@inproceedings{abeille2017linear,
  title={Linear {T}hompson {S}ampling revisited},
  author={Abeille, Marc and Lazaric, Alessandro},
  booktitle={Artificial Intelligence and Statistics},
  pages={176--184},
  year={2017},
  organization={PMLR}
}


@inproceedings{dann2019policy,
  title={Policy certificates: {T}owards accountable reinforcement learning},
  author={Dann, Christoph and Li, Lihong and Wei, Wei and Brunskill, Emma},
  booktitle={International Conference on Machine Learning},
  pages={1507--1516},
  year={2019},
  organization={PMLR}
}



@article{osband2019deep,
  title={Deep Exploration via Randomized Value Functions.},
  author={Osband, Ian and Van Roy, Benjamin and Russo, Daniel J and Wen, Zheng and others},
  journal={J. Mach. Learn. Res.},
  volume={20},
  number={124},
  pages={1--62},
  year={2019}
}

@article{thompson1933likelihood,
  title={On the likelihood that one unknown probability exceeds another in view of the evidence of two samples},
  author={Thompson, William R},
  journal={Biometrika},
  volume={25},
  number={3-4},
  pages={285--294},
  year={1933},
  publisher={Oxford University Press}
}

@inproceedings{hu2022near,
  title={{N}ear-optimal {T}hompson {S}ampling-based algorithms for differentially private stochastic bandits},
  author={Hu, Bingshan and Hegde, Nidhi},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={844--852},
  year={2022},
  organization={PMLR}
}



@inproceedings{xiong2021near,
  title={{N}ear-Optimal Randomized Exploration for Tabular {M}arkov Decision Processes},
  author={Xiong, Zhihan and Shen, Ruoqi and Cui, Qiwen and Fazel, Maryam and Du, Simon Shaolei},
  booktitle={Advances in Neural Information Processing Systems},
  year={2022}
}


@inproceedings{jin2021mots,
  title={{MOTS}: {M}inimax optimal {T}hompson {S}ampling},
  author={Jin, Tianyuan and Xu, Pan and Shi, Jieming and Xiao, Xiaokui and Gu, Quanquan},
  booktitle={International Conference on Machine Learning},
  pages={5074--5083},
  year={2021},
  organization={PMLR}
}


@inproceedings{kaufmann2012thompson,
  title={{T}hompson {S}ampling: {A}n asymptotically optimal finite-time analysis},
  author={Kaufmann, Emilie and Korda, Nathaniel and Munos, R{\'e}mi},
  booktitle={Algorithmic Learning Theory: 23rd International Conference, ALT 2012, Lyon, France, October 29-31, 2012. Proceedings 23},
  pages={199--213},
  year={2012},
  organization={Springer}
}

@article{auer2002finite,
  title={Finite-time analysis of the multi-armed bandit problem},
  author={Auer, Peter and Cesa-Bianchi, Nicolo and Fischer, Paul},
  journal={Machine learning},
  volume={47},
  pages={235--256},
  year={2002},
  publisher={Springer}
}

@misc{agrawalnear,
  author = {Agrawal, Shipra and Goyal, Navin},
  title = {{N}ear-optimal Regret Bounds for {T}hompson {S}ampling},
  howpublished = "\url{http://www.columbia.edu/~sa3305/papers/j3-corrected.pdf}",
  year = {2017}, 
}



@inproceedings{kveton2019garbage,
  title={Garbage in, reward out: {B}ootstrapping exploration in multi-armed bandits},
  author={Kveton, Branislav and Szepesvari, Csaba and Vaswani, Sharan and Wen, Zheng and Lattimore, Tor and Ghavamzadeh, Mohammad},
  booktitle={International Conference on Machine Learning},
  pages={3601--3610},
  year={2019},
  organization={PMLR}
}


@inproceedings{pacchiano2021towards,
  title={Towards tractable optimism in model-based reinforcement learning},
  author={Pacchiano, Aldo and Ball, Philip and Parker-Holder, Jack and Choromanski, Krzysztof and Roberts, Stephen},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={1413--1423},
  year={2021},
  organization={PMLR}
}


@inproceedings{osband2016generalization,
  title={Generalization and exploration via randomized value functions},
  author={Osband, Ian and Van Roy, Benjamin and Wen, Zheng},
  booktitle={International Conference on Machine Learning},
  pages={2377--2386},
  year={2016},
  organization={PMLR}
}


@inproceedings{zanette2019tighter,
  title={Tighter problem-dependent regret bounds in reinforcement learning without domain knowledge using value function bounds},
  author={Zanette, Andrea and Brunskill, Emma},
  booktitle={International Conference on Machine Learning},
  pages={7304--7312},
  year={2019},
  organization={PMLR}
}



@inproceedings{tiapkin2022optimistic,
  title={Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guarantees},
  author={Tiapkin, Daniil and Belomestny, Denis and Calandriello, Daniele and Moulines, Eric and Munos, Remi and Naumov, Alexey and Rowland, Mark and Valko, Michal and MENARD, Pierre},
  booktitle={Advances in Neural Information Processing Systems},
  year={2022}
}

@inproceedings{tiapkin2022dirichlet,
  title={From {D}irichlet to {R}ubin: {O}ptimistic Exploration in {RL} without Bonuses},
  author={Tiapkin, Daniil and Belomestny, Denis and Moulines, {\'E}ric and Naumov, Alexey and Samsonov, Sergey and Tang, Yunhao and Valko, Michal and M{\'e}nard, Pierre},
  booktitle={International Conference on Machine Learning},
  pages={21380--21431},
  year={2022},
  organization={PMLR}
}


@article{zhang2020almost,
  title={Almost optimal model-free reinforcement learning via reference-advantage decomposition},
  author={Zhang, Zihan and Zhou, Yuan and Ji, Xiangyang},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={15198--15207},
  year={2020}
}

@inproceedings{azar2017minimax,
  title={Minimax regret bounds for reinforcement learning},
  author={Azar, Mohammad Gheshlaghi and Osband, Ian and Munos, R{\'e}mi},
  booktitle={International Conference on Machine Learning},
  pages={263--272},
  year={2017},
  organization={PMLR}
}

@article{may2012optimistic,
  title={Optimistic {B}ayesian sampling in contextual-bandit problems},
  author={May, Benedict C and Korda, Nathan and Lee, Anthony and Leslie, David S},
  journal={Journal of Machine Learning Research},
  volume={13},
  pages={2069--2106},
  year={2012}
}


@article{chapelle2011empirical,
  title={An empirical evaluation of {T}hompson {S}ampling},
  author={Chapelle, Olivier and Li, Lihong},
  journal={Advances in neural information processing systems},
  volume={24},
  year={2011}
}
@inproceedings{agrawal2021improved,
  title={Improved worst-case regret bounds for randomized least-squares value iteration},
  author={Agrawal, Priyank and Chen, Jinglin and Jiang, Nan},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  number={8},
  pages={6566--6573},
  year={2021}
}

@article{asmuth2012bayesian,
  title={A {B}ayesian sampling approach to exploration in reinforcement learning},
  author={Asmuth, John and Li, Lihong and Littman, Michael L and Nouri, Ali and Wingate, David},
  journal={arXiv preprint arXiv:1205.2664},
  year={2012}
}




@article{russo2019worst,
  title={Worst-case regret bounds for exploration via randomized value functions},
  author={Russo, Daniel},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  year={2019}
}


@article{dann2017unifying,
  title={Unifying {PAC} and regret: {U}niform {PAC} bounds for episodic reinforcement learning},
  author={Dann, Christoph and Lattimore, Tor and Brunskill, Emma},
  journal={Advances in Neural Information Processing Systems},
  volume={30},
  year={2017}
}






@article{agrawal2017posterior,
  title={Posterior sampling for reinforcement learning: {W}orst-case regret bounds},
  author={Agrawal, Shipra and Jia, Randy},
  journal={arXiv preprint arXiv:1705.07041},
  year={2020}
}

