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Structured Robust Submodular Maximization: Offline and Online Algorithms [article]

Alfredo Torrico, Mohit Singh, Sebastian Pokutta, Nika Haghtalab, Joseph Naor, Nima Anari
2020 arXiv   pre-print
In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees.  ...  For the offline setting, we give a general (nearly) optimal bi-criteria approximation algorithm that relies on new extensions of classical algorithms for submodular maximization.  ...  We also thank Shabbir Ahmed for the discussions about the distributionally robust problem (16).  ... 
arXiv:1710.04740v3 fatcat:3kaoks2l5vd5vp4mnar4mq4rqa

Distributionally Robust Submodular Maximization [article]

Matthew Staib, Bryan Wilder, Stefanie Jegelka
2018 arXiv   pre-print
Algorithmically, we accomplish this by showing how to carry out distributionally robust optimization (DRO) for submodular functions, providing efficient algorithms backed by theoretical guarantees which  ...  In this paper, we achieve better performance on the actual underlying function f by directly optimizing a combination of bias and variance.  ...  , 32 CFR 168a, and NSF Graduate Research Fellowship Program (GRFP).  ... 
arXiv:1802.05249v2 fatcat:2dvla6pbvfhizk7lgfet4vvnuy

Robust and Adaptive Sequential Submodular Optimization [article]

Vasileios Tzoumas, Ali Jadbabaie, George J. Pappas
2020 arXiv   pre-print
However, in this paper we propose Robust and Adaptive Maximization (RAM), the first scalable algorithm. RAM runs in an online fashion, adapting in every step to the history of failures.  ...  We call the novel problem Robust Sequential submodular Maximization (RSM). Generally, the problem is computationally hard and no scalable algorithm is known for its solution.  ...  ACKNOWLEDGEMENTS We thank Rakesh Vohra of the University of Pennsylvania, and Luca Carlone of the Massachusetts Institute of Technology for inspiring comments and discussions.  ... 
arXiv:1909.11783v3 fatcat:27gfhyqk4jh43n466osj2xqjxu

Online Continuous Submodular Maximization [article]

Lin Chen, Hamed Hassani, Amin Karbasi
2018 arXiv   pre-print
Finally, we demonstrate the efficiency of our algorithms on a few problem instances, including non-convex/non-concave quadratic programs, multilinear extensions of submodular set functions, and D-optimal  ...  We also generalize our results to γ-weakly submodular functions and prove the same sublinear regret bounds.  ...  In this subsection, we show how we can use Online Gradient Ascent to design an algorithm with sublinear regret and robust to stochastic gradients when the functions f t are monotone and continuous DR-submodular  ... 
arXiv:1802.06052v1 fatcat:2szcbuixangxzhzxhm24wfskbq

Online Risk-Averse Submodular Maximization [article]

Tasuku Soma, Yuichi Yoshida
2021 arXiv   pre-print
We present a polynomial-time online algorithm for maximizing the conditional value at risk (CVaR) of a monotone stochastic submodular function.  ...  Compared with previous offline algorithms, which require Ω(T) space, our online algorithm only requires O(√(T)) space.  ...  In robust submodular maximization, we maximize the minimum of N submodular functions, i.e., min N i=1 f i (X).  ... 
arXiv:2105.09838v1 fatcat:pew3u7tzmzg7to45p5ki43h75m

Scalable and distributed submodular maximization with matroid constraints

Andrew Clark, Basel Alomair, Linda Bushnell, Radha Poovendran
2015 2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)  
We then develop an algorithm for maximizing time-varying submodular functions under partition matroid constraints, which arises in sensor placement and data caching.  ...  Submodular maximization enables efficient approximation of machine learning, networking, and language processing problems.  ...  Section V introduces our offline distributed algorithm for submodular maximization with an arbitrary matroid constraint.  ... 
doi:10.1109/wiopt.2015.7151103 dblp:conf/wiopt/ClarkABP15 fatcat:of4s2m4oknfi5aumuq2ahs4cem

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).  ...  A stream of T submodular functions over a common finite ground set U arrives online, and at each time-step the decision maker must choose at most k elements of U before observing the function.  ...  We provide a differentially private online learning algorithm for DR-submodular maximization that achieves low expected regret.  ... 
arXiv:2010.12816v1 fatcat:jbciay4wxregjf6csjkpg7ouiu

Stream Clipper: Scalable Submodular Maximization on Stream [article]

Tianyi Zhou, Jeff Bilmes
2018 arXiv   pre-print
We propose a streaming submodular maximization algorithm "stream clipper" that performs as well as the offline greedy algorithm on document/video summarization in practice.  ...  In news and video summarization experiments, the algorithm consistently outperforms other streaming methods, and, while using significantly less computation and memory, performs similarly to the offline  ...  CONCLUSION In this paper, we introduce stream clipper, a fast and memoryefficient streaming submodular maximization algorithm that can achieve similar performance as commonly used greedy algorithm.  ... 
arXiv:1606.00389v3 fatcat:ikbjc3w7xvf2pn34arwagu4jlm

Multi-Round Influence Maximization [article]

Lichao Sun and Weiran Huang and Philip S. Yu and Wei Chen
2019 arXiv   pre-print
For the non-adaptive setting, we design two algorithms that exhibit an interesting tradeoff between efficiency and effectiveness: a cross-round greedy algorithm that selects seeds at a global level and  ...  In this paper, we study the Multi-Round Influence Maximization (MRIM) problem, where influence propagates in multiple rounds independently from possibly different seed sets, and the goal is to select seeds  ...  They focus on the online learning aspect of learning edge probabilities, while we study the offline non-adaptive and adaptive maximization problem when the edge probabilities are known.  ... 
arXiv:1802.04189v3 fatcat:dxqze26jvrh5zhzbzqyupxukfm

DUM: Diversity-Weighted Utility Maximization for Recommendations [article]

Azin Ashkan, Branislav Kveton, Shlomo Berkovsky, Zheng Wen
2014 arXiv   pre-print
We evaluate the proposed method in two online user studies as well as in an offline analysis incorporating a number of evaluation metrics.  ...  In this work we propose a novel method for maximizing the utility of the recommended items subject to the diversity of user's tastes, and show that an optimal solution to this problem can be found greedily  ...  In this paper, we elaborate on the intuitions and details behind the proposed greedy algorithm, and provide extensive online and offline evaluations on its performance in practice.  ... 
arXiv:1411.3650v1 fatcat:wgbp7fnbkvgqfcpwsyzpaixjim

Predicting Contextual Sequences via Submodular Function Maximization [article]

Debadeepta Dey, Tian Yu Liu, Martial Hebert, J. Andrew Bagnell
2012 arXiv   pre-print
Our approach leverages recent work on submodular function maximization to provide a formal regret reduction from submodular sequence optimization to simple cost-sensitive prediction.  ...  We apply our contextual sequence prediction algorithm to optimize control libraries and demonstrate results on two robotics problems: manipulator trajectory prediction and mobile robot path planning.  ...  Such loss functions are monotone, submodular -i.e., one with diminishing returns. 1 We define these functions in section II and review the online submodular function maximization approach of Streeter  ... 
arXiv:1202.2112v1 fatcat:3dyvxeysnrhwfleulat7qyf7fu

Online Influence Maximization under Linear Threshold Model [article]

Shuai Li, Fang Kong, Kejie Tang, Qizhi Li, Wei Chen
2021 arXiv   pre-print
In the end, we also provide an algorithm OIM-ETC with regret bound O(poly(m) T^2/3), which is model-independent, simple and has less requirement on online feedback and offline computation.  ...  Online influence maximization (OIM) is a popular problem in social networks to learn influence propagation model parameters and maximize the influence spread at the same time.  ...  [18] Kyomin Jung, Wooram Heo, and Wei Chen. IRIE: Scalable and robust influence maximization in social networks.  ... 
arXiv:2011.06378v3 fatcat:w2fjslj4xjgtpczutznx7zabmu

Influence Maximization on Social Graphs: A Survey

Yuchen Li, Ju Fan, Yanhao Wang, Kian-Lee Tan
2018 IEEE Transactions on Knowledge and Data Engineering  
Influence Maximization (IM), which selects a set of k users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem  ...  , and time.  ...  ., music and book) offline. Then, given an online query, it selects RR sets from the query topics and merges the RR sets to compute the result.  ... 
doi:10.1109/tkde.2018.2807843 fatcat:f6vnhknlevckbkqwkkqotgalc4

Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection Summarization [article]

Adish Singla, Sebastian Tschiatschek, Andreas Krause
2015 arXiv   pre-print
We provide a generic algorithm -- -- for maximizing an unknown submodular function under cardinality constraints.  ...  For summarization tasks with the goal of maximizing coverage and diversity, submodular set functions are a natural choice.  ...  This research is supported in part by SNSF grant 200021 137971 and the Nano-Tera.ch program as part of the Opensense II project.  ... 
arXiv:1511.07211v2 fatcat:wyggs6sihng4lcvsc4xhelnupm

Fractionally Subadditive Maximization under an Incremental Knapsack Constraint [article]

Yann Disser and Max Klimm and David Weckbecker
2021 arXiv   pre-print
We present an algorithm that finds an incremental solution of competitive ratio at most max{3.293√(M),2M}, under the assumption that the values of singleton sets are in the range [1,M], and we give a lower  ...  In addition, we establish that our framework captures potential-based flows between two vertices, and we give a tight bound of 2 for the incremental maximization of classical flows with unit capacities  ...  [2] and Orlin et al. [25] considered general robust submodular maximization problems. The class of fractionally additive valuations was introduced by Nisan [24] and Lehman et al.  ... 
arXiv:2106.14454v1 fatcat:btdkoz3gjnef7djiwlomqy4dqi
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