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Oral
Projection-Free Online Optimization with Stochastic Gradient: From Convexity to Submodularity
Lin Chen · Christopher Harshaw · Hamed Hassani · Amin Karbasi

Thu Jul 12 07:00 AM -- 07:20 AM (PDT) @ A5
in Online Learning 2 »
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.
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Author Information

Lin Chen (Yale University)
Christopher Harshaw (Yale University)
Hamed Hassani (University of Pennsylvania)
Amin Karbasi (Yale)
Amin Karbasi

Amin Karbasi is currently an assistant professor of Electrical Engineering, Computer Science, and Statistics at Yale University. He has been the recipient of the National Science Foundation (NSF) Career Award 2019, Office of Naval Research (ONR) Young Investigator Award 2019, Air Force Office of Scientific Research (AFOSR) Young Investigator Award 2018, DARPA Young Faculty Award 2016, National Academy of Engineering Grainger Award 2017, Amazon Research Award 2018, Google Faculty Research Award 2016, Microsoft Azure Research Award 2016, Simons Research Fellowship 2017, and ETH Research Fellowship 2013. His work has also been recognized with a number of paper awards, including Medical Image Computing and Computer Assisted Interventions Conference (MICCAI) 2017, International Conference on Artificial Intelligence and Statistics (AISTAT) 2015, IEEE ComSoc Data Storage 2013, International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2011, ACM SIGMETRICS 2010, and IEEE International Symposium on Information Theory (ISIT) 2010 (runner-up). His Ph.D. thesis received the Patrick Denantes Memorial Prize 2013 from the School of Computer and Communication Sciences at EPFL, Switzerland.

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