%% Theory of Computing
%% File: v018a009.bib
%% Publication date: April 30, 2022
%% Authors: Zongchen Chen and Santosh S. Vempala
%
%
%
%
%%
@misc{LSV18,
author={Lee, Yin Tat and Song, Zhao and Vempala, Santosh S.},
title={Algorithmic Theory of {ODE}s and Sampling from well-conditioned Logconcave Densities},
eprint = {1812.06243},
year={2018},
}
%
%
@inproceedings{LV18,
title={Convergence rate of {R}iemannian {H}amiltonian {M}onte {C}arlo and faster polytope volume computation},
author={Lee, Yin Tat and Vempala, Santosh S.},
crossref = {pstoc18},
pages={1115--1121},
doi = {10.1145/3188745.3188774},
eprint={1710.06261},
}
%
@inproceedings{MS19,
title={Mixing of {H}amiltonian {M}onte {C}arlo on strongly log-concave distributions 2: {N}umerical integrators},
author={Mangoubi, Oren and Smith, Aaron},
crossref = {paistats19},
pages={89:586--595},
note = {\href{https://proceedings.mlr.press/v89/mangoubi19a.html}{PMLR}},
}
%
@misc{MS17,
title={Mixing of {H}amiltonian {M}onte {C}arlo on strongly log-concave distributions 1: Continuous dynamics},
author={Mangoubi, Oren and Smith, Aaron},
eprint={1708.07114},
year={2017},
}
%
@inproceedings{MV18,
author={Mangoubi, Oren and Vishnoi, Nisheeth},
title={Dimensionally tight bounds for second-order {H}amiltonian {M}onte {C}arlo},
crossref = {pnips18},
pages={6027--6037},
note = {\href{https://papers.nips.cc/paper/2018/hash/e07bceab69529b0f0b43625953fbf2a0-Abstract.html}{NeurIPS}},
}
%
%
@article{O09,
	title={Ricci curvature of {M}arkov chains on metric spaces},
	author={Ollivier, Yann},
	journal=jfa,
	volume={256},
	number={3},
	pages={810--864},
	year={2009},
	doi = {10.1016/j.jfa.2008.11.001},
        eprint = {math/0701886},
}
%
%
%
@article{D17,
	title={Theoretical guarantees for approximate sampling from smooth and log-concave densities},
	author={Dalalyan, Arnak S.},
	journal= JRoyalStatSocB,
	volume={79},
	number={3},
	pages={651--676},
	year={2017},
        doi={10.1111/rssb.12183},
        eprint={1412.7392},
}
%
%
%
%
@article{DK19,
title={User-friendly guarantees for the {L}angevin {M}onte {C}arlo with inaccurate gradient},
author={Dalalyan, Arnak S. and Karagulyan, Avetik},
journal = StochProcAppl,
year={2019},
volume = {129},
number = {12},
pages = {5278--5311},
doi={10.1016/j.spa.2019.02.016},
eprint={1710.00095},
}
%
%
%
@inproceedings{ZLC17,
title={A Hitting Time Analysis of Stochastic Gradient {L}angevin Dynamics},
author={Zhang, Yuchen and Liang, Percy S. and Charikar, Moses},
crossref={pcolt17},
pages = {65:1980--2022},
note = {\href{http://proceedings.mlr.press/v65/zhang17b.html}{PMLR}},
eprint = {1702.05575},                  
}

@inproceedings{RRT17,
title={Non-convex learning via Stochastic Gradient {L}angevin Dynamics: {A} nonasymptotic analysis},
author={Raginsky, Maxim and Rakhlin, Alexander and Telgarsky, Matus},
crossref = {pcolt17},
pages = {65:1--30},
note = {\href{http://proceedings.mlr.press/v65/raginsky17a.html}{PMLR}},
eprint = {1702.03849},
}
%
@misc{DRD18-arxiv,
title={On sampling from a log-concave density using kinetic {L}angevin diffusions},
author={Dalalyan, Arnak S. and Riou-Durand, Lionel},
eprint={1807.09382},
year={2018},
}
%
%
@article{DRD18, 
title = {On sampling from a log-concave density using kinetic {L}angevin diffusions},
author = {Arnak S. Dalalyan and Lionel Riou-Durand},
journal = {Bernoulli},
volume = {26},
number = {3},
year={2020},
pages = {1956--1988},
doi = {10.3150/19-BEJ1178},
eprint={1807.09382},
}
%
%
%
@inproceedings{CCBJ,
title={Underdamped {L}angevin {MCMC}: {A} non-asymptotic analysis},
author={Cheng, Xiang and Chatterji, Niladri S. and Bartlett, Peter L. and Jordan, Michael I.},
crossref = {pcolt18},
pages = {75:1--24},
note = {\href{https://proceedings.mlr.press/v75/cheng18a.html}{PMLR}},
eprint = {1707.03663},
}
%
%
@misc{CCABJ18,
title={Sharp convergence rates for {L}angevin dynamics in the nonconvex setting},
author={Cheng, Xiang and Chatterji, Niladri S. and Abbasi-Yadkori, Yasin and Bartlett, Peter L. and Jordan, Michael I.},
eprint={1805.01648},
year={2018},
}
%
%
%
@inproceedings{CFMBJ18,
title={On the theory of variance reduction for stochastic gradient {M}onte {C}arlo},
author={Chatterji, Niladri S. and Flammarion, Nicolas and Ma, Yi-An and Bartlett, Peter L. and Jordan, Michael I.},
crossref = {picml18},
pages={80:764--773},
note = {\href{http://proceedings.mlr.press/v80/chatterji18a.html}{PMLR}},
eprint = {1802.05431},
}
%
%
%
@article{DCWY18,
title={Log-concave sampling: {M}etropolis-{H}astings algorithms are fast!},
author={Dwivedi, Raaz and Chen, Yuansi and Wainwright, Martin J. and Yu, Bin},
journal = jmlr,
year = {2019},
volume = {20},
number = {183},
pages = {1--42},
note = {\href{https://jmlr.org/papers/v20/19-306.html}{JMLR},
\prelim \href{https://proceedings.mlr.press/v75/dwivedi18a.html}{COLT'18}},
eprint = {1801.02309},
}
%
%
%
@inproceedings{DCWY18-conf,
title={Log-concave sampling: {M}etropolis-{H}astings algorithms are fast!},
author={Dwivedi, Raaz and Chen, Yuansi and Wainwright, Martin J. and Yu, Bin},
crossref = {pcolt18},
pages = {75:793--797},
note = {\href{https://proceedings.mlr.press/v75/dwivedi18a.html}{PMLR}},
eprint = {1801.02309},
}
%
%
%
@inproceedings{W18,
title={Sampling as optimization in the space of measures: {T}he {L}angevin dynamics as a composite optimization problem},
author={Wibisono, Andre},
crossref = {pcolt18},
pages = {75:2093--3027},
note = {\href{http://proceedings.mlr.press/v75/wibisono18a.html}{PMLR}},
eprint = {1802.08089},
}
%
@misc{MCCFBJ19,
title={Is There an Analog of {N}esterov Acceleration for {MCMC}?},
author={Ma, Yi-An and Chatterji, Niladri and Cheng, Xiang and Flammarion, Nicolas and Bartlett, Peter and Jordan, Michael I.},
eprint = {1902.00996},
year={2019},
}
%
@inproceedings{SRH14,
title={Positive curvature and {H}amiltonian {M}onte {C}arlo},
author={Seiler, Christof and Rubinstein-Salzedo, Simon and Holmes, Susan},
crossref = {pnips14},
pages={586--594},
note = {\href{https://papers.nips.cc/paper/2014/hash/beed13602b9b0e6ecb5b568ff5058f07-Abstract.html}{NIPS}},
}
%
@InProceedings{AK91,
Title = {Sampling and integration of near log-concave functions},
Author = {Applegate, David and Kannan, Ravi},
crossref = {pstoc91}, 
Pages    = {156--163},
doi = {10.1145/103418.103439},
}

@comment{doi added},
@InProceedings{LV06,
Title = {Fast Algorithms for Logconcave Functions: {S}ampling, Rounding, Integration and Optimization},
Author = {Lov{\'a}sz, L{\'a}szl{\'o} and Vempala, Santosh S.},
crossref = {pfocs06},
Pages    = {57--68},
doi = {10.1109/FOCS.2006.28},
}
%
%
%
@InProceedings{conf-version,
author ={Zongchen Chen and Santosh S. Vempala},
title ={Optimal Convergence Rate of {H}amiltonian  {M}onte {C}arlo for Strongly Logconcave Distributions},
crossref = {prandom19},
pages ={64:1--12},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.64},
eprint = {1905.02313},
}
%
@misc{CDWY19-orig,
title={Fast mixing of {M}etropolized {H}amiltonian {M}onte {C}arlo: {B}enefits of multi-step gradients},
author={Chen, Yuansi and Dwivedi, Raaz and Wainwright, Martin J. and Yu, Bin},
eprint ={1905.12247},
year={2019},
}
%
@article{CDWY19,
title={Fast mixing of {M}etropolized {H}amiltonian {M}onte {C}arlo: {B}enefits of multi-step gradients},
author={Chen, Yuansi and Dwivedi, Raaz and Wainwright, Martin J. and Yu, Bin},
journal = jmlr,
year={2019},
volume = {21},
number = {92},
pages = {1--72},
note = {\href{https://jmlr.org/papers/v21/19-441.html}{JMLR}},
eprint ={1905.12247},
}
%
@inproceedings{VW19,
title = {Rapid Convergence of the Unadjusted {L}angevin Algorithm: {I}soperimetry Suffices},
author = {Vempala, Santosh S. and Wibisono, Andre},
crossref = {pnips19},
pages = {8094--8106},
note = {\href{https://proceedings.neurips.cc/paper/2019/hash/65a99bb7a3115fdede20da98b08a370f-Abstract.html}{NeurIPS}},
eprint ={1903.08568},
}
%
@inproceedings{SL19,
title = {The {R}andomized {M}idpoint {M}ethod for Log-Concave Sampling},
author = {Shen, Ruoqi and Lee, Yin Tat},
crossref = {pnips19},
pages = {2100--2111},
note = {\href{https://proceedings.neurips.cc/paper/2019/hash/eb86d510361fc23b59f18c1bc9802cc6-Abstract.html}{NeurIPS}},
eprint = {1909.05503},
}
%
@misc{W19,
title={Proximal {L}angevin algorithm: {R}apid convergence under isoperimetry},
author={Wibisono, Andre},
eprint = {1911.01469},
year={2019},
}
%
@misc{LST20-orig,
title={Logsmooth Gradient Concentration and Tighter Runtimes for {M}etropolized {H}amiltonian {M}onte {C}arlo},
author={Lee, Yin Tat and Shen, Ruoqi and Tian, Kevin},
eprint = {2002.04121},
year={2020},
}
%
@inproceedings{LST20,
title={Logsmooth Gradient Concentration and Tighter Runtimes for {M}etropolized {H}amiltonian {M}onte {C}arlo},
author={Lee, Yin Tat and Shen, Ruoqi and Tian, Kevin},
crossref = {pcolt20},
pages = {125:2565-2597},
note = {\href{http://proceedings.mlr.press/v125/lee20b.html}{PMLR}},
eprint = {2002.04121},
}
%
@misc{DRK19,
title={Bounding the error of discretized {L}angevin algorithms for non-strongly log-concave targets},
author={Dalalyan, Arnak S. and Riou-Durand, Lionel and Karagulyan, Avetik},
eprint={1906.08530},
year={2019}
}
%
%
%
@inproceedings{GLL20,
title={Estimating Normalizing Constants for Log-Concave Distributions: {A}lgorithms and Lower Bounds},
author={Ge, Rong and Lee, Holden and Lu, Jianfeng},
crossref = {pstoc20},
pages = {579--586},
doi = {10.1145/3357713.3384289},
eprint ={1911.03043},
}
%
@misc{MMWBJ19-orig,
title={High-Order {L}angevin Diffusion Yields an Accelerated {MCMC} Algorithm},
author={Mou, Wenlong and Ma, Yi-An and Wainwright, Martin J. and Bartlett, Peter L. and Jordan, Michael I.},
eprint = {1908.10859},
year={2019},
}
%
@article{MMWBJ19,
title={High-Order {L}angevin Diffusion Yields an Accelerated {MCMC} Algorithm},
author={Mou, Wenlong and Ma, Yi-An and Wainwright, Martin J. and Bartlett, Peter L. and Jordan, Michael I.},
journal = jmlr,
volume = {22},
number = {42},
pages = {1--41},
year={2021},
note = {\href{https://jmlr.org/papers/v22/20-576.html}{JMLR}},
eprint = {1908.10859},
}
%
@misc{CLW19,
title={On explicit ${L}^2$-convergence rate estimate for underdamped {L}angevin dynamics},
author={Cao, Yu and Lu, Jianfeng and Wang, Lihan},
eprint={1908.04746},
year={2019},
}
%
@misc{Zhou18-orig,
title={On the {F}enchel {D}uality between Strong Convexity and {L}ipschitz {C}ontinuous {G}radient},
author={Zhou, Xingyu},
eprint = {1803.06573},
year={2018}
}
%
%
@misc{Zhou18,
title={On the {F}enchel {D}uality between Strong Convexity and {L}ipschitz {C}ontinuous {G}radient},
author={Zhou, Xingyu},
year={2018},
note = {\href{https://xingyuzhou.org/talks/Fenchel_duality.pdf}{SLIDES}},
eprint = {1803.06573},
}
