Fetching the paper…
Reading the bibliography…
We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations.
J Matyas, Random optimization , Automation and Remote control 26
1965
Earlier work this paper cites.
John A Nelder and Roger Mead, A simplex method for function minimization , The computer journal 7
1965
Earlier work this paper cites.
Richard L Bishop and Barrett O’Neill, Manifolds of negative curvature , Transactions of the American Mathematical Society 145
1969
Earlier work this paper cites.
Charles Stein, A bound for the error in the Normal approximation to the distribution of a sum of dependent random variables , Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Probability Theory, The Regents of the University of California, 1972
1972
Earlier work this paper cites.
Mikhael Gromov, Manifolds of negative curvature , Journal of Differential Geometry 13
1978
Earlier work this paper cites.
Arkadi S. Nemirovski and David B. Yudin, Problem complexity and method efficiency in optimization , Wiley & Sons (1983)
1983
Earlier work this paper cites.
Amit Chattopadhyay, Suviseshamuthu Easter Selvan, and Umberto Amato, A derivative-free Riemannian Powell’s method, minimizing hartley-entropy-based ICA contrast , IEEE transactions on neural networks and learning systems 27
1990
Earlier work this paper cites.
Manfredo Perdigao do Carmo, Riemannian geometry , Birkhäuser, 1992
1992
Earlier work this paper cites.
Jonas Mockus, Application of Bayesian approach to numerical methods of global and stochastic optimization , Journal of Global Optimization 4
1994
Earlier work this paper cites.
Elton P Hsu, Stochastic analysis on manifolds , vol. 38, American Mathematical Soc., 2002
2002
Earlier work this paper cites.
I. Jolliffe, N.Trendafilov, and M. Uddin, A modified principal component technique based on the LASSO , Journal of computational and Graphical Statistics 12
2003
Earlier work this paper cites.
2003
Earlier work this paper cites.
K. Q. Weinberger and L. K. Saul, Unsupervised learning of image manifolds by semidenite programming , CVPR, 2004
2004
Earlier work this paper cites.
James C Spall, Introduction to stochastic search and optimization: Estimation, simulation, and control , vol. 65, John Wiley & Sons, 2005
2005
Earlier work this paper cites.
Yurii Nesterov and Boris T Polyak, Cubic regularization of Newton method and its global performance , Mathematical Programming 108
2006
Earlier work this paper cites.
H. Zou, T. Hastie, and R. Tibshirani, Sparse principal component analysis , J. Comput. Graph. Stat. 15
2006
Earlier work this paper cites.
John A Lee and Michel Verleysen, Nonlinear dimensionality reduction , Springer Science & Business Media, 2007
2007
Earlier work this paper cites.
P-A Absil, Robert Mahony, and Rodolphe Sepulchre, Optimization algorithms on matrix manifolds , Princeton University Press, 2009
2009
Earlier work this paper cites.
Andrew Conn, Katya Scheinberg, and Luis Vicente, Introduction to derivative-free optimization , vol. 8, SIAM, 2009
2009
Earlier work this paper cites.
J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, ImageNet: A Large-Scale Hierarchical Image Database , CVPR09, 2009
2009
Earlier work this paper cites.
Emmanuel Rio, Moment inequalities for sums of dependent random variables under projective conditions , Journal of Theoretical Probability 22
2009
Earlier work this paper cites.
Christopher JC Burges, Dimension reduction: A guided tour , Now Publishers Inc, 2010
2010
Earlier work this paper cites.
Nicolas Boumal and Pierre Absil, RTRMC: A Riemannian trust-region method for low-rank matrix completion , Advances in neural information processing systems, 2011, pp. 406–414
2011
Earlier work this paper cites.
Yu Nesterov, Random gradient-free minimization of convex functions , Technical Report. Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (2011)
2011
Earlier work this paper cites.
Kevin G Jamieson, Robert Nowak, and Ben Recht, Query complexity of derivative-free optimization , Advances in Neural Information Processing Systems, 2012, pp. 2672–2680
2012
Earlier work this paper cites.
Dario A Bini and Bruno Iannazzo, Computing the Karcher mean of symmetric positive definite matrices , Linear Algebra and its Applications 438
2013
Earlier work this paper cites.
Silvere Bonnabel, Stochastic gradient descent on Riemannian manifolds , IEEE Transactions on Automatic Control 58
2013
Earlier work this paper cites.
Persi Diaconis, Susan Holmes, Mehrdad Shahshahani, et al., Sampling from a manifold , Advances in modern statistical theory and applications: a Festschrift in honor of Morris L. Eaton, Institute of Mathematical Statistics, 2013, pp. 102–125
2013
Earlier work this paper cites.
Saeed Ghadimi and Guanghui Lan, Stochastic first-and zeroth-order methods for nonconvex stochastic programming , SIAM Journal on Optimization 23
2013
Earlier work this paper cites.
2013
Earlier work this paper cites.
Bart Vandereycken, Low-rank matrix completion by Riemannian optimization , SIAM Journal on Optimization 23
2013
Earlier work this paper cites.
Pierre B Borckmans, S Easter Selvan, Nicolas Boumal, and P-A Absil, A Riemannian subgradient algorithm for economic dispatch with valve-point effect , Journal of Computational and Applied Mathematics 255
2014
Earlier work this paper cites.
2014
Cited alongside, same era.
Rongjie Lai and Stanley Osher, A splitting method for orthogonality constrained problems , Journal of Scientific Computing 58
2014
Cited alongside, same era.
2014
Cited alongside, same era.
Wei Hong Yang, Lei-Hong Zhang, and Ruyi Song, Optimality conditions for the nonlinear programming problems on Riemannian manifolds , Pacific Journal of Optimization 10
2014
Cited alongside, same era.
John C Duchi, Michael I Jordan, Martin J Wainwright, and Andre Wibisono, Optimal rates for zero-order convex optimization: The power of two function evaluations , IEEE Transactions on Information Theory 61
2018
Later among the works it cites.
Mojmir Mutny and Andreas Krause, Efficient high dimensional Bayesian optimization with additivity and quadrature fourier features , Advances in Neural Information Processing Systems, 2018, pp. 9005–9016
2018
Later among the works it cites.
ChangYong Oh, Efstratios Gavves, and Max Welling, BOCK: Bayesian optimization with cylindrical kernels , International Conference on Machine Learning, 2018, pp. 3868–3877
2018
Later among the works it cites.
Paul Rolland, Jonathan Scarlett, Ilija Bogunovic, and Volkan Cevher, High-dimensional Bayesian optimization via additive models with overlapping groups , International Conference on Artificial Intelligence and Statistics, 2018, pp. 298–307
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2015
Cited alongside, same era.
Chunchuan Lyu, Kaizhu Huang, and Hai-Ning Liang, A unified gradient regularization family for adversarial examples , 2015 IEEE International Conference on Data Mining, IEEE, 2015, pp. 301–309
2015
Cited alongside, same era.
Bobak Shahriari, Kevin Swersky, Ziyu Wang, Ryan P Adams, and Nando De Freitas, Taking the human out of the loop: A review of Bayesian optimization , Proceedings of the IEEE 104
2015
Cited alongside, same era.
Anoop Cherian and Suvrit Sra, Riemannian dictionary learning and sparse coding for positive definite matrices , IEEE transactions on neural networks and learning systems 28
2016
Cited alongside, same era.
Artiom Kovnatsky, Klaus Glashoff, and Michael M Bronstein, MADMM: a generic algorithm for non-smooth optimization on manifolds , European Conference on Computer Vision, Springer, 2016, pp. 680–696
2016
Cited alongside, same era.
Chun-Liang Li, Kirthevasan Kandasamy, Barnabás Póczos, and Jeff Schneider, High dimensional bayesian optimization via restricted projection pursuit models , Artificial Intelligence and Statistics, 2016, pp. 884–892
2016
Cited alongside, same era.
Alonso Marco, Philipp Hennig, Jeannette Bohg, Stefan Schaal, and Sebastian Trimpe, Automatic LQR tuning based on Gaussian process global optimization , 2016 IEEE international conference on robotics and automation (ICRA), IEEE, 2016, pp. 270–277
2016
Cited alongside, same era.
Ju Sun, Qing Qu, and John Wright, Complete dictionary recovery over the sphere I: Overview and the geometric picture , IEEE Transactions on Information Theory 63
2016
Cited alongside, same era.
Nilesh Tripuraneni, Nicolas Flammarion, Francis Bach, and Michael I Jordan, Averaging stochastic gradient descent on Riemannian manifolds , Conference On Learning Theory, 2018, pp. 650–687
2018
Later among the works it cites.
Yining Wang, Simon Du, Sivaraman Balakrishnan, and Aarti Singh, Stochastic zeroth-order optimization in high dimensions , International Conference on Artificial Intelligence and Statistics, 2018, pp. 1356–1365
2018
Later among the works it cites.
Xiantao Xiao, Yongfeng Li, Zaiwen Wen, and Liwei Zhang, A regularized semi-smooth Newton method with projection steps for composite convex programs , Journal of Scientific Computing 76
2018
Later among the works it cites.
Hui Zou and Lingzhou Xue, A selective overview of sparse principal component analysis , Proceedings of the IEEE 106
2018
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
Jeffrey Larson, Matt Menickelly, and Stefan M Wild, Derivative-free optimization methods , Acta Numerica 28
2019
Later among the works it cites.
2019
Later among the works it cites.
Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria, and Atul Saroop, A Riemannian gossip approach to subspace learning on Grassmann manifold , Machine Learning (2019), 1–21
2019
Later among the works it cites.
Raúl Rabadán and Andrew J Blumberg, Topological data analysis for genomics and evolution: Topology in biology , Cambridge University Press, 2019
2019
Later among the works it cites.
Chun-Chen Tu, Paishun Ting, Pin-Yu Chen, Sijia Liu, Huan Zhang, Jinfeng Yi, Cho-Jui Hsieh, and Shin-Ming Cheng, AutoZOOM: Autoencoder-based zeroth order optimization method for attacking black-box neural networks , Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, 2019, pp. 742–749
2019
Later among the works it cites.
2019
Later among the works it cites.
Kai Yuan, Iordanis Chatzinikolaidis, and Zhibin Li, Bayesian optimization for whole-body control of high-degree-of-freedom robots through reduction of dimensionality , IEEE Robotics and Automation Letters 4
2019
Later among the works it cites.
Pan Zhou, Xiaotong Yuan, Shuicheng Yan, and Jiashi Feng, Faster first-order methods for stochastic non-convex optimization on Riemannian manifolds , IEEE transactions on pattern analysis and machine intelligence (2019)
2019
Later among the works it cites.
Naman Agarwal, Nicolas Boumal, Brian Bullins, and Coralia Cartis, Adaptive regularization with cubics on manifolds , Mathematical Programming (to appear) (2020)
2020
Closest in time.
2020
Closest in time.
Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, and Tong Zhang, Proximal gradient method for nonsmooth optimization over the Stiefel manifold , SIAM Journal on Optimization 30
2020
Closest in time.
2020
Closest in time.
Noémie Jaquier and Leonel Rozo, High-dimensional Bayesian optimization via nested Riemannian manifolds , Advances in Neural Information Processing Systems 33
2020
Closest in time.
Noémie Jaquier, Leonel Rozo, Sylvain Calinon, and Mathias Bürger, Bayesian optimization meets Riemannian manifolds in robot learning , Conference on Robot Learning, PMLR, 2020, pp. 233–246
2020
Closest in time.
Oleg Kachan, Persistent homology-based projection pursuit , Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2020, pp. 856–857
2020
Closest in time.
2020
Closest in time.
Linnan Wang, Rodrigo Fonseca, and Yuandong Tian, Learning search space partition for black-box optimization using monte carlo tree search , Advances in Neural Information Processing Systems 33
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
J. Zhang, S. Ma, and S. Zhang, Primal-dual optimization algorithms over Riemannian manifolds: an iteration complexity analysis , Mathematical Programming Series A 184
2020
Closest in time.