Optimal Algorithms for Continuous Non-monotone Submodular Maximization
Rad Niazadeh
Stanford University
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2018-11-28 16:00:00
2018-11-28 17:00:00
America/New_York
Optimal Algorithms for Continuous Non-monotone Submodular Maximization
Abstract:In this talk, I will explain our recent result on designing optimal approximation algorithms for maximizing continuous non-monotone submodular functions over the hypercube. This family of optimization problems has several applications in machine learning, finance and social network analysis. Our main result is the first 1/2-approximation algorithm for this problem; this approximation factor is the best possible for algorithms that only query the objective function at polynomially many points. For the special case of DR-submodular maximization, i.e., when the submodular functions is also coordinate wise concave along all coordinates, we provide a different 1/2-approximation algorithm that runs in quasilinear time in dimension. Both of these results improve upon prior work [Bian et al, 2017, Buchbinder et al, 2012].Our first algorithm uses novel ideas such as reducing the guaranteed approximation problem to analyzing a stylized zero-sum game for each coordinate, and incorporates the geometry of this zero-sum game to find a value for this coordinate. Our second algorithm exploits coordinate-wise concavity to identify a monotone equilibrium condition sufficient for getting the required approximation guarantee, and hunts for the equilibrium point using binary search.The talk is based on joint work with Tim Roughgarden and Joshua Wang, accepted for an oral presentation at NIPS'18.Bio:Rad Niazadeh is a Motwani postdoctoral fellow at Stanford University, Department of Computer Science, where he is hosted by Tim Roughgarden, Amin Saberi and Moses Charikar. Prior to Stanford, he obtained his Ph.D. in Computer Science from Cornell University under Bobby Kleinberg. During his graduate studies, he was a research intern at Microsoft Research (Redmond), Microsoft Research (New England) and Yahoo! Research. He also has been awarded the Google PhD fellowship (in market algorithms), INFORMS Revenue Management and Pricing Dissertation Honorable Mention(runner up), Stanford Motwani fellowship and Cornell Irwin Jacobs fellowship. His research interests are broadly at the intersection of algorithms, game theory and optimization, with a focus on applications in market design, machine learning, and operations research.
32-D463 (Stata Center, Star Conference Room)