Faster Convergence of Riemannian Stochastic Gradient Descent with Increasing Batch Size

• URL: http://arxiv.org/abs/2501.18164v1
• Date: Thu, 30 Jan 2025 06:23:28 GMT
• Title: Faster Convergence of Riemannian Stochastic Gradient Descent with Increasing Batch Size
• Authors: Kanata Oowada, Hideaki Iiduka,
• Abstract summary: Using an increasing batch size leads to faster RSGD than using a constant batch size.<n>Experiments on principal component analysis and low-rank matrix problems confirmed that, using a growth batch size or an exponential growth batch size results in better performance than using a constant batch size.
• Score: 0.6906005491572401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many models used in machine learning have become so large that even computer computation of the full gradient of the loss function is impractical. This has made it necessary to efficiently train models using limited available information, such as batch size and learning rate. We have theoretically analyzed the use of Riemannian stochastic gradient descent (RSGD) and found that using an increasing batch size leads to faster RSGD convergence than using a constant batch size not only with a constant learning rate but also with a decaying learning rate, such as cosine annealing decay and polynomial decay. In particular, RSGD has a better convergence rate $O(\frac{1}{\sqrt{T}})$ than the existing rate $O(\frac{\sqrt{\log T}}{\sqrt[4]{T}})$ with a diminishing learning rate, where $T$ is the number of iterations. The results of experiments on principal component analysis and low-rank matrix completion problems confirmed that, except for the MovieLens dataset and a constant learning rate, using a polynomial growth batch size or an exponential growth batch size results in better performance than using a constant batch size.

Related papers

• VAMO: Efficient Large-Scale Nonconvex Optimization via Adaptive Zeroth Order Variance Reduction [3.130722489512822]
  VAMO combines FO mini-batch gradients with ZO finite-difference probes under an ZOG-style framework.<n>VAMO outperforms established FO and ZO methods, offering a faster, more flexible option for improved efficiency.
  arXiv  Detail & Related papers  (2025-05-20T05:31:15Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture. Non-smooth regularization is often incorporated into machine learning tasks. We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs [24.305423716384272]
  We study the impact of the batch size on the iteration time $T$ of training two-layer neural networks with one-pass gradient descent (SGD) We show that performing gradient updates with large batches minimizes the training time without changing the total sample complexity. We show that one can track the training progress by a system of low-dimensional ordinary differential equations (ODEs)
  arXiv  Detail & Related papers  (2024-06-04T09:44:49Z)
• 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)
• 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)
• Winner-Take-All Column Row Sampling for Memory Efficient Adaptation of Language Model [89.8764435351222]
  We propose a new family of unbiased estimators called WTA-CRS, for matrix production with reduced variance. Our work provides both theoretical and experimental evidence that, in the context of tuning transformers, our proposed estimators exhibit lower variance compared to existing ones.
  arXiv  Detail & Related papers  (2023-05-24T15:52:08Z)
• Communication-Efficient Adam-Type Algorithms for Distributed Data Mining [93.50424502011626]
  We propose a class of novel distributed Adam-type algorithms (emphi.e., SketchedAMSGrad) utilizing sketching. Our new algorithm achieves a fast convergence rate of $O(frac1sqrtnT + frac1(k/d)2 T)$ with the communication cost of $O(k log(d))$ at each iteration.
  arXiv  Detail & Related papers  (2022-10-14T01:42:05Z)
• 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)
• Trajectory of Mini-Batch Momentum: Batch Size Saturation and Convergence in High Dimensions [2.575030923243061]
  We show that the dynamics of SGD+M converge to a deterministic discrete Volterra equation as dimension increases. For batch sizes smaller than the ICR, SGD+M has rates that scale like a multiple of the single batch SGD rate.
  arXiv  Detail & Related papers  (2022-06-02T13:03:14Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• Distributed stochastic optimization with large delays [59.95552973784946]
  One of the most widely used methods for solving large-scale optimization problems is distributed asynchronous gradient descent (DASGD) We show that DASGD converges to a global optimal implementation model under same delay assumptions.
  arXiv  Detail & Related papers  (2021-07-06T21:59:49Z)
• Gradient Boosted Binary Histogram Ensemble for Large-scale Regression [60.16351608335641]
  We propose a gradient boosting algorithm for large-scale regression problems called textitGradient Boosted Binary Histogram Ensemble (GBBHE) based on binary histogram partition and ensemble learning. In the experiments, compared with other state-of-the-art algorithms such as gradient boosted regression tree (GBRT), our GBBHE algorithm shows promising performance with less running time on large-scale datasets.
  arXiv  Detail & Related papers  (2021-06-03T17:05:40Z)
• 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)
• On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems [75.58134963501094]
  This paper analyzes the trajectories of gradient descent (SGD) We show that SGD avoids saddle points/manifolds with $1$ for strict step-size policies.
  arXiv  Detail & Related papers  (2020-06-19T14:11:26Z)
• Convergence of Meta-Learning with Task-Specific Adaptation over Partial Parameters [152.03852111442114]
  Although model-agnostic metalearning (MAML) is a very successful algorithm meta-learning practice, it can have high computational complexity. Our paper shows that such complexity can significantly affect the overall convergence performance of ANIL.
  arXiv  Detail & Related papers  (2020-06-16T19:57:48Z)
• Accelerated Convergence for Counterfactual Learning to Rank [65.63997193915257]
  We show that convergence rate of SGD approaches with IPS-weighted gradients suffers from the large variance introduced by the IPS weights. We propose a novel learning algorithm, called CounterSample, that has provably better convergence than standard IPS-weighted gradient descent methods. We prove that CounterSample converges faster and complement our theoretical findings with empirical results.
  arXiv  Detail & Related papers  (2020-05-21T12:53:36Z)

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.