Minimization of Stochastic First-order Oracle Complexity of Adaptive Methods for Nonconvex Optimization

• URL: http://arxiv.org/abs/2112.07163v2
• Date: Thu, 16 Dec 2021 06:24:21 GMT
• Title: Minimization of Stochastic First-order Oracle Complexity of Adaptive Methods for Nonconvex Optimization
• Authors: Hideaki Iiduka
• Abstract summary: We prove that there exist critical batch sizes in the sense of minimizing the lower and upper bounds of the first-order oracle (SFO) complexity. We also discuss the conditions needed for the SFO complexity to fit the lower and upper bounds and provide numerical results that support our theoretical results.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Numerical evaluations have definitively shown that, for deep learning optimizers such as stochastic gradient descent, momentum, and adaptive methods, the number of steps needed to train a deep neural network halves for each doubling of the batch size and that there is a region of diminishing returns beyond the critical batch size. In this paper, we determine the actual critical batch size by using the global minimizer of the stochastic first-order oracle (SFO) complexity of the optimizer. To prove the existence of the actual critical batch size, we set the lower and upper bounds of the SFO complexity and prove that there exist critical batch sizes in the sense of minimizing the lower and upper bounds. This proof implies that, if the SFO complexity fits the lower and upper bounds, then the existence of these critical batch sizes demonstrates the existence of the actual critical batch size. We also discuss the conditions needed for the SFO complexity to fit the lower and upper bounds and provide numerical results that support our theoretical results.

Related papers

• Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity [59.75300530380427]
  We consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.
  arXiv  Detail & Related papers  (2024-06-28T02:56:22Z)
• Iteration and Stochastic First-order Oracle Complexities of Stochastic Gradient Descent using Constant and Decaying Learning Rates [0.8158530638728501]
  We show that the performance of descent (SGD) depends on not only the learning rate but also the batch size. We show that measured critical batch sizes are close to the sizes estimated from our theoretical results.
  arXiv  Detail & Related papers  (2024-02-23T14:24:45Z)
• Faster Stochastic Variance Reduction Methods for Compositional MiniMax Optimization [50.10952609321302]
  compositional minimax optimization is a pivotal challenge across various machine learning domains. Current methods of compositional minimax optimization are plagued by sub-optimal complexities or heavy reliance on sizable batch sizes. This paper introduces a novel method, called Nested STOchastic Recursive Momentum (NSTORM), which can achieve the optimal sample complexity of $O(kappa3 /epsilon3 )$.
  arXiv  Detail & Related papers  (2023-08-18T14:57:21Z)
• Relationship between Batch Size and Number of Steps Needed for Nonconvex Optimization of Stochastic Gradient Descent using Armijo Line Search [0.8158530638728501]
  We show that SGD performs better than other deep learning networks when it uses deep numerical line. The results indicate that the number of steps needed for SFO as the batch size grows can be estimated.
  arXiv  Detail & Related papers  (2023-07-25T21:59:17Z)
• Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm [101.44676036551537]
  One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC) measures the average performance of a binary classifier. Most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. We present a simpler reformulation of the PAUC problem via distributional robust optimization AUC.
  arXiv  Detail & Related papers  (2022-10-08T08:26:22Z)
• Critical Bach Size Minimizes Stochastic First-Order Oracle Complexity of Deep Learning Optimizer using Hyperparameters Close to One [0.0]
  We show that deep learnings using small constant learning rates, hyper parameters close to one, and large batch sizes can find the model parameters of deep neural networks that minimize the loss functions. Results indicate that Adam using a small constant learning rate, hyper parameters close to one, and the critical batch size minimizing SFO complexity has faster convergence than Momentum and gradient descent.
  arXiv  Detail & Related papers  (2022-08-21T06:11:23Z)
• Large-scale Optimization of Partial AUC in a Range of False Positive Rates [51.12047280149546]
  The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. We develop an efficient approximated gradient descent method based on recent practical envelope smoothing technique. Our proposed algorithm can also be used to minimize the sum of some ranked range loss, which also lacks efficient solvers.
  arXiv  Detail & Related papers  (2022-03-03T03:46:18Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Balancing Rates and Variance via Adaptive Batch-Size for Stochastic Optimization Problems [120.21685755278509]
  In this work, we seek to balance the fact that attenuating step-size is required for exact convergence with the fact that constant step-size learns faster in time up to an error. Rather than fixing the minibatch the step-size at the outset, we propose to allow parameters to evolve adaptively.
  arXiv  Detail & Related papers  (2020-07-02T16:02:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.