Gradient Descent Converges to Minimizers: Optimal and Adaptive Step-Size RulesAs mentioned in Chap. 3 , gradient descent (GD) and its variants provide the core optimization methodology in machine learning problems. Given a C 1 or C 2 function \\(f: \\mathbb {R}^{n} ightarrow \\mathbb ...
Gradient descent only converges to minimizers. Conference on learning theory, 1246-1257, 2016.[11] Simon S. Du, Chi Jin, Jason D. Lee, Michael I. Jordan, Barnabas Poczos, Aarti Singh. Gradient descent can take exponential time to escape saddle points. Advances in neural information ...
Lee, J.D., Simchowitz, M., Jordan, M.I., Recht, B.: Gradient descent only converges to minimizers. JMRL 49, 1–12 (2016) Google Scholar lrfinder. https://github.com/davidtvs/pytorch-lr-finder (2018) Mahrsereci, M., Hennig, P.: Probabilistic line searches for stochastic optimis...
Only the first derivative is used in theconjugate gradient method, which overcomes the shortcomings of the gradient descent method and Newton's method. Aboulissane et al.[138]used the conjugate gradient algorithm to optimize the workspace of 3RPR and Delta PMs. The conjugate gradient method is...
The main weakness of this result is that is only qualitative: we cannot quantify how big mm need to be to be close to the infinite width limit, or how fast the gradient flow converges to the global optimum. These are still open problems. Additional interesting areas of research are to ...
Only the first derivative is used in the conjugate gradient method, which overcomes the shortcomings of the gradient descent method and Newton's method. Aboulissane et al. [138] used the conjugate gradient algorithm to optimize the workspace of 3RPR and Delta PMs. The conjugate gradient method...
For binary and multiclass classification, only the normalized weights are needed. To provide some intuition, consider that GD is steepest descent wrt the L2 norm and the steepest direction of the gradient depends on the norm. The fact that the direction of the weights converge to stationary ...
Towards stability and optimality in stochastic gradient descent Panos Toulis Harvard University Dustin Tran Harvard University Edoardo M. Airoldi Harvard University Abstract Iterative procedures for parameter estimation based on stochastic gradient descent ( ) allow the estimation to scale to massive data ...
QUOTE: We apply Stochastic Meta-Descent (SMD), a stochastic gradient optimization method with gain vector adaptation, to the training of Conditional Random Fields (CRFs). On several large data sets, the resulting optimizer converges to the same quality of solution over an order of magnitude faste...
Wojtowytsch, S.: Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis. (2021) arXiv:2106.02588 [cs.LG] Ward, R., Wu, X., Bottou, L.: Adagrad stepsizes: Sharp convergence over nonconvex landscapes. In: International Conference on Machine Learni...