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 probl
classical regime, n > D, where D is the fixed number of weights; consistency (informally the expected error of the empirical minimizer converges to the best in the class) and generalization (the empirical error of the minimizer converges to the expected error of the minimizer) are ...
Lee, J.D., Simchowitz, M., Jordan, M.I., Recht, B.: Gradient descent only converges to minimizers. In: Conference on learning Theory, pp. 1246–1257 (2016) Li, G., Cai, C., Chen, Y., Wei, Y., Chi, Y.: Is Q-learning minimax optimal? A tight sample complexity analysis....
update. For convex error surface, batch gradient descent method converges to global minimum. For nonconvex surface, this method converges to local minimum. For the N number of samples and M number of features, the computational complexity per iteration of batch gradient descent method will be O(...
Newton's method, often called the tangent method, is based on the tangent of the current position to determine the next position. Compared with the gradient descent method with first-order convergence, Newton's method has second-order convergence with a fast convergence speed. However, the invers...
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...
We can now describe the main result from our recent work with Lénaïc [13]: under assumptions described below, for the function FF defined above, if the Wasserstein gradient flow converges to a measure, this measure has to be a global minimum of FF (note that we cannot prove it is ...
Then, we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem, and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable tensors. This result, combined with the landscape ...
Thus so does the blue term 0 ≤ 2γt ∇C(wt ) 2 < ∞ t Using the fact that γt = ∞ we have5 ∇C(wt ) converges a.s. to 0. 5as soon as ∇C(wt ) is proved to converge. Outline 1 Stochastic gradient descent • Introduction and examples • SGD and machine learning...
where,converges to the solution X. There are many variations and modifications of the GI algorithm [32], namely the RGI algorithm [34], the MGI algorithm [35], the JGI algorithm [36], and the AJGI algorithm [36]. In this paper, we introduce a gradient-descent iterative algorithm for ...