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An Optimal Learning Algorithm for Online Unconstrained Submodular Maximization

Tim Roughgarden, Joshua R. Wang
2018 Annual Conference Computational Learning Theory  
We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning.  ...  In the online unconstrained submodular maximization (online USM) problem, there is a universe [n] = {1, 2, . . . , n} and a sequence of T nonnegative (not necessarily monotone) submodular functions arrive  ...  Introduction The problem we study, online unconstrained submodular maximization (online USM), lies in the intersection of two fundamental fields: submodular optimization and online learning.  ... 
dblp:conf/colt/RoughgardenW18 fatcat:sionamfounb4rif7z7d6jh524i

Distributed online submodular maximization in resource-constrained networks

Andrew Clark, Basel Alomair, Linda Bushnell, Radha Poovendran
2014 2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)  
For the unconstrained submodular maximization problem, our algorithm achieves an expected optimality gap of 1/3.  ...  We present algorithms for unconstrained distributed submodular maximization, as well as monotone submodular maximization subject to cardinality constraints.  ...  Recently, algorithms have been proposed for submodular maximization in an online setting [14] , [15] .  ... 
doi:10.1109/wiopt.2014.6850325 dblp:conf/wiopt/ClarkABP14 fatcat:jqhk6bnvsreqxe5zyvwjoo57iy

No-regret algorithms for online k-submodular maximization [article]

Tasuku Soma
2018 arXiv   pre-print
For online (nonmonotone) k-submodular maximization, our algorithm achieves a tight approximate factor in an approximate regret.  ...  We present a polynomial time algorithm for online maximization of k-submodular maximization.  ...  Wang for sharing a draft of [19] . This work was supported by ACT-I, JST.  ... 
arXiv:1807.04965v1 fatcat:pzdkowapgngzvfvjasuk6en36m

Improved Algorithms for Online Submodular Maximization via First-order Regret Bounds

Nicholas J. A. Harvey, Christopher Liaw, Tasuku Soma
2020 Neural Information Processing Systems  
In this work, we give a general approach for improving regret bounds in online submodular maximization by exploiting "first-order" regret bounds for online linear optimization. • For monotone submodular  ...  We consider the problem of nonnegative submodular maximization in the online setting. At time step t, an algorithm selects a set S t ∈ C ⊆ 2 V where C is a feasible family of sets.  ...  Acknowledgments and Disclosure of Funding The authors thank the anonymous referees for their useful comments. N.H. was supported by Canada Research Chairs Program and an NSERC Discovery Grant.  ... 
dblp:conf/nips/HarveyLS20 fatcat:hsgaamcpyraztntvui4q2jwyxa

Bounds on Double-Sided Myopic Algorithms for Unconstrained Non-monotone Submodular Maximization [article]

Norman Huang, Allan Borodin
2014 arXiv   pre-print
Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems.  ...  Recently, Buchbinder et al. presented a surprisingly simple linear time randomized greedy-like online algorithm that achieves a constant approximation ratio of 1/2, matching optimally the hardness result  ...  Acknowledgments The authors would like to thank Yuval Filmus for the idea of employing linear programming, and Matthias Poloczek and Charles Rackoff for their comments and suggestions.  ... 
arXiv:1312.2173v3 fatcat:7nizpjswubafnktz3cdq25sr4q

Differentially Private Online Submodular Maximization [article]

Sebastian Perez-Salazar, Rachel Cummings
2020 arXiv   pre-print
In this work we consider the problem of online submodular maximization under a cardinality constraint with differential privacy (DP).  ...  This algorithm contains k ordered experts that learn the best marginal increments for each item over the whole time horizon while maintaining privacy of the functions.  ...  We provide a differentially private online learning algorithm for DR-submodular maximization that achieves low expected regret.  ... 
arXiv:2010.12816v1 fatcat:jbciay4wxregjf6csjkpg7ouiu

Bounds on Double-Sided Myopic Algorithms for Unconstrained Non-monotoneSubmodular Maximization [chapter]

Norman Huang, Allan Borodin
2014 Lecture Notes in Computer Science  
Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems.  ...  Recently, Buchbinder et al. [8] presented a surprisingly simple linear time randomized greedy-like online algorithm that achieves a constant approximation ratio of 1 2 , matching optimally the hardness  ...  Acknowledgments The authors would like to thank Yuval Filmus for the idea of employing linear programming, and Matthias Poloczek and Charles Rackoff for their comments and suggestions.  ... 
doi:10.1007/978-3-319-13075-0_42 fatcat:4sfklwwbtjac5aghmq4kq2ucta

Submodular Order Functions and Assortment Optimization [article]

Rajan Udwani
2021 arXiv   pre-print
As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model.  ...  While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order.  ...  Let A represent an algorithm for constrained submodular order maximization (out of Algorithms 1, 3, 5 and 7).  ... 
arXiv:2107.02743v3 fatcat:aku6tt3khrg37jyvbalpewul5u

Maximizing Profit with Convex Costs in the Random-order Model

Anupam Gupta, Ruta Mehta, Marco Molinaro, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
Here α is the competitive ratio of the best algorithm for the submodular secretary problem. These extend and improve previous results known for this problem.  ...  If the set of accepted demands must also be independent in a given matroid, we give an O(d 3 α)-competitive algorithm for the supermodular case, and an improved O(d 2 α) if the convex cost function is  ...  They give an O(d)-competitive algorithm for the unconstrained case, and an O(d 5 α)-competitive algorithm for the problem with a downward closed constraint set F , where α is the competitive ratio for  ... 
doi:10.4230/lipics.icalp.2018.71 dblp:conf/icalp/GuptaMM18 fatcat:y4tzqvo6cvap7jjmskmzwjwoza

Budgeted Nonparametric Learning from Data Streams

Ryan Gomes, Andreas Krause
2010 International Conference on Machine Learning  
We develop an efficient algorithm, Stream-Greedy, which is guaranteed to obtain a constant fraction of the value achieved by the optimal solution to this NP-hard optimization problem.  ...  We show that these problems require maximization of a submodular function that captures the informativeness of a set of exemplars, over a data stream.  ...  Acknowledgements We thank Pietro Perona, Piotr Dollar, Kristin Branson, and the anonymous reviewers for their helpful comments.  ... 
dblp:conf/icml/GomesK10 fatcat:f5dxjrstkvhvzj67n37b6n4fzy

Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly [article]

Baharan Mirzasoleiman, Stefanie Jegelka, Andreas Krause
2017 arXiv   pre-print
We develop the first efficient single pass streaming algorithm, Streaming Local Search, that for any streaming monotone submodular maximization algorithm with approximation guarantee α under a collection  ...  Such problems can often be reduced to maximizing a submodular set function subject to various constraints.  ...  Streaming algorithms for submodular maximization have gained increasing attention for producing online summaries. For monotone submodular maximization, Badanidiyuru et al.  ... 
arXiv:1706.03583v3 fatcat:j3d5wz7m6vdkfjvdzeyahgv3u4

An Optimal Algorithm for Online Unconstrained Submodular Maximization [article]

Tim Roughgarden, Joshua R. Wang
2018 arXiv   pre-print
In the online unconstrained submodular maximization (online USM) problem, there is a universe [n]={1,2,...  ...  We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning.  ...  Perhaps the most basic problems in submodular optimization are to minimize or maximize a submodular function (without constraints).  ... 
arXiv:1806.03349v1 fatcat:fqjmoa7ifjdkrhanqzx5n3jigu

Online Submodular Maximization with Preemption [chapter]

Niv Buchbinder, Moran Feldman, Roy Schwartz
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
There exists a 1/e-competitive algorithm for the unconstrained-model, which can be implemented in polynomial time at the cost of an ε loss in the competitive ratio (for an arbitrary small constant ε >  ...  The dicut-model can be viewed as an online model of the well-known Max-DiCut problem (see Section 1.2 for a discussion of another online model of Max-DiCut).  ...  Our first objective is to show that Algorithm 5 is an online algorithm according to the unconstrained-model. Lemma B.1.  ... 
doi:10.1137/1.9781611973730.80 dblp:conf/soda/BuchbinderFS15a fatcat:vyiffkegznbfzprl62k2y3rlgm

Online Submodular Minimization for Combinatorial Structures

Stefanie Jegelka, Jeff A. Bilmes
2011 International Conference on Machine Learning  
Going beyond linearity, we address online approximation algorithms for structured concepts that allow the cost to be submodular, i.e., nonseparable.  ...  In particular, we show regret bounds for three Hannan-consistent strategies that capture different settings. Our results also tighten a regret bound for unconstrained online submodular minimization.  ...  For approximate submodular maximization, an online greedy method exists (Streeter & Golovin, 2008 ) that satisfies given constraints in expectation only.  ... 
dblp:conf/icml/JegelkaB11 fatcat:gjjnliur7fe23j6bs7tjr5vup4

Online Non-Monotone DR-submodular Maximization [article]

Nguyen Kim Thang, Abhinav Srivastav
2020 arXiv   pre-print
Next, we give an online algorithm that achieves an approximation guarantee (depending on the search space) for the problem of maximizing non-monotone continuous DR-submodular functions over a general convex  ...  First, we present an online algorithm that achieves a 1/e-approximation ratio with the regret of O(T^2/3) for maximizing DR-submodular functions over any down-closed convex set.  ...  Online DR-Submodular Maximization over Down-Closed Convex Sets Online Vee Learning In this section, we give an algorithm for an online problem that will be the main building block in the design of algorithms  ... 
arXiv:1909.11426v2 fatcat:5y44n77njfcnfnmnymw7udx73a
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