Efficient Second-Order Neural Network Optimization via Adaptive Trust Region Methods

• URL: http://arxiv.org/abs/2410.02293v1
• Date: Thu, 3 Oct 2024 08:23:06 GMT
• Title: Efficient Second-Order Neural Network Optimization via Adaptive Trust Region Methods
• Authors: James Vo,
• Abstract summary: SecondOrderAdaptive (SOAA) is a novel optimization algorithm designed to overcome limitations of traditional second-order techniques. We empirically demonstrate that SOAA achieves faster and more stable convergence compared to first-order approximations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Second-order optimization methods offer notable advantages in training deep neural networks by utilizing curvature information to achieve faster convergence. However, traditional second-order techniques are computationally prohibitive, primarily due to the large matrix inversions and high memory demands they require. While adaptive trust-region methods have been developed to mitigate these issues, their performance is often hindered by conservative estimates of key parameters, such as the Lipschitz constant of the Hessian, resulting in suboptimal outcomes. In this paper, we introduce SecondOrderAdaptiveAdam (SOAA), a novel optimization algorithm designed to overcome these limitations. SOAA approximates the Fisher information matrix using a diagonal representation, reducing computational complexity from \(O(n^{2})\) to \(O(n)\), thereby making it suitable for large-scale deep learning models, including large language models (LLMs). Additionally, the algorithm integrates an adaptive trust-region mechanism that dynamically adjusts the trust region size based on observed loss reduction, ensuring both robust convergence and computational efficiency. We empirically demonstrate that SOAA achieves faster and more stable convergence compared to first-order optimizers, such as Adam, under similar computational constraints. However, the diagonal approximation of the Fisher information matrix may be less effective in capturing higher-order interactions between gradients, suggesting potential areas for further refinement and future research.

Related papers

• AdaFisher: Adaptive Second Order Optimization via Fisher Information [22.851200800265914]
  We present AdaFisher, an adaptive second-order that leverages a block-diagonal approximation to the Fisher information matrix for adaptive preconditioning gradient. We demonstrate that AdaFisher outperforms the SOTAs in terms of both accuracy and convergence speed.
  arXiv  Detail & Related papers  (2024-05-26T01:25:02Z)
• Regularized Adaptive Momentum Dual Averaging with an Efficient Inexact Subproblem Solver for Training Structured Neural Network [9.48424754175943]
  We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) for training structured neural networks. We show that RAMDA attains the ideal structure induced by the regularizer at the stationary point of convergence. Experiments in large-scale modern computer vision, language modeling, and speech tasks show that the proposed RAMDA is efficient and consistently outperforms state of the art for training structured neural network.
  arXiv  Detail & Related papers  (2024-03-21T13:43:49Z)
• SGD with Partial Hessian for Deep Neural Networks Optimization [18.78728272603732]
  We propose a compound, which is a combination of a second-order with a precise partial Hessian matrix for updating channel-wise parameters and the first-order gradient descent (SGD) algorithms for updating the other parameters. Compared with first-orders, it adopts a certain amount of information from the Hessian matrix to assist optimization, while compared with the existing second-order generalizations, it keeps the good performance of first-order generalizations imprecise.
  arXiv  Detail & Related papers  (2024-03-05T06:10:21Z)
• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Improved Algorithms for Neural Active Learning [74.89097665112621]
  We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. We introduce two regret metrics by minimizing the population loss that are more suitable in active learning than the one used in state-of-the-art (SOTA) related work.
  arXiv  Detail & Related papers  (2022-10-02T05:03:38Z)
• Dual Optimization for Kolmogorov Model Learning Using Enhanced Gradient Descent [8.714458129632158]
  Kolmogorov model (KM) is an interpretable and predictable representation approach to learning the underlying probabilistic structure of a set of random variables. We propose a computationally scalable KM learning algorithm, based on the regularized dual optimization combined with enhanced gradient descent (GD) method. It is shown that the accuracy of logical relation mining for interpretability by using the proposed KM learning algorithm exceeds $80%$.
  arXiv  Detail & Related papers  (2021-07-11T10:33:02Z)
• Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
  We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network. We design two optimal algorithms that attain these lower bounds. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-08T15:54:44Z)
• BAMSProd: A Step towards Generalizing the Adaptive Optimization Methods to Deep Binary Model [34.093978443640616]
  Recent methods have significantly reduced the performance of Binary Neural Networks (BNNs) guaranteeing the effective and efficient training of BNNs is an unsolved problem. We propose a BAMSProd algorithm with a key observation that the convergence property of optimizing deep binary model is strongly related to the quantization errors.
  arXiv  Detail & Related papers  (2020-09-29T06:12:32Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)
• Steepest Descent Neural Architecture Optimization: Escaping Local Optimum with Signed Neural Splitting [60.97465664419395]
  We develop a significant and surprising extension of the splitting descent framework that addresses the local optimality issue. By simply allowing both positive and negative weights during splitting, we can eliminate the appearance of splitting stability in S2D. We verify our method on various challenging benchmarks such as CIFAR-100, ImageNet and ModelNet40, on which we outperform S2D and other advanced methods on learning accurate and energy-efficient neural networks.
  arXiv  Detail & Related papers  (2020-03-23T17:09:27Z)

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.