@inproceedings{LattimoreLR16,
  author    = {Finnian Lattimore and
               Tor Lattimore and
               Mark D. Reid},
  title     = {Causal Bandits: Learning Good Interventions via Causal Inference},
  booktitle = {Annual Conference on Neural Information Processing Systems, 2016},
  pages     = {1181--1189},
  year      = {2016}
}

@misc{lu2021causal,
      title={Causal Markov Decision Processes: Learning Good Interventions Efficiently}, 
      author={Yangyi Lu and Amirhossein Meisami and Ambuj Tewari},
      year={2021}
}

@book{PEARL2009,
  title={Causality},
  author={Pearl, Judea},
  year={2009},
  publisher={Cambridge university press}
}

@article{Slivkins_Book,
  author    = {Aleksandrs Slivkins},
  title     = {Introduction to Multi-Armed Bandits},
  journal   = {CoRR},
  volume    = {abs/1904.07272},
  year      = {2019},
  url       = {http://arxiv.org/abs/1904.07272}
}

@inproceedings{BareinboimFP15,
  author    = {Elias Bareinboim and
               Andrew Forney and
               Judea Pearl},
  title     = {Bandits with Unobserved Confounders: {A} Causal Approach},
  booktitle = {Annual Conference on Neural Information Processing Systems, 2015},
  pages     = {1342--1350},
  year      = {2015}
}

@inproceedings{LU2020,
  title={Regret Analysis of Bandit Problems with Causal Background Knowledge},
  author={Lu, Yangyi and Meisami, Amirhossein and Tewari, Ambuj and Yan, William},
  booktitle={Conference on Uncertainty in Artificial Intelligence, 2020},
  pages={141--150},
  year={2020},
  organization={PMLR}
}

@inproceedings{YabeHSIKFK18,
  author    = {Akihiro Yabe and
               Daisuke Hatano and
               Hanna Sumita and
               Shinji Ito and
               Naonori Kakimura and
               Takuro Fukunaga and
               Ken{-}ichi Kawarabayashi},
  title     = {Causal Bandits with Propagating Inference},
  booktitle = {International Conference on Machine Learning, 2018},
  series    = {Proceedings of Machine Learning Research},
  volume    = {80},
  pages     = {5508--5516},
  publisher = {{PMLR}},
  year      = {2018}
}

@inproceedings{SenSDS17,
  author    = {Rajat Sen and
               Karthikeyan Shanmugam and
               Alexandros G. Dimakis and
               Sanjay Shakkottai},
  title     = {Identifying Best Interventions through Online Importance Sampling},
  booktitle = {International Conference on Machine Learning, 2017},
  series    = {Proceedings of Machine Learning Research},
  volume    = {70},
  pages     = {3057--3066},
  publisher = {{PMLR}},
  year      = {2017}
}

@inproceedings{SenSKDS17,
  author    = {Rajat Sen and
               Karthikeyan Shanmugam and
               Murat Kocaoglu and
               Alexandros G. Dimakis and
               Sanjay Shakkottai},
  title     = {Contextual Bandits with Latent Confounders: An {NMF} Approach},
  booktitle = {International Conference on Artificial Intelligence
               and Statistics, 2017},
  series    = {Proceedings of Machine Learning Research},
  volume    = {54},
  pages     = {518--527},
  publisher = {{PMLR}},
  year      = {2017}
}

@inproceedings{LeeB18,
  author    = {Sanghack Lee and
               Elias Bareinboim},
  title     = {Structural Causal Bandits: Where to Intervene?},
  booktitle = {Annual Conference on Neural Information Processing Systems, 2018},
  pages     = {2573--2583},
  year      = {2018}
}

@inproceedings{LeeB19,
  author    = {Sanghack Lee and
               Elias Bareinboim},
  title     = {Structural Causal Bandits with Non-Manipulable Variables},
  booktitle = {{AAAI} Conference on Artificial Intelligence, 2019},
  pages     = {4164--4172},
  publisher = {{AAAI} Press},
  year      = {2019}
}


@InProceedings{BhattacharyyaGKMV20,
  title = 	 {Learning and Sampling of Atomic Interventions from Observations},
  author =       {Bhattacharyya, Arnab and Gayen, Sutanu and Kandasamy, Saravanan and Maran, Ashwin and Variyam, Vinodchandran N.},
  booktitle = 	 {Proceedings of the 37th International Conference on Machine Learning},
  pages = 	 {842--853},
  year = 	 {2020},
  editor = 	 {III, Hal Daumé and Singh, Aarti},
  volume = 	 {119},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--18 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v119/bhattacharyya20a/bhattacharyya20a.pdf},
  url = 	 {https://proceedings.mlr.press/v119/bhattacharyya20a.html},
}


@inproceedings{TianP02,
  author    = {Jin Tian and
               Judea Pearl},
  title     = {A General Identification Condition for Causal Effects},
  booktitle = {National Conference on Artificial Intelligence and Conference on Innovative Applications of Artificial
               Intelligence, 2002},
  pages     = {567--573},
  year      = {2002}
}

@book{Pearl00,
author = {Pearl, Judea},
title = {Causality: Models, Reasoning, and Inference},
year = {2000},
isbn = {0521773628},
publisher = {Cambridge University Press},
address = {USA}
}

@article{Haigh2004,
 ISSN = {00219398, 15375374},
 author = {Michael S. Haigh and David A. Bessler},
 journal = {The Journal of Business},
 number = {4},
 pages = {1099--1121},
 publisher = {The University of Chicago Press},
 title = {Causality and Price Discovery: An Application of Directed Acyclic Graphs},
 volume = {77},
 year = {2004}
}

@article{Bottou2013,
author = {Bottou, L\'{e}on and Peters, Jonas and Qui\~{n}onero-Candela, Joaquin and Charles, Denis X. and Chickering, D. Max and Portugaly, Elon and Ray, Dipankar and Simard, Patrice and Snelson, Ed},
title = {Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising},
year = {2013},
issue_date = {January 2013},
publisher = {JMLR.org},
volume = {14},
number = {1},
issn = {1532-4435},
journal = {J. Mach. Learn. Res.},
month = jan,
pages = {3207–3260},
numpages = {54},
keywords = {counterfactual reasoning, causation, computational advertising}
}

@article{Velikova2014,
title = {Exploiting causal functional relationships in Bayesian network modelling for personalised healthcare},
journal = {International Journal of Approximate Reasoning},
volume = {55},
number = {1, Part 1},
pages = {59-73},
year = {2014},
note = {Applications of Bayesian Networks},
issn = {0888-613X},
doi = {https://doi.org/10.1016/j.ijar.2013.03.016},
url = {https://www.sciencedirect.com/science/article/pii/S0888613X13000777},
author = {Marina Velikova and Josien Terwisscha {van Scheltinga} and Peter J.F. Lucas and Marc Spaanderman},
keywords = {Temporal Bayesian networks, Causal independence models, Clinical decision support, Pregnancy disorders, eHealth, Home monitoring}
}

@inproceedings{NairPS21,
  author    = {Vineet Nair and
               Vishakha Patil and
               Gaurav Sinha},
  title     = {Budgeted and Non-Budgeted Causal Bandits},
  booktitle = {The 24th International Conference on Artificial Intelligence and Statistics,
               {AISTATS} 2021, April 13-15, 2021, Virtual Event},
  series    = {Proceedings of Machine Learning Research},
  volume    = {130},
  pages     = {2017--2025},
  publisher = {{PMLR}},
  year      = {2021}
}

@article{LuMT21,
  author    = {Yangyi Lu and
               Amirhossein Meisami and
               Ambuj Tewari},
  title     = {Causal Markov Decision Processes: Learning Good Interventions Efficiently},
  journal   = {CoRR},
  volume    = {abs/2102.07663},
  year      = {2021}
}

@inproceedings{AudibertBM10,
  author    = {Jean{-}Yves Audibert and
               S{\'{e}}bastien Bubeck and
               R{\'{e}}mi Munos},
  title     = {Best Arm Identification in Multi-Armed Bandits},
  booktitle = {The 23rd Conference on Learning Theory {COLT}},
  pages     = {41--53},
  publisher = {Omnipress},
  year      = {2010}
}

@article{BubeckC12,
  author    = {S{\'{e}}bastien Bubeck and
               Nicol{\`{o}} Cesa{-}Bianchi},
  title     = {Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit
               Problems},
  journal   = {Found. Trends Mach. Learn.},
  volume    = {5},
  number    = {1},
  pages     = {1--122},
  year      = {2012}
}

@article{AuerCF02,
  author    = {Peter Auer and
               Nicol{\`{o}} Cesa{-}Bianchi and
               Paul Fischer},
  title     = {Finite-time Analysis of the Multiarmed Bandit Problem},
  journal   = {Mach. Learn.},
  volume    = {47},
  number    = {2-3},
  pages     = {235--256},
  year      = {2002}
}

@inproceedings{GreenewaldKSMKA19,
  author    = {Kristjan H. Greenewald and
               Dmitriy Katz and
               Karthikeyan Shanmugam and
               Sara Magliacane and
               Murat Kocaoglu and
               Enric Boix Adser{\`{a}} and
               Guy Bresler},
  title     = {Sample Efficient Active Learning of Causal Trees},
  booktitle = {Annual Conference
               on Neural Information Processing Systems, NeurIPS},
  pages     = {14279--14289},
  year      = {2019}
}

@book{10.5555/1522486,
author = {Tsybakov, Alexandre B.},
title = {Introduction to Nonparametric Estimation},
year = {2008},
isbn = {0387790519},
publisher = {Springer Publishing Company, Incorporated},
edition = {1st},
abstract = {This is a concise text developed from lecture notes and ready to be used for a course on the graduate level. The main idea is to introduce the fundamental concepts of the theory while maintaining the exposition suitable for a first approach in the field. Therefore, the results are not always given in the most general form but rather under assumptions that lead to shorter or more elegant proofs. The book has three chapters. Chapter 1 presents basic nonparametric regression and density estimators and analyzes their properties. Chapter 2 is devoted to a detailed treatment of minimax lower bounds. Chapter 3 develops more advanced topics: Pinskers theorem, oracle inequalities, Stein shrinkage, and sharp minimax adaptivity. This book will be useful for researchers and grad students interested in theoretical aspects of smoothing techniques. Many important and useful results on optimal and adaptive estimation are provided. As one of the leading mathematical statisticians working in nonparametrics, the author is an authority on the subject.}
}

@INPROCEEDINGS{492488,
  author={Auer, P. and Cesa-Bianchi, N. and Freund, Y. and Schapire, R.E.},
  booktitle={Proceedings of IEEE 36th Annual Foundations of Computer Science}, 
  title={Gambling in a rigged casino: The adversarial multi-armed bandit problem}, 
  year={1995},
  volume={},
  number={},
  pages={322-331},
  doi={10.1109/SFCS.1995.492488}}


@misc{Lu2021,
      title={Causal Bandits with Unknown Graph Structure}, 
      author={Yangyi Lu and Amirhossein Meisami and Ambuj Tewari},
      year={2021},
      eprint={2106.02988},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@article{Hauser2012,
author = {Hauser, Alain and B\"{u}hlmann, Peter},
title = {Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs},
year = {2012},
issue_date = {January 2012},
publisher = {JMLR.org},
volume = {13},
number = {1},
issn = {1532-4435},
journal = {J. Mach. Learn. Res.},
month = aug,
pages = {2409–2464},
numpages = {56},
keywords = {Markov equivalence, causal inference, interventions, graphical model, greedy equivalence search}
}

@inproceedings{Acharya2018,
author = {Acharya, Jayadev and Bhattacharyya, Arnab and Daskalakis, Constantinos and Kandasamy, Saravanan},
title = {Learning and Testing Causal Models with Interventions},
year = {2018},
publisher = {Curran Associates Inc.},
address = {Red Hook, NY, USA},
pages = {9469–9481},
numpages = {13},
location = {Montr\'{e}al, Canada},
series = {NIPS'18}
}

@book{Mitzenmacher2005,
author = {Mitzenmacher, Michael and Upfal, Eli},
title = {Probability and Computing: Randomized Algorithms and Probabilistic Analysis},
year = {2005},
isbn = {0521835402},
publisher = {Cambridge University Press},
address = {USA}
}

@book{Massart2007,
  title={Concentration Inequalities and Model Selection: Ecole d'Et{\'e} de Probabilit{\'e}s de Saint-Flour XXXIII - 2003},
  author={Massart, P. and Picard, J.},
  isbn={9783540485032},
  lccn={2007921691},
  series={Lecture Notes in Mathematics},
  url={https://books.google.co.in/books?id=ZI67BQAAQBAJ},
  year={2007},
  publisher={Springer Berlin Heidelberg}
}

@article{Chernoff1952,
author = {Herman Chernoff},
title = {{A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations}},
volume = {23},
journal = {The Annals of Mathematical Statistics},
number = {4},
publisher = {Institute of Mathematical Statistics},
pages = {493 -- 507},
year = {1952},
doi = {10.1214/aoms/1177729330},
URL = {https://doi.org/10.1214/aoms/1177729330}
}

@article{Hoeffding1963,
 ISSN = {01621459},
 URL = {http://www.jstor.org/stable/2282952},
 author = {Wassily Hoeffding},
 journal = {Journal of the American Statistical Association},
 number = {301},
 pages = {13--30},
 publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
 title = {Probability Inequalities for Sums of Bounded Random Variables},
 volume = {58},
 year = {1963}
}

@inproceedings{Verma1988,
  title={Causal networks: semantics and expressiveness},
  author={Thomas Verma and Judea Pearl},
  booktitle={UAI},
  year={1988}
}

@inproceedings{Tian2002b,
author = {Tian, Jin and Pearl, Judea},
title = {A General Identification Condition for Causal Effects},
year = {2002},
isbn = {0262511290},
publisher = {American Association for Artificial Intelligence},
address = {USA},
abstract = {This paper concerns the assessment of the effects of actions or policy interventions from a combination of: (i) nonexperimental data, and (ii) substantive assumptions. The assumptions are encoded in the form of a directed acyclic graph, also called "causal graph", in which some variables are presumed to be unobserved. The paper establishes a necessary and sufficient criterion for the identifiability of the causal effects of a singleton variable on all other variables in the model, and a powerful sufficient criterion for the effects of a singleton variable on any set of variables.},
booktitle = {Eighteenth National Conference on Artificial Intelligence},
pages = {567–573},
numpages = {7},
location = {Edmonton, Alberta, Canada}
}

