Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning

• URL: http://arxiv.org/abs/2209.00361v1
• Date: Thu, 1 Sep 2022 11:05:26 GMT
• Title: Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning
• Authors: Kazusato Oko, Shunta Akiyama, Tomoya Murata, and Taiji Suzuki
• Abstract summary: We present a single-loop algorithm named SLEDGE (Single-Loop-E Gradient Estimator) for periodic convergence. Unlike existing methods, SLEDGE has the advantage of versatility; (ii) second-order optimal, (ii) in the PL region, and (iii) smaller complexity under less of data.
• Score: 45.78238792836363
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While variance reduction methods have shown great success in solving large scale optimization problems, many of them suffer from accumulated errors and, therefore, should periodically require the full gradient computation. In this paper, we present a single-loop algorithm named SLEDGE (Single-Loop mEthoD for Gradient Estimator) for finite-sum nonconvex optimization, which does not require periodic refresh of the gradient estimator but achieves nearly optimal gradient complexity. Unlike existing methods, SLEDGE has the advantage of versatility; (i) second-order optimality, (ii) exponential convergence in the PL region, and (iii) smaller complexity under less heterogeneity of data. We build an efficient federated learning algorithm by exploiting these favorable properties. We show the first and second-order optimality of the output and also provide analysis under PL conditions. When the local budget is sufficiently large and clients are less (Hessian-)~heterogeneous, the algorithm requires fewer communication rounds then existing methods such as FedAvg, SCAFFOLD, and Mime. The superiority of our method is verified in numerical experiments.

Related papers

• Provably Faster Algorithms for Bilevel Optimization via Without-Replacement Sampling [96.47086913559289]
  gradient-based algorithms are widely used in bilevel optimization. We introduce a without-replacement sampling based algorithm which achieves a faster convergence rate. We validate our algorithms over both synthetic and real-world applications.
  arXiv  Detail & Related papers  (2024-11-07T17:05:31Z)
• Optimal Guarantees for Algorithmic Reproducibility and Gradient Complexity in Convex Optimization [55.115992622028685]
  Previous work suggests that first-order methods would need to trade-off convergence rate (gradient convergence rate) for better. We demonstrate that both optimal complexity and near-optimal convergence guarantees can be achieved for smooth convex minimization and smooth convex-concave minimax problems.
  arXiv  Detail & Related papers  (2023-10-26T19:56:52Z)
• Ordering for Non-Replacement SGD [7.11967773739707]
  We seek to find an ordering that can improve the convergence rates for the non-replacement form of the algorithm. We develop optimal orderings for constant and decreasing step sizes for strongly convex and convex functions. In addition, we are able to combine the ordering with mini-batch and further apply it to more complex neural networks.
  arXiv  Detail & Related papers  (2023-06-28T00:46:58Z)
• A Variance-Reduced Stochastic Gradient Tracking Algorithm for Decentralized Optimization with Orthogonality Constraints [7.028225540638832]
  We propose a novel algorithm for decentralized optimization with orthogonality constraints. VRSGT is the first algorithm for decentralized optimization with orthogonality constraints that reduces both sampling and communication complexities simultaneously. In the numerical experiments, VRGTS has a promising performance in a real-world autonomous sample.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization [0.0]
  We prove that Nesterov's extrapolation has the strength to make the individual convergence of gradient descent methods optimal for nonsmooth problems. We give an extension of the derived algorithms to solve regularized learning tasks with nonsmooth losses in settings. Our method is applicable as an efficient tool for solving large-scale $l$1-regularized hinge-loss learning problems.
  arXiv  Detail & Related papers  (2020-06-08T03:35:41Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

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.