Zeroth-order (non)-convex stochastic optimization via conditional gradient and gradient updates

Advances in Neural Information Processing Systems

Volumn 2018-December, Issue , 2018, Pages 3455-3464

  Balasubramanian, Krishnakumar ^a   Ghadimi, Saeed ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX OPTIMIZATION; STOCHASTIC SYSTEMS;

CONDITIONAL GRADIENT; NONCONVEX; STEP SIZE; STOCHASTIC APPROXIMATION ALGORITHMS; STOCHASTIC GRADIENT ALGORITHMS; STOCHASTIC OPTIMIZATIONS;

APPROXIMATION ALGORITHMS;

EID: 85064838956     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. Sébastien Bubeck. Convex optimization: Algorithms and complexity. Foundations and TrendsR in Machine Learning, 8(3-4):231-357, 2015.
2. Sébastien Bubeck and Nicolo Cesa-Bianchi. Regret analysis of stochastic and nonstochastic multi-armed bandit problems. Foundations and TrendsR in Machine Learning, 5(1):1-122, 2012.
3. Pin-Yu Chen, Huan Zhang, Yash Sharma, Jinfeng Yi, and Cho-Jui Hsieh. Zoo: Zeroth order optimization based black-box attacks to deep neural networks without training substitute models. In Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security, pages 15-26. ACM, 2017.
4. Krzysztof Choromanski, Mark Rowland, Vikas Sindhwani, Richard Turner, and Adrian Weller. Structured evolution with compact architectures for scalable policy optimization. In Proceedings of the 35th International Conference on Machine Learning. PMLR, 2018.
5. Andrew Conn, Katya Scheinberg, and Luis Vicente. Introduction to derivative-free optimization, volume 8. Siam, 2009.
6. V. Demyanov and A. Rubinov. Approximate methods in optimization problems. American Elsevier Publishing Co, 1970.
7. John Duchi, Michael Jordan, Martin Wainwright, and Andre Wibisono. Optimal rates for zero-order convex optimization: The power of two function evaluations. IEEE Transactions on Information Theory, 61(5):2788-2806, 2015.
8. Marguerite Frank and Philip Wolfe. An algorithm for quadratic programming. Naval Research Logistics Quarterly, 3:95-110, 1956.
9. S. Ghadimi and G. Lan. Stochastic first- and zeroth-order methods for nonconvex stochastic programming. SIAM Journal on Optimization, 23(4):2341-2368, 2013.
10. Saeed Ghadimi. Conditional gradient type methods for composite nonlinear and stochastic optimization. Mathematical Programming, 2018.
11. Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio. Deep learning, volume 1. MIT press Cambridge, 2016.
12. Elad Hazan and Satyen Kale. Projection-free online learning. In Proceedings of the 29th International Coference on International Conference on Machine Learning, pages 1843-1850. Omnipress, 2012.
13. Elad Hazan and Haipeng Luo. Variance-reduced and projection-free stochastic optimization. In International Conference on Machine Learning, pages 1263-1271, 2016.
14. Donald Hearn. The gap function of a convex program. Operations Research Letters, 2, 1982.
15. Martin Jaggi. Revisiting frank-wolfe: Projection-free sparse convex optimization. In ICML (1), pages 427-435, 2013.
16. Prateek Jain and Purushottam Kar. Non-convex optimization for machine learning. Foundations and Trends® in Machine Learning, 10(3-4):142-336, 2017.
17. Prateek Jain, Ambuj Tewari, and Purushottam Kar. On iterative hard thresholding methods for high-dimensional m-estimation. In Advances in Neural Information Processing Systems, pages 685-693, 2014.
18. Kevin Jamieson, Robert Nowak, and Ben Recht. Query complexity of derivative-free optimization. In Advances in Neural Information Processing Systems, pages 2672-2680, 2012.
19. Guanghui Lan and Yi Zhou. Conditional gradient sliding for convex optimization. SIAM Journal on Optimization, 26(2):1379-1409, 2016.
20. Horia Mania, Aurelia Guy, and Benjamin Recht. Simple random search provides a competitive approach to reinforcement learning. In Advances in Neural Information Processing Systems, 2018.
21. Jonas Mockus. Bayesian approach to global optimization: theory and applications, volume 37. Springer Science & Business Media, 2012.
22. Aryan Mokhtari, Hamed Hassani, and Amin Karbasi. Conditional gradient method for stochastic submodular maximization: Closing the gap. In International Conference on Artificial Intelligence and Statistics, pages 1886-1895, 2018.
23. Aryan Mokhtari, Hamed Hassani, and Amin Karbasi. Stochastic conditional gradient methods: From convex minimization to submodular maximization. arXiv preprint arXiv:1804.09554, 2018.
24. A. S. Nemirovski and D. Yudin. Problem complexity and method efficiency in optimization. Wiley-Interscience Series in Discrete Mathematics. John Wiley, XV, 1983.
25. Y. E. Nesterov. Introductory Lectures on Convex Optimization: a basic course. Kluwer Academic Publishers, Massachusetts, 2004.
26. Yurii Nesterov. Introductory lectures on convex optimization: A basic course, volume 87. Springer Science & Business Media, 2013.
27. Yurii Nesterov and Vladimir Spokoiny. Random gradient-free minimization of convex functions. Foundations of Computational Mathematics, 17(2):527-566, 2017.
28. Sashank Reddi, Suvrit Sra, Barnabás Póczos, and Alexander Smola. Stochastic Frank-Wolfe Methods for Nonconvex Optimization. 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1244-1251, 2016.
29. Reuven Rubinstein and Dirk Kroese. Simulation and the Monte Carlo method, volume 10. John Wiley & Sons, 2016.
30. Tim Salimans, Jonathan Ho, Xi Chen, Szymon Sidor, and Ilya Sutskever. Evolution strategies as a scalable alternative to reinforcement learning. arXiv preprint arXiv:1703.03864, 2017.
31. Ohad Shamir. On the complexity of bandit and derivative-free stochastic convex optimization. In Conference on Learning Theory, pages 3-24, 2013.
32. Jasper Snoek, Hugo Larochelle, and Ryan Adams. Practical bayesian optimization of machine learning algorithms. In Advances in neural information processing systems, pages 2951-2959, 2012.
33. James Spall. Introduction to stochastic search and optimization: estimation, simulation, and control, volume 65. John Wiley & Sons, 2005.
34. Yining Wang, Simon Du, Sivaraman Balakrishnan, and Aarti Singh. Stochastic zeroth-order optimization in high dimensions. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, 2018.