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Decentralized Submodular Maximization: Bridging Discrete and Continuous Settings
Aryan Mokhtari · Hamed Hassani · Amin Karbasi

Thu Jul 12 07:00 AM -- 07:20 AM (PDT) @ K11
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that possess a diminishing returns property. More specifically, given an arbitrary connected network and a global continuous submodular function, formed by a sum of local functions, we develop Decentralized Continuous Greedy (DCG), a message passing algorithm that converges to the tight $(1-1/e)$ approximation factor of the optimum global solution using only local computation and communication. We also provide strong convergence bounds as a function of network size and spectral characteristics of the underlying topology. Interestingly, DCG readily provides a simple recipe for decentralized discrete submodular maximization through the means of continuous relaxations. Formally, we demonstrate that by lifting the local discrete functions to continuous domains and using DCG as an interface we can develop a consensus algorithm that also achieves the tight $(1-1/e)$ approximation guarantee of the global discrete solution once a proper rounding scheme is applied.

Author Information

Aryan Mokhtari (MIT)
Hamed Hassani (University of Pennsylvania)
Hamed Hassani

I am an assistant professor in the Department of Electrical and Systems Engineering (as of July 2017). I hold a secondary appointment in the Department of Computer and Information Systems. I am also a faculty affiliate of the Warren Center for Network and Data Sciences. Before joining Penn, I was a research fellow at the Simons Institute, UC Berkeley (program: Foundations of Machine Learning). Prior to that, I was a post-doctoral scholar and lecturer in the Institute for Machine Learning at ETH Zürich. I received my Ph.D. degree in Computer and Communication Sciences from EPFL.

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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