% Encoding: UTF-8


@InProceedings{sigma_k,
  author    = {Gorbunov, Eduard and Hanzely, Filip and Richt\'{a}rik, Peter},
  title     = {A Unified Theory of {SGD}: Variance Reduction, Sampling, Quantization and Coordinate Descent},
  booktitle = {The 23rd International Conference on Artificial Intelligence and Statistics},
  year      = {2020},
}

@article{huang2021improved,
	title={An Improved Analysis and Rates for Variance Reduction under Without-replacement Sampling Orders},
	author={Huang, Xinmeng and Yuan, Kun and Mao, Xianghui and Yin, Wotao},
	journal={Advances in Neural Information Processing Systems},
	volume={34},
	year={2021}
}


@article{chang2011libsvm,
  title={LIBSVM: a library for support vector machines},
  author={Chang, Chih-Chung and Lin, Chih-Jen},
  journal={ACM Transactions on Intelligent Systems and Technology (TIST)},
  volume={2},
  number={3},
  pages={1--27},
  year={2011},
  publisher={ACM New York, NY, USA}
}

@inproceedings{kovalev2020don,
  title={Don’t jump through hoops and remove those loops: {SVRG} and Katyusha are better without the outer loop},
  author={Kovalev, Dmitry and Horv{\'a}th, Samuel and Richt{\'a}rik, Peter},
  booktitle={Algorithmic Learning Theory},
  pages={451--467},
  year={2020},
  organization={PMLR}
}

@article{sayed2014adaptation,
  title={Adaptive networks},
  author={Sayed, Ali H},
  journal={Proceedings of the IEEE},
  volume={102},
  number={4},
  pages={460--497},
  year={2014},
  publisher={IEEE}
}

@inproceedings{shamir2016without,
  title={Without-replacement sampling for stochastic gradient methods},
  author={Shamir, Ohad},
  booktitle={Proceedings of the 30th International Conference on Neural Information Processing Systems},
  pages={46--54},
  year={2016}
}

@article{park2020linear,
  title={Linear convergence of cyclic {SAGA}},
  author={Park, Youngsuk and Ryu, Ernest K},
  journal={Optimization Letters},
  volume={14},
  number={6},
  pages={1583--1598},
  year={2020},
  publisher={Springer}
}


@article{gurbuzbalaban2019random,
  title={Why random reshuffling beats stochastic gradient descent},
  author={G{\"u}rb{\"u}zbalaban, Mert and Ozdaglar, Asu and Parrilo, Pablo A},
  journal={Mathematical Programming},
  pages={1--36},
  year={2019},
  publisher={Springer}
}

@article{mishchenko2020random,
  title={Random reshuffling: Simple analysis with vast improvements},
  author={Mishchenko, Konstantin and Khaled, Ahmed and Richt{\'a}rik, Peter},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  year={2020}
}

@article{recht2013parallel,
  title={Parallel stochastic gradient algorithms for large-scale matrix completion},
  author={Recht, Benjamin and R{\'e}, Christopher},
  journal={Mathematical Programming Computation},
  volume={5},
  number={2},
  pages={201--226},
  year={2013},
  publisher={Springer}
}

@article{bottou2009curiously,
  title={Curiously Fast Convergence of some Stochastic Gradient Descent Algorithms},
  author={Bottou, L{\'e}on},
  year={2009},
  publisher={Citeseer}
}

@article{gower2020variance,
  title={Variance-reduced methods for machine learning},
  author={Gower, Robert M and Schmidt, Mark and Bach, Francis and Richt{\'a}rik, Peter},
  journal={Proceedings of the IEEE},
  volume={108},
  number={11},
  pages={1968--1983},
  year={2020},
  publisher={IEEE}
}go

@article{roux2012stochastic,
  title={A stochastic gradient method with an exponential convergence rate for finite training sets},
  author={Roux, Nicolas Le and Schmidt, Mark and Bach, Francis},
  journal={arXiv preprint arXiv:1202.6258},
  year={2012}
}

@article{defazio2014saga,
  title={{SAGA} : A fast incremental gradient method with support for non-strongly convex composite objectives},
  author={Defazio, Aaron and Bach, Francis and Lacoste-Julien, Simon},
  journal={arXiv preprint arXiv:1407.0202},
  year={2014}
}

@article{johnson2013accelerating,
  title={Accelerating stochastic gradient descent using predictive variance reduction},
  author={Johnson, Rie and Zhang, Tong},
  journal={Advances in Neural Information Processing Systems},
  volume={26},
  pages={315--323},
  year={2013},
  publisher={Citeseer}
}
@InProceedings{pmlr-v32-defazio14,
  title = 	 {Finito: A faster, permutable incremental gradient method for big data problems},
  author = 	 {Aaron Defazio and Justin Domke and  Caetano},
  booktitle = 	 {Proceedings of the 31st International Conference on Machine Learning},
  pages = 	 {1125--1133},
  year = 	 {2014},
  editor = 	 {Eric P. Xing and Tony Jebara},
  volume = 	 {32},
  number =       {2},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Bejing, China},
  month = 	 {22--24 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v32/defazio14.pdf},
  abstract = 	 {Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical convergence rate four times faster than existing methods, for sums with sufficiently many terms. This method is also amendable to a sampling without replacement scheme that in practice gives further speed-ups. We give empirical results showing state of the art performance.}
}
@inproceedings{hardt2016train,
  title={Train faster, generalize better: Stability of stochastic gradient descent},
  author={Hardt, Moritz and Recht, Ben and Singer, Yoram},
  booktitle={International Conference on Machine Learning},
  pages={1225--1234},
  year={2016},
  organization={PMLR}
}

@book{bertsekas1996neuro,
  title={Neuro-dynamic programming},
  author={Bertsekas, Dimitri P and Tsitsiklis, John N},
  year={1996},
  publisher={Athena Scientific}
}

@article{needell2013stochastic,
  title={Stochastic gradient descent, weighted sampling, and the randomized {K}aczmarz algorithm},
  author={Needell, Deanna and Srebro, Nathan and Ward, Rachel},
  journal={arXiv preprint arXiv:1310.5715},
  year={2013}
}

@inproceedings{gower2019sgd,
  title={{SGD}: {G}eneral analysis and improved rates},
  author={Gower, Robert Mansel and Loizou, Nicolas and Qian, Xun and Sailanbayev, Alibek and Shulgin, Egor and Richt{\'a}rik, Peter},
  booktitle={International Conference on Machine Learning},
  pages={5200--5209},
  year={2019},
  organization={PMLR}
}

@article{robbins1951stochastic,
  title={A stochastic approximation method},
  author={Robbins, Herbert and Monro, Sutton},
  journal={The Annals of Mathematical Statistics},
  pages={400--407},
  year={1951},
  publisher={JSTOR}
}


@article{mokhtari2018surpassing,
  title={Surpassing gradient descent provably: A cyclic incremental method with linear convergence rate},
  author={Mokhtari, Aryan and G\"{u}rb\"{u}zbalaban, Mert and Ribeiro, Alejandro},
  journal={SIAM Journal on Optimization},
  volume={28},
  number={2},
  pages={1420--1447},
  year={2018},
  publisher={SIAM}
}


@article{ying2020variance,
  title={Variance-reduced stochastic learning under random reshuffling},
  author={Ying, Bicheng and Yuan, Kun and Sayed, Ali H},
  journal={IEEE Transactions on Signal Processing},
  volume={68},
  pages={1390--1408},
  year={2020},
  publisher={IEEE}
}

@Article{Recht-Re_conj_is_false_ICML_2020,
  author  = {Lai, Zehua and Lim, Lek-Heng},
  journal = {arXiv preprint arXiv:2006.01510},
  title   = {{Recht-R\'{e} Noncommutative arithmetic-geometric mean conjecture is false}},
  title   = {{R}echt-{R}\'{e} Noncommutative Arithmetic-Geometric Mean Conjecture is False},
  year    = {2020},
}

@InProceedings{RR-conjecture2012,
  author    = {Recht, Benjamin and R\'{e}, Christopher},
  booktitle = {Proceedings of the 25th Annual Conference on Learning Theory},
  title     = {{Toward a noncommutative arithmetic-geometric mean inequality: Conjectures, case-studies, and consequences.}},
  year      = {2012},
  editor    = {Mannor, S. and Srebro, N. and Williamson, R. C.},
  note      = {Edinburgh, Scotland},
  pages     = {11.1–11.24},
  volume    = {23},
  edition   = {Proceedings of Machine Learning Research},
}

@Article{Li2019,
  author  = {Xiao Li and Zhihui Zhu and Anthony Man-Cho So and Jason D Lee},
  title   = {{Incremental methods for weakly convex optimization}},
  year    = {2019},
  journal = {arXiv preprint arXiv:1907.11687},
}

@article{GhadimiLan13,
   title={{Stochastic first- and zeroth-order methods for nonconvex stochastic programming}},
   volume={23},
   ISSN={1095-7189},
   DOI={10.1137/120880811},
   number={4},
   journal={SIAM Journal on Optimization},
   publisher={Society for Industrial & Applied Mathematics (SIAM)},
   author={Ghadimi, Saeed and Lan, Guanghui},
   year={2013},
   month={Jan},
   pages={2341–2368}
}

@inproceedings{Ying2019,
    author = {Ying, Bicheng and Yuan, Kun and Vlaski, Stefan and Sayed, Ali H.},
    booktitle = {IEEE Transactions on Signal Processing},
    eprint = {1803.07964v2},
    issn = {1053587X},
    number = {2},
    pages = {474--489},
    title = {Stochastic learning under random reshuffling with constant step-sizes},
    volume = {67},
    year = {2019}
}

@InProceedings{haochen2018random,
  title = 	 {{Random shuffling beats {SGD} after finite epochs}},
  author = 	 {Haochen, Jeff and Sra, Suvrit},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {2624--2633},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Long Beach, California, USA},
  month = 	 {09--15 Jun},
  publisher = 	 {PMLR}
}

@article{Gurbuzbalaban2019IG,
  author = {G\"{u}rb\"{u}zbalaban, M. and Ozdaglar, A. and Parrilo, P. A.},
  title = {{Convergence rate of incremental gradient and incremental newton methods}},
  journal = {SIAM Journal on Optimization},
  volume = {29},
  number = {4},
  pages = {2542-2565},
  year = {2019},
  doi = {10.1137/17M1147846}
}

@article{Khaled2020,
    title={{Better theory for SGD in the nonconvex world}},
    author={Ahmed Khaled and Peter Richt\'{a}rik},
    year={2020},
    journal={arXiv preprint arXiv:2002.03329}
}

@article{Bottou2018,
  author =        {Bottou, L{\'e}on and Curtis, Frank E. and
                   Nocedal, Jorge},
  journal =       {SIAM Review},
  number =        {2},
  pages =         {223-311},
  title =         {{Optimization methods for large-scale machine
                   learning}},
  volume =        {60},
  year =          {2018},
  doi =           {10.1137/16M1080173},
}

@article{Nguyen2020,
    title={{A unified convergence analysis for shuffling-type gradient methods}},
    author={Lam M. Nguyen and Quoc Tran-Dinh and Dzung T. Phan and Phuong Ha Nguyen and Marten van Dijk},
    year={2020},
    journal={arXiv preprint arXiv:2002.08246}
}

@InProceedings{Nagaraj2019,
  title = 	 {{SGD without replacement: sharper rates for general smooth convex functions}},
  author = 	 {Nagaraj, Dheeraj and Jain, Prateek and Netrapalli, Praneeth},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {4703--4711},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Long Beach, California, USA},
  month = 	 {09--15 Jun},
  publisher = 	 {PMLR}
}

@article{Rajput2020,
    title={{Closing the convergence gap of SGD without replacement}},
    author={Shashank Rajput and Anant Gupta and Dimitris Papailiopoulos},
    year={2020},
    journal={arXiv preprint arXiv:2002.10400}
}


@Article{Khaled2019a,
  author  = {Ahmed Khaled and Konstantin Mishchenko and Peter Richt{\'a}rik},
  title   = {{First Analysis of Local GD on Heterogeneous Data}},
  journal = {arXiv preprint arXiv:1909.04715},
  year    = {2019},
}


@Article{Karimireddy2019,
  author  = {Sai Praneeth Karimireddy and Satyen Kale and Mehryar Mohri and Sashank J. Reddi and Sebastian U. Stich and Ananda Theertha Suresh},
  title   = {{SCAFFOLD: Stochastic Controlled Averaging for On-Device Federated Learning}},
  journal = {arXiv preprint arXiv:1910.06378},
  year    = {2019},
}

@InProceedings{Gower2019,
  author    = {Gower, Robert Mansel and Loizou, Nicolas and Qian, Xun and Sailanbayev, Alibek and Shulgin, Egor and Richt\'{a}rik, Peter},
  title     = {{SGD}: {General analysis and improved rates}},
  booktitle = {Proceedings of the 36th International Conference on Machine Learning},
  year      = {2019},
  editor    = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume    = {97},
  series    = {Proceedings of Machine Learning Research},
  pages     = {5200--5209},
  address   = {Long Beach, California, USA},
  month     = {09--15 Jun},
  publisher = {PMLR},
}

@InCollection{Bertsekas2011,
  author    = {Dimitri P. Bertsekas},
  title     = {{Incremental gradient, subgradient, and proximal methods for convex optimization: a survey}},
  booktitle = {Optimization for Machine Learning},
  publisher = {The MIT Press},
  year      = {2011},
  editor    = {Suvrit Sra and Sebastan Nowozin and Stephen J. Wright},
  chapter   = {4},
  isbn      = {9780262298773},
}

@Unpublished{Bottou2009,
  author = {Bottou, L\'{e}on},
  title  = {Curiously fast convergence of some stochastic gradient descent algorithms},
  note   = {Unpublished open problem offered to the attendance of the SLDS 2009 conference},
  year   = {2009},
  url    = {http://leon.bottou.org/papers/bottou-slds-open-problem-2009},
}

@Article{Gurbuzbalaban2019RR,
  author    = {G\"{u}rb\"{u}zbalaban, M. and Ozdaglar, A. and Parrilo, P. A.},
  title     = {{Why random reshuffling beats stochastic gradient descent}},
  journal   = {Mathematical Programming},
  year      = {2019},
  month     = {Oct},
  issn      = {1436-4646},
  doi       = {10.1007/s10107-019-01440-w},
  publisher = {Springer Science and Business Media LLC},
}

@InProceedings{Shamir2016,
  author    = {Shamir, Ohad},
  title     = {{Without-replacement sampling for stochastic gradient methods}},
  booktitle = {Proceedings of the 30th International Conference on Neural Information Processing Systems},
  year      = {2016},
  series    = {NIPS’16},
  pages     = {46–54},
  address   = {Red Hook, NY, USA},
  publisher = {Curran Associates Inc.},
  isbn      = {9781510838819},
  location  = {Barcelona, Spain},
  numpages  = {9},
}


@Article{Meng2019,
  author        = {Qi Meng and Wei Chen and Yue Wang and Zhi-Ming Ma and Tie-Yan Liu},
  title         = {{Convergence analysis of distributed stochastic gradient descent with shuffling}},
  journal       = {Neurocomputing},
  year          = {2019},
  volume        = {337},
  pages         = {46 - 57},
  issn          = {0925-2312},
  __markedentry = {[rka:6]},
  doi           = {https://doi.org/10.1016/j.neucom.2019.01.037},
}

@InProceedings{Raman2019,
  author    = {Raman, Parameswaran and Srinivasan, Sriram and Matsushima, Shin and Zhang, Xinhua and Yun, Hyokun and Vishwanathan, S.V.N.},
  title     = {{Scaling multinomial logistic regression via hybrid parallelism}},
  booktitle = {Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  year      = {2019},
  series    = {KDD ’19},
  pages     = {1460–1470},
  address   = {New York, NY, USA},
  publisher = {Association for Computing Machinery},
  doi       = {10.1145/3292500.3330837},
  isbn      = {9781450362016},
  location  = {Anchorage, AK, USA},
  numpages  = {11},
}


@InProceedings{Recht2012,
  author    = {Benjamin Recht and Christopher R{\'{e}}},
  title     = {{Toward a Noncommutative Arithmetic-geometric Mean Inequality: Conjectures, Case-studies, and Consequences}},
  booktitle = {Proceedings of the 25th Annual Conference on Learning Theory},
  year      = {2012},
  editor    = {Shie Mannor and Nathan Srebro and Robert C. Williamson},
  volume    = {23},
  series    = {Proceedings of Machine Learning Research},
  pages     = {11.1--11.24},
  address   = {Edinburgh, Scotland},
  month     = {25--27 Jun},
  publisher = {PMLR},
}





@Article{Gurbuzbalaban2017,
  author    = {G\"{u}rb\"{u}zbalaban, M. and Ozdaglar, A. and Parrilo, P. A.},
  title     = {{On the convergence rate of incremental aggregated gradient algorithms}},
  journal   = {SIAM Journal on Optimization},
  year      = {2017},
  volume    = {27},
  number    = {2},
  pages     = {1035–1048},
  month     = {Jan},
  issn      = {1095-7189},
  doi       = {10.1137/15m1049695},
  publisher = {Society for Industrial \& Applied Mathematics (SIAM)},
}


@Article{RuoyuSun2019,
  author    = {Ruoyu Sun and Yinyu Ye},
  title     = {{Worst-case Complexity of Cyclic Coordinate Descent: O($n^2$) Gap with Randomized Version}},
  journal   = {Mathematical Programming},
  year      = {2019},
  month     = oct,
  doi       = {10.1007/s10107-019-01437-5},
  publisher = {Springer Science and Business Media {LLC}},
}


@Article{Lee2018,
  author    = {{Ching-pei} Lee and Stephen J. Wright},
  title     = {Random permutations fix a worst case for cyclic coordinate descent},
  journal   = {{IMA} Journal of Numerical Analysis},
  year      = {2018},
  volume    = {39},
  number    = {3},
  pages     = {1246--1275},
  month     = jul,
  doi       = {10.1093/imanum/dry040},
  publisher = {Oxford University Press ({OUP})},
}

@article{Recht2013,
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  publisher = {Springer Science and Business Media {LLC}},
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  number = {2},
  pages = {201--226},
  author = {Benjamin Recht and Christopher R{\'{e}}},
  title = {{Parallel Stochastic Gradient Algorithms for Large-Scale Matrix Completion}},
  journal = {Mathematical Programming Computation}
}

@article{Sun2020,
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  publisher = {Springer Science and Business Media {LLC}},
  author = {Ruo-Yu Sun},
  title = {{Optimization for deep learning: an overview}},
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}

@Article{Stich2019b,
  author      = {Sebastian U. Stich},
  title       = {{Unified Optimal Analysis of the (Stochastic) Gradient Method}},
  journal     = {arXiv preprint arXiv:1907.04232},
  year        = {2019},
  date        = {2019-07-09},
  eprint      = {1907.04232v2},
  eprintclass = {cs.LG},
  eprinttype  = {arXiv},
  file        = {online:http\://arxiv.org/pdf/1907.04232v2:PDF},
  keywords    = {cs.LG, cs.NA, math.NA, math.OC, stat.ML},
}

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@article{Nedic2001,
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  title = {{Incremental subgradient methods for nondifferentiable optimization}},
  journal = {{SIAM} Journal on Optimization}
}
@inproceedings{safran2020good,
  title={How good is {SGD} with random shuffling?},
  author={Safran, Itay and Shamir, Ohad},
  booktitle={Conference on Learning Theory},
  pages={3250--3284},
  year={2020},
  organization={PMLR}
}


@article{Nemirovski2009,
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  title = {{Robust Stochastic Approximation Approach to Stochastic Programming}},
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}

@article{Bengio2012,
  title={{Practical recommendations for gradient-based training of deep architectures}},
  ISBN={9783642352898},
  ISSN={1611-3349},
  DOI={10.1007/978-3-642-35289-8_26},
  journal={Neural Networks: Tricks of the Trade},
  publisher={Springer Berlin Heidelberg},
  author={Bengio, Yoshua},
  year={2012},
  pages={437–478}
}

@inproceedings{nguyen2018sgd,
  title={{SGD} and {H}ogwild! Convergence Without the Bounded Gradients Assumption},
  author={Nguyen, Lam and Nguyen, Phuong Ha and van Dijk, Marten and Richt{\'a}rik, Peter and Scheinberg, Katya and Tak\'{a}\v{c}, Martin},
  booktitle={International Conference on Machine Learning},
  pages={3747--3755},
  year={2018}
}

@article{Drori2019,
  title={{The complexity of finding stationary points with stochastic gradient descent}},
  author={Yoel Drori and Ohad Shamir},
  year={2019},
  journal={arXiv preprint arXiv:1910.01845}
}

@incollection{HaNguyen2019,
  title = {{Tight Dimension Independent Lower Bound on the Expected Convergence Rate for Diminishing Step Sizes in SGD}},
  author = {Nguyen, Phuong Ha and Nguyen, Lam and van Dijk, Marten},
  booktitle = {Advances in Neural Information Processing Systems 32},
  editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d' Alch\'{e}-Buc and E. Fox and R. Garnett},
  pages = {3660--3669},
  year = {2019},
  publisher = {Curran Associates, Inc.},
}

@book{nemirovsky1983problem,
  title={{Problem Complexity and Method Efficiency in Optimization}},
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@InProceedings{Rakhlin2012,
  author    = {Rakhlin, Alexander and Shamir, Ohad and Sridharan, Karthik},
  title     = {{Making gradient descent optimal for strongly convex stochastic optimization}},
  booktitle = {Proceedings of the 29th International Coference on International Conference on Machine Learning},
  year      = {2012},
  series    = {ICML’12},
  pages     = {1571–1578},
  address   = {Madison, WI, USA},
  publisher = {Omnipress},
  isbn      = {9781450312851},
  location  = {Edinburgh, Scotland},
  numpages  = {8},
}

@article{Ahn2020,
    title={{On Tight Convergence Rates of Without-replacement SGD}},
    author={Kwangjun Ahn and Suvrit Sra},
    year={2020},
    journal={arXiv preprint arXiv:2004.08657},
    archivePrefix={arXiv},
    primaryClass={math.OC}
}

@inproceedings{needell2014stochastic,
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@inproceedings{bottou2004large,
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@article{malitsky2019adaptive,
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  author={Malitsky, Yura and Mishchenko, Konstantin},
  journal={arXiv preprint arXiv:1910.09529},
  year={2019}
}


@Comment{jabref-meta: databaseType:bibtex;}
