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title={A note on two problems in connexion with graphs},
author={Dijkstra, EW},
journal={Numerische Mathematik},
volume={1},
pages={269--271},
year={1959},
publisher={Springer}
}
@article{latif2014banach,
title={Banach contraction principle and its generalizations},
author={Latif, Abdul},
journal={Topics in fixed point theory},
pages={33--64},
year={2014},
publisher={Springer}
}
@book{JacobsonMayne1970,
title={Differential Dynamic Programming},
author={Jacobson, Donald E. and Mayne, David Q.},
year={1970},
publisher={American Elsevier Publishing Company},
address={New York}
}
@inproceedings{todorov2005generalized,
title={A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems},
author={Todorov, Emanuel and Li, Weiwei},
booktitle={Proceedings of the 2005, American Control Conference, 2005.},
pages={300--306},
year={2005},
organization={IEEE}
}
@article{viterbi1967error,
title={Error bounds for convolutional codes and an asymptotically optimum decoding algorithm},
author={Viterbi, Andrew},
journal={IEEE transactions on Information Theory},
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pages={260--269},
year={1967},
publisher={IEEE}
}
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title={A formal basis for the heuristic determination of minimum cost paths},
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pages={100--107},
year={1968},
publisher={IEEE}
}
@inproceedings{ng1999policy,
title={Policy invariance under reward transformations: Theory and application to reward shaping},
author={Ng, Andrew Y and Harada, Daishi and Russell, Stuart},
booktitle={International Conference on Machine Learning},
volume={99},
pages={278--287},
year={1999}
}
@article{greensmith2004variance,
title={Variance Reduction Techniques for Gradient Estimates in Reinforcement Learning.},
author={Greensmith, Evan and Bartlett, Peter L and Baxter, Jonathan},
journal={Journal of Machine Learning Research},
volume={5},
number={9},
year={2004}
}
@inproceedings{scherrer2014local,
title={Local policy search in a convex space and conservative policy iteration as boosted policy search},
author={Scherrer, Bruno and Geist, Matthieu},
booktitle={Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2014, Nancy, France, September 15-19, 2014. Proceedings, Part III 14},
pages={35--50},
year={2014},
organization={Springer}
}
@article{schulman2017proximal,
title={Proximal policy optimization algorithms},
author={Schulman, John and Wolski, Filip and Dhariwal, Prafulla and Radford, Alec and Klimov, Oleg},
journal={arXiv preprint arXiv:1707.06347},
year={2017}
}
@article{KearnsS02,
author = {Michael J. Kearns and
Satinder P. Singh},
title = {Near-Optimal Reinforcement Learning in Polynomial Time},
journal = {Machine Learning},
volume = {49},
number = {2-3},
pages = {209--232},
year = {2002},
url = {https://doi.org/10.1023/A:1017984413808},
doi = {10.1023/A:1017984413808},
timestamp = {Sun, 28 May 2017 13:18:23 +0200},
biburl = {https://dblp.org/rec/bib/journals/ml/KearnsS02},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@book{kushner2003stochastic,
title={{Stochastic approximation and recursive algorithms and applications}},
author={Kushner, H.J. and Yin, G.},
year={2003},
publisher={Springer Verlag}
}
@book{borkar2009stochastic,
title={Stochastic approximation: a dynamical systems viewpoint},
author={Borkar, Vivek S},
volume={48},
year={2009},
publisher={Springer}
}
@article{munos2007performance,
title={Performance bounds in l\_p-norm for approximate value iteration},
author={Munos, R{\'e}mi},
journal={SIAM journal on control and optimization},
volume={46},
number={2},
pages={541--561},
year={2007},
publisher={SIAM}
}
@inproceedings{kearns2000bias,
title={Bias-Variance Error Bounds for Temporal Difference Updates.},
author={Kearns, Michael J and Singh, Satinder},
booktitle={COLT},
pages={142--147},
year={2000}
}
@inproceedings{KearnsS98a,
author = {Michael J. Kearns and
Satinder P. Singh},
title = {Finite-Sample Convergence Rates for Q-Learning and Indirect Algorithms},
booktitle = {Advances in Neural Information Processing Systems 11, {[NIPS} Conference,
Denver, Colorado, USA, November 30 - December 5, 1998]},
pages = {996--1002},
year = {1998}
}
@article{BrafmanT02,
author = {Ronen I. Brafman and
Moshe Tennenholtz},
title = {{R-MAX} - {A} General Polynomial Time Algorithm for Near-Optimal Reinforcement
Learning},
journal = {Journal of Machine Learning Research},
volume = {3},
pages = {213--231},
year = {2002},
url = {http://www.jmlr.org/papers/v3/brafman02a.html},
timestamp = {Thu, 05 Feb 2004 13:43:02 +0100},
biburl = {https://dblp.org/rec/bib/journals/jmlr/BrafmanT02},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{StrehlLL09,
author = {Alexander L. Strehl and
Lihong Li and
Michael L. Littman},
title = {Reinforcement Learning in Finite MDPs: {PAC} Analysis},
journal = {Journal of Machine Learning Research},
volume = {10},
pages = {2413--2444},
year = {2009},
url = {http://doi.acm.org/10.1145/1577069.1755867},
doi = {10.1145/1577069.1755867},
timestamp = {Mon, 13 Nov 2017 02:31:07 +0100},
biburl = {https://dblp.org/rec/bib/journals/jmlr/StrehlLL09},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Inbook{Li2012,
author="Li, Lihong",
title="Sample Complexity Bounds of Exploration",
bookTitle="Reinforcement Learning: State-of-the-Art",
year="2012",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="175--204",
abstract="Efficient exploration is widely recognized as a fundamental challenge inherent in reinforcement learning. Algorithms that explore efficiently converge faster to near-optimal policies. While heuristics techniques are popular in practice, they lack formal guarantees and may not work well in general. This chapter studies algorithms with polynomial sample complexity of exploration, both model-based and model-free ones, in a unified manner. These so-called PAC-MDP algorithms behave near-optimally except in a ``small'' number of steps with high probability. A new learning model known as KWIK is used to unify most existing model-based PAC-MDP algorithms for various subclasses of Markov decision processes.We also compare the sample-complexity framework to alternatives for formalizing exploration efficiency such as regret minimization and Bayes optimal solutions.",
isbn="978-3-642-27645-3",
doi="10.1007/978-3-642-27645-3_6",
url="https://doi.org/10.1007/978-3-642-27645-3_6"
}
@article{SinghS96,
author = {Satinder P. Singh and
Richard S. Sutton},
title = {Reinforcement Learning with Replacing Eligibility Traces},
journal = {Machine Learning},
volume = {22},
number = {1-3},
pages = {123--158},
year = {1996},
url = {https://doi.org/10.1023/A:1018012322525},
doi = {10.1023/A:1018012322525},
timestamp = {Sun, 28 May 2017 13:18:24 +0200},
biburl = {https://dblp.org/rec/bib/journals/ml/SinghS96},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Even-DarM03,
author = {Eyal Even{-}Dar and
Yishay Mansour},
title = {Learning Rates for Q-learning},
journal = {Journal of Machine Learning Research},
volume = {5},
pages = {1--25},
year = {2003},
url = {http://www.jmlr.org/papers/v5/evendar03a.html},
timestamp = {Thu, 05 Feb 2004 13:53:36 +0100},
biburl = {https://dblp.org/rec/bib/journals/jmlr/Even-DarM03},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{SeijenHWW09,
author = {Harm van Seijen and
Hado van Hasselt and
Shimon Whiteson and
Marco A. Wiering},
title = {A theoretical and empirical analysis of Expected Sarsa},
booktitle = {{IEEE} Symposium on Adaptive Dynamic Programming and Reinforcement
Learning, {ADPRL} 2009, Nashville, TN, USA, March 31 - April 1, 2009},
pages = {177--184},
year = {2009}
}
@book{SuttonB98,
author = {Richard S. Sutton and
Andrew G. Barto},
title = {Reinforcement learning - an introduction},
series = {Adaptive computation and machine learning},
publisher = {{MIT} Press},
year = {1998},
url = {http://www.worldcat.org/oclc/37293240},
isbn = {0262193981},
timestamp = {Wed, 26 Apr 2017 17:48:08 +0200},
biburl = {https://dblp.org/rec/bib/books/lib/SuttonB98},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Tesauro95,
author = {Gerald Tesauro},
title = {Temporal Difference Learning and TD-Gammon},
journal = {Commun. {ACM}},
volume = {38},
number = {3},
pages = {58--68},
year = {1995},
url = {http://doi.acm.org/10.1145/203330.203343},
doi = {10.1145/203330.203343},
timestamp = {Tue, 07 Jun 2011 16:52:36 +0200},
biburl = {https://dblp.org/rec/bib/journals/cacm/Tesauro95},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Tesauro02,
author = {Gerald Tesauro},
title = {Programming backgammon using self-teaching neural nets},
journal = {Artif. Intell.},
volume = {134},
number = {1-2},
pages = {181--199},
year = {2002},
url = {https://doi.org/10.1016/S0004-3702(01)00110-2},
doi = {10.1016/S0004-3702(01)00110-2},
timestamp = {Sat, 27 May 2017 14:24:43 +0200},
biburl = {https://dblp.org/rec/bib/journals/ai/Tesauro02},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{MnihKSRVBGRFOPB15,
author = {Volodymyr Mnih and
Koray Kavukcuoglu and
David Silver and
Andrei A. Rusu and
Joel Veness and
Marc G. Bellemare and
Alex Graves and
Martin A. Riedmiller and
Andreas Fidjeland and
Georg Ostrovski and
Stig Petersen and
Charles Beattie and
Amir Sadik and
Ioannis Antonoglou and
Helen King and
Dharshan Kumaran and
Daan Wierstra and
Shane Legg and
Demis Hassabis},
title = {Human-level control through deep reinforcement learning},
journal = {Nature},
volume = {518},
number = {7540},
pages = {529--533},
year = {2015},
url = {https://doi.org/10.1038/nature14236},
doi = {10.1038/nature14236},
timestamp = {Sat, 20 May 2017 00:24:51 +0200},
biburl = {https://dblp.org/rec/bib/journals/nature/MnihKSRVBGRFOPB15},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{KohlS04,
author = {Nate Kohl and
Peter Stone},
title = {Policy Gradient Reinforcement Learning for Fast Quadrupedal Locomotion},
booktitle = {Proceedings of the 2004 {IEEE} International Conference on Robotics
and Automation, {ICRA} 2004, April 26 - May 1, 2004, New Orleans,
LA, {USA}},
pages = {2619--2624},
year = {2004}
}
@article{SilverHMGSDSAPL16,
author = {David Silver and
Aja Huang and
Chris J. Maddison and
Arthur Guez and
Laurent Sifre and
George van den Driessche and
Julian Schrittwieser and
Ioannis Antonoglou and
Vedavyas Panneershelvam and
Marc Lanctot and
Sander Dieleman and
Dominik Grewe and
John Nham and
Nal Kalchbrenner and
Ilya Sutskever and
Timothy P. Lillicrap and
Madeleine Leach and
Koray Kavukcuoglu and
Thore Graepel and
Demis Hassabis},
title = {Mastering the game of {Go} with deep neural networks and tree search},
journal = {Nature},
volume = {529},
number = {7587},
pages = {484--489},
year = {2016},
url = {https://doi.org/10.1038/nature16961},
doi = {10.1038/nature16961},
timestamp = {Sat, 20 May 2017 00:24:51 +0200},
biburl = {https://dblp.org/rec/bib/journals/nature/SilverHMGSDSAPL16},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{AbbeelCN2010,
author = {Abbeel, Pieter and Coates, Adam and Ng, Andrew Y.},
title = {Autonomous Helicopter Aerobatics Through Apprenticeship Learning},
journal = {Int. J. Rob. Res.},
issue_date = {November 2010},
volume = {29},
number = {13},
month = nov,
year = {2010},
issn = {0278-3649},
pages = {1608--1639},
numpages = {32},
url = {http://dx.doi.org/10.1177/0278364910371999},
doi = {10.1177/0278364910371999},
acmid = {1894944},
publisher = {Sage Publications, Inc.},
address = {Thousand Oaks, CA, USA},
keywords = {Apprenticeship learning, autonomous flight, autonomous helicopter, helicopter aerobatics, learning from demonstrations},
}
@inproceedings{KearnsMN99,
author = {Michael J. Kearns and
Yishay Mansour and
Andrew Y. Ng},
title = {Approximate Planning in Large POMDPs via Reusable Trajectories},
booktitle = {Advances in Neural Information Processing Systems 12, {[NIPS} Conference,
Denver, Colorado, USA, November 29 - December 4, 1999]},
pages = {1001--1007},
year = {1999},
crossref = {DBLP:conf/nips/1999},
url = {http://papers.nips.cc/paper/1664-approximate-planning-in-large-pomdps-via-reusable-trajectories},
timestamp = {Thu, 11 Dec 2014 17:34:08 +0100},
biburl = {https://dblp.org/rec/bib/conf/nips/KearnsMN99},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{KearnsMN02,
author = {Michael J. Kearns and
Yishay Mansour and
Andrew Y. Ng},
title = {A Sparse Sampling Algorithm for Near-Optimal Planning in Large Markov
Decision Processes},
journal = {Machine Learning},
volume = {49},
number = {2-3},
pages = {193--208},
year = {2002},
url = {https://doi.org/10.1023/A:1017932429737},
doi = {10.1023/A:1017932429737},
timestamp = {Sun, 28 May 2017 13:18:23 +0200},
biburl = {https://dblp.org/rec/bib/journals/ml/KearnsMN02},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{PieterN04,
author = {Pieter Abbeel and
Andrew Y. Ng},
title = {Apprenticeship learning via inverse reinforcement learning},
booktitle = {Machine Learning, Proceedings of the Twenty-first International Conference
{(ICML} 2004), Banff, Alberta, Canada, July 4-8, 2004},
year = {2004}
}
@inproceedings{NgR00,
author = {Andrew Y. Ng and
Stuart J. Russell},
title = {Algorithms for Inverse Reinforcement Learning},
booktitle = {Proceedings of the Seventeenth International Conference on Machine
Learning {(ICML} 2000), Stanford University, Stanford, CA, USA, June
29 - July 2, 2000},
pages = {663--670},
year = {2000}
}
@article{TsitsiklisVR97,
author = {J. Tsitsiklis and B. Van Roy},
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doi = {https://doi.org/10.1016/S0004-3702(01)00129-1},
url = {https://www.sciencedirect.com/science/article/pii/S0004370201001291},
author = {Murray Campbell and A.Joseph Hoane and Feng-hsiung Hsu},
keywords = {Computer chess, Game tree search, Parallel search, Selective search, Search extensions, Evaluation function},
abstract = {Deep Blue is the chess machine that defeated then-reigning World Chess Champion Garry Kasparov in a six-game match in 1997. There were a number of factors that contributed to this success, including: •a single-chip chess search engine,•a massively parallel system with multiple levels of parallelism,•a strong emphasis on search extensions,•a complex evaluation function, and•effective use of a Grandmaster game database. This paper describes the Deep Blue system, and gives some of the rationale that went into the design decisions behind Deep Blue.}
}
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@comment{Papers for policy and value iteration discounted, chapter 5 discounted}
@inproceedings{LittmanDK95,
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Thomas L. Dean and
Leslie Pack Kaelbling},
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@article{MelekopoglouC94,
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@inproceedings{MansourS99,
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pages = {401--408},
year = {1999}
}
@inproceedings{Fearnley10,
author = {John Fearnley},
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booktitle = {Automata, Languages and Programming
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pages = {551--562},
year = {2010}
}
@inproceedings{HollandersDJ12,
author = {Romain Hollanders and
Jean{-}Charles Delvenne and
Rapha{\"{e}}l M. Jungers},
title = {The complexity of Policy Iteration is exponential for discounted Markov
Decision Processes},
booktitle = {Proceedings of the 51th {IEEE} Conference on Decision and Control (CDC)},
pages = {5997--6002},
year = {2012}
}
@article{Ye11,
author = {Yinyu Ye},
title = {The Simplex and Policy-Iteration Methods Are Strongly Polynomial for the Markov Decision Problem with a Fixed Discount Rate},
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volume = {36},
number = {4},
pages = {593--603},
year = {2011}
}
@article{HansenMZ13,
author = {Thomas Dueholm Hansen and
Peter Bro Miltersen and
Uri Zwick},
title = {Strategy Iteration Is Strongly Polynomial for 2-Player Turn-Based
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journal = {J. {ACM}},
volume = {60},
number = {1},
pages = {1:1--1:16},
year = {2013}
}
@article{MadaniTZ10,
author = {Omid Madani and Mikkel Thorup and Uri Zwick},
title = {Discounted deterministic Markov decision processes and discounted all-pairs shortest paths},
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volume = {6},
number = {2},
pages = {33:1--33:25},
year = {2010}
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@inproceedings{PostY13,
author = {Ian Post and Yinyu Ye},
title = {The simplex method is strongly polynomial for deterministic Markov decision processes},
booktitle = {Symposium on Discrete Algorithms (SODA) },
pages = {1465--1473},
publisher = {{SIAM}},
year = {2013}
}
@article{blackwell1965discounted,
title={Discounted dynamic programming},
author={Blackwell, David},
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number={1},
pages={226--235},
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publisher={JSTOR}
}
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publisher={INFORMS}
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@comment{Generative model}
@article{AzarMK13,
author = {Mohammad Gheshlaghi Azar and
R{\'{e}}mi Munos and
Hilbert J. Kappen},
title = {Minimax {PAC} bounds on the sample complexity of reinforcement learning
with a generative model},
journal = {Mach. Learn.},
volume = {91},
number = {3},
pages = {325--349},
year = {2013}
}
@inproceedings{DannB15,
author = {Christoph Dann and
Emma Brunskill},
title = {Sample Complexity of Episodic Fixed-Horizon Reinforcement Learning},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2015}
}
@inproceedings{DannLB17,
author = {Christoph Dann and
Tor Lattimore and
Emma Brunskill},
title = {Unifying {PAC} and Regret: Uniform {PAC} Bounds for Episodic Reinforcement Learning},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2017}
}
@inproceedings{AgarwalKY20,
author = {Alekh Agarwal and
Sham M. Kakade and
Lin F. Yang},
editor = {Jacob D. Abernethy and
Shivani Agarwal},
title = {Model-Based Reinforcement Learning with a Generative Model is Minimax
Optimal},
booktitle = {Conference on Learning Theory, {COLT} },
year = {2020}
}
@phdthesis{Kakade2003,
author = "Sham Kakade",
title = "On the sample complexity of reinforcement learning",
school = "University College London",
year = "2003"
}
@inproceedings{kakade2002approximately,
title={Approximately optimal approximate reinforcement learning},
author={Kakade, Sham and Langford, John},
booktitle={Proceedings of the Nineteenth International Conference on Machine Learning},
pages={267--274},
year={2002}
}
@article{StrehlL08,
author = {Alexander L. Strehl and
Michael L. Littman},
title = {An analysis of model-based Interval Estimation for Markov Decision
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journal = {J. Comput. Syst. Sci.},
volume = {74},
number = {8},
pages = {1309--1331},
year = {2008}
}
@inproceedings{Fiechter94,
author = {Claude{-}Nicolas Fiechter},
title = {Efficient Reinforcement Learning},
booktitle = {Computational
Learning Theory (COLT) },
year = {1994}
}
@inproceedings{KaufmannMDJLV21,
author = {Emilie Kaufmann and
Pierre M{\'{e}}nard and
Omar Darwiche Domingues and
Anders Jonsson and
Edouard Leurent and
Michal Valko},
title = {Adaptive Reward-Free Exploration},
booktitle = {Algorithmic Learning Theory (ALT)},
year = {2021}
}
@inproceedings{JinKSY20,
author = {Chi Jin and
Akshay Krishnamurthy and
Max Simchowitz and
Tiancheng Yu},
title = {Reward-Free Exploration for Reinforcement Learning},
booktitle = { International Conference on Machine Learning (ICML)},
year = {2020}
}
@inproceedings{MenardDJKLV21,
author = {Pierre M{\'{e}}nard and
Omar Darwiche Domingues and
Anders Jonsson and
Emilie Kaufmann and
Edouard Leurent and
Michal Valko},
title = {Fast active learning for pure exploration in reinforcement learning},
booktitle = { International Conference on Machine Learning (ICML)},
year = {2021}
}
@inproceedings{SzitaS10,
author = {Istvan Szita and
Csaba Szepesv{\'{a}}ri},
title = {Model-based reinforcement learning with nearly tight exploration complexity
bounds},
booktitle = { International Conference on Machine Learning (ICML)},
year = {2010}
}
@inproceedings{SzitaL09,
author = {Istvan Szita and
Andr{\'{a}}s L{\"{o}}rincz},
editor = {Andrea Pohoreckyj Danyluk and
L{\'{e}}on Bottou and
Michael L. Littman},
title = {Optimistic initialization and greediness lead to polynomial time learning
in factored MDPs},
booktitle = { International Conference on Machine Learning (ICML)},
year = {2009}
}
@article{LattimoreH14a,
author = {Tor Lattimore and
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title = {Near-optimal {PAC} bounds for discounted MDPs},
journal = {Theor. Comput. Sci.},
volume = {558},
pages = {125--143},
year = {2014}
}
@comment{Model free}
@article{Sutton88,
author = {Richard S. Sutton},
title = {Learning to Predict by the Methods of Temporal Differences},
journal = {Mach. Learn.},
volume = {3},
pages = {9--44},
year = {1988},
comment ={Tabular TD(0)}
}
@article{WatkinsD92,
author = {Christopher J. C. H. Watkins and
Peter Dayan},
title = {Q-Learning},
journal = {Mach. Learn.},
volume = {8},
pages = {279--292},
year = {1992},
url = {https://doi.org/10.1007/BF00992698},
doi = {10.1007/BF00992698},
timestamp = {Fri, 27 Mar 2020 08:37:06 +0100},
biburl = {https://dblp.org/rec/journals/ml/WatkinsD92.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Dayan92,
author = {Peter Dayan},
title = {The Convergence of TD(lambda) for General lambda},
journal = {Mach. Learn.},
volume = {8},
pages = {341--362},
year = {1992},
url = {https://doi.org/10.1007/BF00992701},
doi = {10.1007/BF00992701},
timestamp = {Fri, 27 Mar 2020 08:37:06 +0100},
biburl = {https://dblp.org/rec/journals/ml/Dayan92.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{JaakkolaJS94,
author = {Tommi S. Jaakkola and
Michael I. Jordan and
Satinder P. Singh},
title = {On the Convergence of Stochastic Iterative Dynamic Programming Algorithms},
journal = {Neural Comput.},