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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

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

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

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

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

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

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.  ...  Moreover, as conducting online sampling cannot meet the real-time processing requirement, they further devise disk-based index structures to push the sampling procedure from online to offline.  ... 
doi:10.1109/tkde.2018.2807843 fatcat:f6vnhknlevckbkqwkkqotgalc4

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

Efficient influence maximization in social networks

Wei Chen, Yajun Wang, Siyu Yang
2009 Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '09  
We evaluate our algorithms by experiments on two large academic collaboration graphs obtained from the online archival database arXiv.org.  ...  One is to improve the original greedy algorithm of [5] and its improvement [7] to further reduce its running time, and the second is to propose new degree discount heuristics that improves influence spread  ...  disconnected offline social networks together.  ... 
doi:10.1145/1557019.1557047 dblp:conf/kdd/ChenWY09 fatcat:ejvr3f4zr5drjcwxqbs42l3dr4

How to Maximize the Spread of Social Influence: A Survey [article]

Giuseppe De Nittis, Nicola Gatti
2018 arXiv   pre-print
This survey presents the main results achieved for the influence maximization problem in social networks.  ...  Finally, we present one of the main application that has been developed and deployed exploiting tools and techniques previously discussed.  ...  It is shown that with sufficiently many rounds T , the parameters learned by the online MLE algorithm are nearly as good as those learned by the offline algorithm.  ... 
arXiv:1806.07757v1 fatcat:qztddep5z5bljocqoblr6jfqsy

Scalable influence maximization for independent cascade model in large-scale social networks

Chi Wang, Wei Chen, Yajun Wang
2012 Data mining and knowledge discovery  
Online bounds from sequence submodularity We have proved the approximation guarantee of (1 − 1/e). This approximation bound is offline, which can be stated before running the actual algorithm.  ...  , online bounds of the optimal influence, and qualitative study of the effectiveness of influence maximization.  ...  Beyond influence maximization, one interesting direction that requires further research is the data mining of social influence from real online social network datasets.  ... 
doi:10.1007/s10618-012-0262-1 fatcat:mbwq5pnxfrdmlou65icnjfcd5u

Overcommitment in Cloud Services -- Bin packing with Chance Constraints [article]

Maxime C. Cohen, Philipp W. Keller, Vahab Mirrokni, Morteza Zadimoghaddam
2017 arXiv   pre-print
We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal.  ...  We then propose an alternative formulation that transforms each chance constraint into a submodular function.  ...  Acknowledgments We would like to thank the Google Cloud Analytics team for helpful discussions and feedback.  ... 
arXiv:1705.09335v1 fatcat:x247fptbmvabjirxqzyf4yhlxu

Non-monotone DR-submodular Maximization over General Convex Sets

Christoph Dürr, Nguyen Kim Thang, Abhinav Srivastav, Léo Tible
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
In this paper, we show that for maximizing non-monotone DR-submodular functions over a general convex set (such as up-closed convex sets, conic convex set, etc) the Frank-Wolfe algorithm achieves an approximation  ...  In addition, they capture a subclass of non-convex optimization that provides both practical and theoretical guarantees.  ...  Figure 2 (center) present a qualitative comparison between the offline LRS-OPT schedule and the online ones, for indicative values of µ.  ... 
doi:10.24963/ijcai.2020/293 dblp:conf/ijcai/DoniniFMPF20 fatcat:our6aysxnra7xlgaptsyxocl3m
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