single stochastic gradient estimate in each round and achieves an $O(T^{2/3})$ stochastic regret bound for convex and continuous submodular optimization. We apply our methods to develop a novel lifting framework for the online discrete submodular maximization and also see that they outperform current state-of-the-art techniques on various experiments." @default.
• W2788590923 created "2018-03-06" @default.
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• W2788590923 date "2018-02-22" @default.
• W2788590923 modified "2023-09-23" @default.
• W2788590923 title "Projection-Free Online Optimization with Stochastic Gradient: From Convexity to Submodularity" @default.
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• W2788590923 hasPublicationYear "2018" @default.
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