


@article{yue2011linear,
  title={Linear submodular bandits and their application to diversified retrieval},
  author={Yue, Yisong and Guestrin, Carlos},
  journal={Advances in Neural Information Processing Systems},
  volume={24},
  year={2011}
}





@inproceedings{lin2015stochastic,
  title={Stochastic Online Greedy Learning with Semi-bandit Feedbacks.},
  author={Lin, Tian and Li, Jian and Chen, Wei},
  booktitle={NIPS},
  pages={352--360},
  year={2015}
}


@inproceedings{takemori2020submodular,
  title={Submodular Bandit Problem Under Multiple Constraints},
  author={Takemori, Sho and Sato, Masahiro and Sonoda, Takashi and Singh, Janmajay and Ohkuma, Tomoko},
  booktitle={Conference on Uncertainty in Artificial Intelligence},
  pages={191--200},
  year={2020},
  organization={PMLR}
}



@inproceedings{yu2016linear,
  title={Linear submodular bandits with a knapsack constraint},
  author={Yu, Baosheng and Fang, Meng and Tao, Dacheng},
  booktitle={Thirtieth AAAI Conference on Artificial Intelligence},
  year={2016}
}





@article{zhu2021projection,
  title={Projection-free Decentralized Online Learning for Submodular Maximization over Time-Varying Networks},
  author={Zhu, Junlong and Wu, Qingtao and Zhang, Mingchuan and Zheng, Ruijuan and Li, Keqin},
  journal={Journal of Machine Learning Research},
  volume={22},
  number={51},
  pages={1--42},
  year={2021}
}


@inproceedings{chen2018projection,
  title={Projection-free online optimization with stochastic gradient: From convexity to submodularity},
  author={Chen, Lin and Harshaw, Christopher and Hassani, Hamed and Karbasi, Amin},
  booktitle={International Conference on Machine Learning},
  pages={814--823},
  year={2018},
  organization={PMLR}
}



@inproceedings{chen2016combinatorial,
  title={Combinatorial multi-armed bandit with general reward functions},
  author={Chen, Wei and Hu, Wei and Li, Fu and Li, Jian and Liu, Yu and Lu, Pinyan},
  booktitle={Proceedings of the 30th International Conference on Neural Information Processing Systems},
  pages={1659--1667},
  year={2016}
}

@InProceedings{mokhtari2018conditional,
  title = 	 {Conditional Gradient Method for Stochastic Submodular Maximization: Closing the Gap},
  author = 	 {Aryan Mokhtari and Hamed Hassani and Amin Karbasi},
  booktitle = 	 {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1886--1895},
  year = 	 {2018},
  _editor = 	 {Amos Storkey and Fernando Perez-Cruz},
  volume = 	 {84},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--11 Apr},
  publisher =    {PMLR}
}

@inproceedings{merlis2019batch,
  title={Batch-size independent regret bounds for the combinatorial multi-armed bandit problem},
  author={Merlis, Nadav and Mannor, Shie},
  booktitle={Conference on Learning Theory},
  pages={2465--2489},
  year={2019},
  organization={PMLR}
}

@inproceedings{jourdan2021efficient,
  title={Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback},
  author={Jourdan, Marc and Mutn{\`y}, Mojm{\'\i}r and Kirschner, Johannes and Krause, Andreas},
  booktitle={Algorithmic Learning Theory},
  pages={805--849},
  year={2021},
  organization={PMLR}
}

@inproceedings{du2021combinatorial,
  title={Combinatorial pure exploration with full-bandit or partial linear feedback},
  author={Du, Yihan and Kuroki, Yuko and Chen, Wei},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  pages={7262--7270},
  year={2021}
}



@inproceedings{dani2008stochastic,
  title={Stochastic linear optimization under bandit feedback},
  author={Dani, Varsha and Hayes, Thomas P and Kakade, Sham M},
  booktitle={21st Annual Conference on Learning Theory},
  year={2008},
  pages={355-366}
}

@article{golovin2014online,
  title={Online submodular maximization under a matroid constraint with application to learning assignments},
  author={Golovin, Daniel and Krause, Andreas and Streeter, Matthew},
  journal={arXiv preprint arXiv:1407.1082},
  year={2014}
}


@inproceedings{zimmert2019optimal,
  title={An optimal algorithm for stochastic and adversarial bandits},
  author={Zimmert, Julian and Seldin, Yevgeny},
  booktitle={The 22nd International Conference on Artificial Intelligence and Statistics},
  pages={467--475},
  year={2019},
  organization={PMLR}
}

@inproceedings{auer2016algorithm,
  title={An algorithm with nearly optimal pseudo-regret for both stochastic and adversarial bandits},
  author={Auer, Peter and Chiang, Chao-Kai},
  booktitle={Conference on Learning Theory},
  pages={116--120},
  year={2016},
  organization={PMLR}
}

@inproceedings{bubeck2012best,
  title={The best of both worlds: Stochastic and adversarial bandits},
  author={Bubeck, S{\'e}bastien and Slivkins, Aleksandrs},
  booktitle={Conference on Learning Theory},
  pages={42--1},
  year={2012},
  organization={JMLR Workshop and Conference Proceedings}
}


@article{bams/1183517370,
author = {Herbert Robbins},
title = {{Some aspects of the sequential design of experiments}},
volume = {58},
journal = {Bulletin of the American Mathematical Society},
number = {5},
publisher = {American Mathematical Society},
pages = {527 -- 535},
year = {1952}
}

@article{nemhauser1978analysis,
  title={An analysis of approximations for maximizing submodular set functions—I},
  author={Nemhauser, George L and Wolsey, Laurence A and Fisher, Marshall L},
  journal={Mathematical programming},
  volume={14},
  number={1},
  pages={265--294},
  year={1978},
  publisher={Springer}
}

@book{lattimore_szepesvari_2020, place={Cambridge}, title={Bandit Algorithms}, publisher={Cambridge University Press}, author={Lattimore, Tor and Szepesvári, Csaba}, year={2020}}

@InProceedings{pmlr-v28-chen13a,
  title = 	 {Combinatorial Multi-Armed Bandit: General Framework and Applications},
  author = 	 {Chen, Wei and Wang, Yajun and Yuan, Yang},
  booktitle = 	 {Proceedings of the 30th International Conference on Machine Learning},
  pages = 	 {151--159},
  year = 	 {2013},
  _editor = 	 {Dasgupta, Sanjoy and McAllester, David},
  volume = 	 {28},
  number =   {1},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Atlanta, Georgia, USA},
  month = 	 {17--19 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v28/chen13a.pdf},
  abstract = 	 {We define a general framework for a large class of combinatorial multi-armed bandit (CMAB) problems, where simple arms with unknown istributions  form \em super arms. In each round, a super arm is played and the outcomes of its related simple arms are observed, which helps the selection of super arms in future rounds. The reward of the super arm depends on the outcomes of played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonlinear reward instances. We assume the availability of an (α,β)-approximation oracle that takes the  means of the distributions of arms and outputs a super arm that with probability βgenerates  an αfraction of the optimal expected reward. The objective of a CMAB algorithm is to minimize \em (α,β)-approximation regret, which is the difference in total expected reward between the αβfraction of expected reward when always playing the optimal super arm, and the expected reward of playing super arms according to the algorithm. We provide CUCB algorithm that achieves O(\log n) regret, where n is the number of rounds played, and we further provide distribution-independent bounds for a large class of reward functions. Our regret analysis is tight in that it matches the bound for classical MAB problem up to a constant factor, and it significantly improves the regret bound in a recent paper on combinatorial bandits with linear rewards. We apply our CMAB framework to two new applications, probabilistic maximum coverage (PMC) for online advertising and social influence maximization for viral marketing, both having nonlinear reward structures.}
}

@inproceedings{NIPS2012_7a614fd0,
 author = {Leskovec, Jure and Mcauley, Julian},
 booktitle = {Advances in Neural Information Processing Systems},
 _editor = {F. Pereira and C. J. C. Burges and L. Bottou and K. Q. Weinberger},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Learning to Discover Social Circles in Ego Networks},
 volume = {25},
 year = {2012}
}

@book{lattimore_szepesvári_2020, place={Cambridge}, title={Bandit Algorithms},  publisher={Cambridge University Press}, author={Lattimore, Tor and Szepesvári, Csaba}, year={2020}}

@article{MAL-068,
year = {2019},
volume = {12},
journal = {Foundations and Trends® in Machine Learning},
title = {Introduction to Multi-Armed Bandits},
issn = {1935-8237},
number = {1-2},
pages = {1-286},
author = {Aleksandrs Slivkins }
}


@article{streeter2010online,
  title={Online learning of assignments},
  author={Streeter, Matthew and Golovin, Daniel and Krause, Andreas},
  year={2010},
  publisher={Neural Information Processing Systems Foundation}
}

@inproceedings{10.1145/1281192.1281239,
author = {Leskovec, Jure and Krause, Andreas and Guestrin, Carlos and Faloutsos, Christos and VanBriesen, Jeanne and Glance, Natalie},
title = {Cost-Effective Outbreak Detection in Networks},
year = {2007},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
abstract = {Given a water distribution network, where should we place sensors toquickly detect contaminants? Or, which blogs should we read to avoid missing important stories?.These seemingly different problems share common structure: Outbreak detection can be modeled as selecting nodes (sensor locations, blogs) in a network, in order to detect the spreading of a virus or information asquickly as possible. We present a general methodology for near optimal sensor placement in these and related problems. We demonstrate that many realistic outbreak detection objectives (e.g., detection likelihood, population affected) exhibit the property of "submodularity". We exploit submodularity to develop an efficient algorithm that scales to large problems, achieving near optimal placements, while being 700 times faster than a simple greedy algorithm. We also derive online bounds on the quality of the placements obtained by any algorithm. Our algorithms and bounds also handle cases where nodes (sensor locations, blogs) have different costs.We evaluate our approach on several large real-world problems,including a model of a water distribution network from the EPA, andreal blog data. The obtained sensor placements are provably near optimal, providing a constant fraction of the optimal solution. We show that the approach scales, achieving speedups and savings in storage of several orders of magnitude. We also show how the approach leads to deeper insights in both applications, answering multicriteria trade-off, cost-sensitivity and generalization questions.},
booktitle = {Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining},
pages = {420–429},
numpages = {10},
keywords = {sensor placement, submodular functions, graphs, information cascades, virus propagation},
location = {San Jose, California, USA},
series = {KDD '07}
}

@inproceedings{NIPS2015_0266e33d,
 author = {Lin, Tian and Li, Jian and Chen, Wei},
 booktitle = {Advances in Neural Information Processing Systems},
 _editor = {C. Cortes and N. Lawrence and D. Lee and M. Sugiyama and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Stochastic Online Greedy Learning with Semi-bandit Feedbacks},
 volume = {28},
 year = {2015}
}

@inproceedings{niazadeh2021online,
  title={Online learning via offline greedy algorithms: Applications in market design and optimization},
  author={Niazadeh, Rad and Golrezaei, Negin and Wang, Joshua R and Susan, Fransisca and Badanidiyuru, Ashwinkumar},
  booktitle={Proceedings of the 22nd ACM Conference on Economics and Computation},
  pages={737--738},
  year={2021}
}

@article{Zhang2020OneSS,
  title={One Sample Stochastic Frank-Wolfe},
  author={Mingrui Zhang and Zebang Shen and Aryan Mokhtari and Hamed Hassani and Amin Karbasi},
  journal={ArXiv},
  year={2020},
  volume={abs/1910.04322}
}


@InProceedings{pmlr-v130-perez-salazar21a,
  title = 	 { Differentially Private Online Submodular Maximization },
  author =       {Perez Salazar, Sebastian and Cummings, Rachel},
  booktitle = 	 {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1279--1287},
  year = 	 {2021},
  _editor = 	 {Banerjee, Arindam and Fukumizu, Kenji},
  volume = 	 {130},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--15 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v130/perez-salazar21a/perez-salazar21a.pdf},
  abstract = 	 { 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. The decision maker obtains a profit equal to the function evaluated on the chosen set and aims to learn a sequence of sets that achieves low expected regret. In the full-information setting, we develop an $(\varepsilon,\delta)$-DP algorithm with expected (1-1/e)-regret bound of $O( \frac{k^2\log |U|\sqrt{T \log k/\delta}}{\varepsilon} )$. 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. In the bandit setting, we provide an $(\varepsilon,\delta+ O(e^{-T^{1/3}}))$-DP algorithm with expected (1-1/e)-regret bound of $O( \frac{\sqrt{\log k/\delta}}{\varepsilon} (k (|U| \log |U|)^{1/3})^2 T^{2/3} )$. One challenge for privacy in this setting is that the payoff and feedback of expert i depends on the actions taken by her i-1 predecessors. This particular type of information leakage is not covered by post-processing, and new analysis is required. Our techniques for maintaining privacy with feedforward may be of independent interest. }
}

@inproceedings{Qin2013PromotingDI,
  title={Promoting Diversity in Recommendation by Entropy Regularizer},
  author={Lijing Qin and Xiaoyan Zhu},
  booktitle={IJCAI},
  year={2013}
}

@inproceedings{Qin2014ContextualCB,
  title={Contextual Combinatorial Bandit and its Application on Diversified Online Recommendation},
  author={Lijing Qin and Shouyuan Chen and Xiaoyan Zhu},
  booktitle={SDM},
  year={2014}
}

@inproceedings{Ashkan2015OptimalGD,
  title={Optimal Greedy Diversity for Recommendation},
  author={Azin Ashkan and Branislav Kveton and Shlomo Berkovsky and Zheng Wen},
  booktitle={IJCAI},
  year={2015}
}

@inproceedings{NIPS2017_f0935e4c,
 author = {Chen, Lin and Krause, Andreas and Karbasi, Amin},
 booktitle = {Advances in Neural Information Processing Systems},
 _editor = {I. Guyon and U. V. Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Interactive Submodular Bandit},
 volume = {30},
 year = {2017}
}

@inproceedings{10.5555/3015812.3016015,
author = {Yu, Baosheng and Fang, Meng and Tao, Dacheng},
title = {Linear Submodular Bandits with a Knapsack Constraint},
year = {2016},
publisher = {AAAI Press},
abstract = {Linear submodular bandits has been proven to be effective in solving the diversification and feature-based exploration problems in retrieval systems. Concurrently, many web-based applications, such as news article recommendation and online ad placement, can be modeled as budget-limited problems. However, the diversification problem under a budget constraint has not been considered. In this paper, we first introduce the budget constraint to linear submodular bandits as a new problem called the linear submodular bandits with a knapsack constraint. We then define an α-approximation unit-cost regret considering that submodular function maximization is NP-hard. To solve this problem, we propose two greedy algorithms based on a modified UCB rule. We then prove these two algorithms with different regret bounds and computational costs. We also conduct a number of experiments and the experimental results confirm our theoretical analyses.},
booktitle = {Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence},
pages = {1380–1386},
numpages = {7},
location = {Phoenix, Arizona},
series = {AAAI'16}
}


@article{zhang2012information,
  title={Information production and link formation in social computing systems},
  author={Zhang, Yu and van der Schaar, Mihaela},
  journal={IEEE Journal on selected Areas in communications},
  volume={30},
  number={11},
  pages={2136--2145},
  year={2012},
  publisher={IEEE}
}

@article{chen2018contextual,
  title={Contextual combinatorial multi-armed bandits with volatile arms and submodular reward},
  author={Chen, Lixing and Xu, Jie and Lu, Zhuo},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  pages={3247--3256},
  year={2018}
}

@inproceedings{nushi2016learning,
  title={Learning and feature selection under budget constraints in crowdsourcing},
  author={Nushi, Besmira and Singla, Adish and Krause, Andreas and Kossmann, Donald},
  booktitle={Fourth AAAI Conference on Human Computation and Crowdsourcing},
  year={2016}
}

@inproceedings{yang2016selecting,
  title={Selecting most informative contributors with unknown costs for budgeted crowdsensing},
  author={Yang, Shuo and Wu, Fan and Tang, Shaojie and Luo, Tie and Gao, Xiaofeng and Kong, Linghe and Chen, Guihai},
  booktitle={2016 IEEE/ACM 24th International Symposium on Quality of Service (IWQoS)},
  pages={1--6},
  year={2016},
  organization={IEEE}
}

@article{yang2017identifying,
  title={Identifying the most valuable workers in fog-assisted spatial crowdsourcing},
  author={Yang, Peng and Zhang, Ning and Zhang, Shan and Yang, Kan and Yu, Li and Shen, Xuemin},
  journal={IEEE Internet of Things Journal},
  volume={4},
  number={5},
  pages={1193--1203},
  year={2017},
  publisher={IEEE}
}

@inproceedings{singla2016noisy,
  title={Noisy submodular maximization via adaptive sampling with applications to crowdsourced image collection summarization},
  author={Singla, Adish and Tschiatschek, Sebastian and Krause, Andreas},
  booktitle={Thirtieth AAAI Conference on Artificial Intelligence},
  year={2016}
}

@inproceedings{li2018multi,
  title={Multi-expertise aware participant selection in mobile crowd sensing via online learning},
  author={Li, Hanshang and Li, Ting and Li, Fan and Yang, Song and Wang, Yu},
  booktitle={2018 IEEE 15th International Conference on Mobile Ad Hoc and Sensor Systems (MASS)},
  pages={433--441},
  year={2018},
  organization={IEEE}
}

@article{han2018quality,
  title={Quality-aware pricing for mobile crowdsensing},
  author={Han, Kai and Huang, He and Luo, Jun},
  journal={IEEE/ACM Transactions on Networking},
  volume={26},
  number={4},
  pages={1728--1741},
  year={2018},
  publisher={IEEE}
}

@inproceedings{song2021minimizing,
  title={Minimizing Entropy for Crowdsourcing with Combinatorial Multi-Armed Bandit},
  author={Song, Yiwen and Jin, Haiming},
  booktitle={IEEE INFOCOM 2021-IEEE Conference on Computer Communications},
  pages={1--10},
  year={2021},
  organization={IEEE}
}

@inproceedings{domingos2001mining,
  title={Mining the network value of customers},
  author={Domingos, Pedro and Richardson, Matt},
  booktitle={Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining},
  pages={57--66},
  year={2001}
}

@inproceedings{kempe2003maximizing,
  title={Maximizing the spread of influence through a social network},
  author={Kempe, David and Kleinberg, Jon and Tardos, {\'E}va},
  booktitle={Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining},
  pages={137--146},
  year={2003}
}

@inproceedings{chen2009efficient,
  title={Efficient influence maximization in social networks},
  author={Chen, Wei and Wang, Yajun and Yang, Siyu},
  booktitle={Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining},
  pages={199--208},
  year={2009}
}

@inproceedings{chen2010scalable,
  title={Scalable influence maximization in social networks under the linear threshold model},
  author={Chen, Wei and Yuan, Yifei and Zhang, Li},
  booktitle={2010 IEEE international conference on data mining},
  pages={88--97},
  year={2010},
  organization={IEEE}
}

@inproceedings{goyal2011celf++,
  title={Celf++ optimizing the greedy algorithm for influence maximization in social networks},
  author={Goyal, Amit and Lu, Wei and Lakshmanan, Laks VS},
  booktitle={Proceedings of the 20th international conference companion on World wide web},
  pages={47--48},
  year={2011}
}

@inproceedings{jiang2011simulated,
  title={Simulated annealing based influence maximization in social networks},
  author={Jiang, Qingye and Song, Guojie and Gao, Cong and Wang, Yu and Si, Wenjun and Xie, Kunqing},
  booktitle={Twenty-fifth AAAI conference on artificial intelligence},
  year={2011}
}

@inproceedings{tang2014influence,
  title={Influence maximization: Near-optimal time complexity meets practical efficiency},
  author={Tang, Youze and Xiao, Xiaokui and Shi, Yanchen},
  booktitle={Proceedings of the 2014 ACM SIGMOD international conference on Management of data},
  pages={75--86},
  year={2014}
}

@article{li2018influence,
  title={Influence maximization on social graphs: A survey},
  author={Li, Yuchen and Fan, Ju and Wang, Yanhao and Tan, Kian-Lee},
  journal={IEEE Transactions on Knowledge and Data Engineering},
  volume={30},
  number={10},
  pages={1852--1872},
  year={2018},
  publisher={IEEE}
}

@inproceedings{lei2015online,
  title={Online influence maximization},
  author={Lei, Siyu and Maniu, Silviu and Mo, Luyi and Cheng, Reynold and Senellart, Pierre},
  booktitle={Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining},
  pages={645--654},
  year={2015}
}

@inproceedings{wen2017online,
  title={Online influence maximization under independent cascade model with semi-bandit feedback},
  author={Wen, Zheng and Kveton, Branislav and Valko, Michal and Vaswani, Sharan},
  booktitle={Proceedings of the 31st International Conference on Neural Information Processing Systems},
  pages={3026--3036},
  year={2017}
}

@inproceedings{vaswani2017model,
  title={Model-independent online learning for influence maximization},
  author={Vaswani, Sharan and Kveton, Branislav and Wen, Zheng and Ghavamzadeh, Mohammad and Lakshmanan, Laks VS and Schmidt, Mark},
  booktitle={Proceedings of the 34th International Conference on Machine Learning-Volume 70},
  pages={3530--3539},
  year={2017},
  organization={JMLR. org}
}

@article{li2020online,
  title={Online Influence Maximization under Linear Threshold Model},
  author={Li, Shuai and Kong, Fang and Tang, Kejie and Li, Qizhi and Chen, Wei},
  journal={arXiv preprint arXiv:2011.06378},
  year={2020}
}

@inproceedings{perrault2020budgeted,
  title={Budgeted online influence maximization},
  author={Perrault, Pierre and Healey, Jennifer and Wen, Zheng and Valko, Michal},
  booktitle={International Conference on Machine Learning},
  pages={7620--7631},
  year={2020},
  organization={PMLR}
}

@article{10.1023/A:1013689704352,
author = {Auer, Peter and Cesa-Bianchi, Nicol\`{o} and Fischer, Paul},
title = {Finite-Time Analysis of the Multiarmed Bandit Problem},
year = {2002},
issue_date = {May-June 2002},
publisher = {Kluwer Academic Publishers},
address = {USA},
volume = {47},
number = {2–3},
issn = {0885-6125},
abstract = {Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy's success in addressing this dilemma is the regret, that is the loss due to the fact that the globally optimal policy is not followed all the times. One of the simplest examples of the exploration/exploitation dilemma is the multi-armed bandit problem. Lai and Robbins were the first ones to show that the regret for this problem has to grow at least logarithmically in the number of plays. Since then, policies which asymptotically achieve this regret have been devised by Lai and Robbins and many others. In this work we show that the optimal logarithmic regret is also achievable uniformly over time, with simple and efficient policies, and for all reward distributions with bounded support.},
journal = {Mach. Learn.},
month = {may},
pages = {235–256},
numpages = {22},
keywords = {bandit problems, finite horizon regret, adaptive allocation rules}
}

@article{10.1137/S0097539701398375,
author = {Auer, Peter and Cesa-Bianchi, Nicol\`{o} and Freund, Yoav and Schapire, Robert E.},
title = {The Nonstochastic Multiarmed Bandit Problem},
year = {2003},
issue_date = {2003},
publisher = {Society for Industrial and Applied Mathematics},
address = {USA},
volume = {32},
number = {1},
issn = {0097-5397},
abstract = {In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff). Past solutions for the bandit problem have almost always relied on assumptions about the statistics of the slot machines. In this work, we make no statistical assumptions whatsoever about the nature of the process generating the payoffs of the slot machines. We give a solution to the bandit problem in which an adversary, rather than a well-behaved stochastic process, has complete control over the payoffs. In a sequence of T plays, we prove that the per-round payoff of our algorithm approaches that of the best arm at the rate O ( T -1/2). We show by a matching lower bound that this is the best possible.We also prove that our algorithm approaches the per-round payoff of any set of strategies at a similar rate: if the best strategy is chosen from a pool of N strategies, then our algorithm approaches the per-round payoff of the strategy at the rate O ((log N 1/2 T -1/2). Finally, we apply our results to the problem of playing an unknown repeated matrix game. We show that our algorithm approaches the minimax payoff of the unknown game at the rate O ( T -1/2).},
journal = {SIAM J. Comput.},
month = {jan},
pages = {48–77},
numpages = {30},
keywords = {unknown matrix games, adversarial bandit problem}
}

@inproceedings{streeter2008online,
author = {Streeter, Matthew and Golovin, Daniel},
title = {An Online Algorithm for Maximizing Submodular Functions},
year = {2008},
publisher = {Curran Associates Inc.},
address = {Red Hook, NY, USA},
abstract = {We present an algorithm for solving a broad class of online resource allocation problems.
Our online algorithm can be applied in environments where abstract jobs arrive one
at a time, and one can complete the jobs by investing time in a number of abstract
activities, according to some schedule. We assume that the fraction of jobs completed
by a schedule is a monotone, submodular function of a set of pairs (v, τ), where τ
is the time invested in activity v. Under this assumption, our online algorithm performs
near-optimally according to two natural metrics: (i) the fraction of jobs completed
within time T, for some fixed deadline T > 0, and (ii) the average time required to
complete each job. We evaluate our algorithm experimentally by using it to learn,
online, a schedule for allocating CPU time among solvers entered in the 2007 SAT solver
competition.},
booktitle = {Proceedings of the 21st International Conference on Neural Information Processing Systems},
pages = {1577–1584},
numpages = {8},
location = {Vancouver, British Columbia, Canada},
series = {NIPS'08}
}


@InProceedings{pmlr-v108-chen20c,
  title = 	 {Black Box Submodular Maximization: Discrete and Continuous Settings},
  author =       {Chen, Lin and Zhang, Mingrui and Hassani, Hamed and Karbasi, Amin},
  booktitle = 	 {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1058--1070},
  year = 	 {2020},
  _editor = 	 {Chiappa, Silvia and Calandra, Roberto},
  volume = 	 {108},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {26--28 Aug},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v108/chen20c/chen20c.pdf},
  abstract = 	 {In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Continuous Greedy, a derivative-free algorithm that provably achieves the tight $[(1-1/e)OPT-\epsilon]$ approximation guarantee with $O(d/\epsilon^3)$ function evaluations. We then extend our result to the stochastic setting where function values are subject to stochastic zero-mean noise. It is through this stochastic generalization that we revisit the discrete submodular maximization problem and use the multi-linear extension as a bridge between discrete and continuous settings. Finally, we extensively evaluate the performance of our algorithm on continuous and discrete submodular objective functions using both synthetic and real data.}
}

@inproceedings{zhang2019online,
 author = {Zhang, Mingrui and Chen, Lin and Hassani, Hamed and Karbasi, Amin},
 booktitle = {Advances in Neural Information Processing Systems},
 _editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback},
 volume = {32},
 year = {2019}
}

@inproceedings{Hassani2017GradientMF,
  title={Gradient Methods for Submodular Maximization},
  author={S. Hamed Hassani and Mahdi Soltanolkotabi and Amin Karbasi},
  booktitle={NIPS},
  year={2017}
}

@article{Mokhtari2020StochasticCG,
  title={Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximization},
  author={Aryan Mokhtari and Hamed Hassani and Amin Karbasi},
  journal={ArXiv},
  year={2020},
  volume={abs/1804.09554}
}

@article{Hassani2020StochasticCG,
  title={Stochastic Conditional Gradient++: (Non)Convex Minimization and Continuous Submodular Maximization},
  author={Hamed Hassani and Amin Karbasi and Aryan Mokhtari and Zebang Shen},
  journal={SIAM J. Optim.},
  year={2020},
  volume={30},
  pages={3315-3344}
}

@inproceedings{Dani2008StochasticLO,
  title={Stochastic Linear Optimization under Bandit Feedback},
  author={Varsha Dani and Thomas P. Hayes and Sham M. Kakade},
  booktitle={COLT},
  year={2008}
}

@article{CESABIANCHI20121404,
title = {Combinatorial bandits},
journal = {Journal of Computer and System Sciences},
volume = {78},
number = {5},
pages = {1404-1422},
year = {2012},
note = {JCSS Special Issue: Cloud Computing 2011},
issn = {0022-0000},
author = {Nicolò Cesa-Bianchi and Gábor Lugosi},
keywords = {Online prediction, Adversarial bandit problems, Online linear optimization},
abstract = {We study sequential prediction problems in which, at each time instance, the forecaster chooses a vector from a given finite set S⊆Rd. At the same time, the opponent chooses a “loss” vector in Rd and the forecaster suffers a loss that is the inner product of the two vectors. The goal of the forecaster is to achieve that, in the long run, the accumulated loss is not much larger than that of the best possible element in S. We consider the “bandit” setting in which the forecaster only has access to the losses of the chosen vectors (i.e., the entire loss vectors are not observed). We introduce a variant of a strategy by Dani, Hayes and Kakade achieving a regret bound that, for a variety of concrete choices of S, is of order ndln|S| where n is the time horizon. This is not improvable in general and is better than previously known bounds. The examples we consider are all such that S⊆{0,1}d, and we show how the combinatorial structure of these classes can be exploited to improve the regret bounds. We also point out computationally efficient implementations for various interesting choices of S.}
}

@article{Bubeck2012TowardsMP,
  title={Towards Minimax Policies for Online Linear Optimization with Bandit Feedback},
  author={S{\'e}bastien Bubeck and Nicol{\`o} Cesa-Bianchi and Sham M. Kakade},
  journal={ArXiv},
  year={2012},
  volume={abs/1202.3079}
}

@article{Audibert2014RegretIO,
  title={Regret in Online Combinatorial Optimization},
  author={Jean-Yves Audibert and S{\'e}bastien Bubeck and G{\'a}bor Lugosi},
  journal={ArXiv},
  year={2014},
  volume={abs/1204.4710}
}

@inproceedings{Combes2015CombinatorialBR,
  title={Combinatorial Bandits Revisited},
  author={Richard Combes and Mohammad Sadegh Talebi and Alexandre Prouti{\`e}re and Marc Lelarge},
  booktitle={NIPS},
  year={2015}
}

@inproceedings{rejwan2020top,
  title={Top-$ k $ Combinatorial Bandits with Full-Bandit Feedback},
  author={Rejwan, Idan and Mansour, Yishay},
  booktitle={Algorithmic Learning Theory},
  pages={752--776},
  year={2020}
}

@inproceedings{agarwal2021stochastic,
  title={Stochastic Top-$ K $ Subset Bandits with Linear Space and Non-Linear Feedback},
  author={Agarwal, Mridul and Aggarwal, Vaneet and Quinn, Christopher J and Umrawal, Abhishek K},
  booktitle={Algorithmic Learning Theory},
  pages={306--339},
  year={2021},
  organization={PMLR}
}

@article{agarwal2021dart, 
title={DART: Adaptive Accept Reject Algorithm for Non-Linear Combinatorial Bandits}, volume={35}, number={8}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Agarwal, Mridul and Aggarwal, Vaneet and Umrawal, Abhishek Kumar and Quinn, Chris}, year={2021}, month={May}, pages={6557-6565} }

@inproceedings{Bubeck2013MultipleII,
  title={Multiple Identifications in Multi-Armed Bandits},
  author={S{\'e}bastien Bubeck and Tengyao Wang and Nitin Viswanathan},
  booktitle={ICML},
  year={2013}
}

@inproceedings{Horadam2006HadamardMA,
  title={Hadamard Matrices and Their Applications},
  author={Kathy J. Horadam},
  year={2006}
}

@article{Blondel2008FastUO,
  title={Fast unfolding of communities in large networks},
  author={Vincent D. Blondel and Jean-Loup Guillaume and Renaud Lambiotte and Etienne Lefebvre},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2008},
  volume={2008},
  pages={10008}
}

@article{Littlestone1994TheWM,
  title={The Weighted Majority Algorithm},
  author={Nick Littlestone and Manfred K. Warmuth},
  journal={Inf. Comput.},
  year={1994},
  volume={108},
  pages={212-261}
}

@article{Kveton2015TightRB,
  title={Tight Regret Bounds for Stochastic Combinatorial Semi-Bandits},
  author={Branislav Kveton and Zheng Wen and Azin Ashkan and Csaba Szepesvari},
  journal={ArXiv},
  year={2015},
  volume={abs/1410.0949}
}

@article{Arora2012TheMW,
  title={The Multiplicative Weights Update Method: a Meta-Algorithm and Applications},
  author={Sanjeev Arora and Elad Hazan and Satyen Kale},
  journal={Theory Comput.},
  year={2012},
  volume={8},
  pages={121-164}
}

@article{Besson2018WhatDT,
  title={What Doubling Tricks Can and Can't Do for Multi-Armed Bandits},
  author={Lilian Besson and Emilie Kaufmann},
  journal={ArXiv},
  year={2018},
  volume={abs/1803.06971}
}