ADAGRAD: adaptive gradient algorithm; Adaptive subgradient methods for online learning and stochastic optimization. We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.

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  1. Huang, Shan; Zhu, Renchuan; Chang, Hongyu; Wang, Hui; Yu, Yun: Machine learning to approximate free-surface Green’s function and its application in wave-body interactions (2022)
  2. Jia, Yichen; Jeong, Jong-Hyeon: Deep learning for quantile regression under right censoring: deepquantreg (2022)
  3. Barakat, Anas; Bianchi, Pascal: Convergence and dynamical behavior of the ADAM algorithm for nonconvex stochastic optimization (2021)
  4. Barakat, Anas; Bianchi, Pascal; Hachem, Walid; Schechtman, Sholom: Stochastic optimization with momentum: convergence, fluctuations, and traps avoidance (2021)
  5. Dehghani, Hamidreza; Zilian, Andreas: A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs (2021)
  6. De Loera, Jesús A.; Haddock, Jamie; Ma, Anna; Needell, Deanna: Data-driven algorithm selection and tuning in optimization and signal processing (2021)
  7. Duchi, John C.; Glynn, Peter W.; Namkoong, Hongseok: Statistics of robust optimization: a generalized empirical likelihood approach (2021)
  8. Duchi, John C.; Ruan, Feng: Asymptotic optimality in stochastic optimization (2021)
  9. Duruisseaux, Valentin; Schmitt, Jeremy; Leok, Melvin: Adaptive Hamiltonian variational integrators and applications to symplectic accelerated optimization (2021)
  10. Fan, Jianqing; Ma, Cong; Zhong, Yiqiao: A selective overview of deep learning (2021)
  11. Frye, Charles G.; Simon, James; Wadia, Neha S.; Ligeralde, Andrew; Deweese, Michael R.; Bouchard, Kristofer E.: Critical point-finding methods reveal gradient-flat regions of deep network losses (2021)
  12. Ghods, Alireza; Cook, Diane J.: A survey of deep network techniques all classifiers can adopt (2021)
  13. Haghighat, Ehsan; Bekar, Ali Can; Madenci, Erdogan; Juanes, Ruben: A nonlocal physics-informed deep learning framework using the peridynamic differential operator (2021)
  14. Haghighat, Ehsan; Raissi, Maziar; Moure, Adrian; Gomez, Hector; Juanes, Ruben: A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics (2021)
  15. He, Xiaolong; He, Qizhi; Chen, Jiun-Shyan: Deep autoencoders for physics-constrained data-driven nonlinear materials modeling (2021)
  16. Huang, Junhao; Sun, Weize; Huang, Lei: Joint structure and parameter optimization of multiobjective sparse neural network (2021)
  17. Kafka, Dominic; Wilke, Daniel N.: Resolving learning rates adaptively by locating stochastic non-negative associated gradient projection points using line searches (2021)
  18. Kan, Kelvin; Fung, Samy Wu; Ruthotto, Lars: PNKH-B: a projected Newton-Krylov method for large-scale bound-constrained optimization (2021)
  19. Liu, Yang; Roosta, Fred: Convergence of Newton-MR under inexact Hessian information (2021)
  20. Ma, Chenxin; Jaggi, Martin; Curtis, Frank E.; Srebro, Nathan; Takáč, Martin: An accelerated communication-efficient primal-dual optimization framework for structured machine learning (2021)

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