Methods with Local Steps and Random Reshuffling for Generally Smooth Non-Convex Federated Optimization

• URL: http://arxiv.org/abs/2412.02781v1
• Date: Tue, 03 Dec 2024 19:20:56 GMT
• Title: Methods with Local Steps and Random Reshuffling for Generally Smooth Non-Convex Federated Optimization
• Authors: Yury Demidovich, Petr Ostroukhov, Grigory Malinovsky, Samuel Horváth, Martin Takáč, Peter Richtárik, Eduard Gorbunov,
• Abstract summary: Non-Machine Learning problems typically do not adhere to the standard smoothness assumption. We propose and analyze new methods with local steps, partial participation of clients, and Random Random Reshuffling. Our theory is consistent with the known results for standard smooth problems.
• Score: 52.61737731453222
• License:
• Abstract: Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0, L_1)$-smoothness assumption, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. However, in the context of Federated Learning, only a few works address this problem but rely on additional limiting assumptions. In this paper, we address this gap in the literature: we propose and analyze new methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. The proposed methods are based on the proper interplay between clients' and server's stepsizes and gradient clipping. Furthermore, we perform the first analysis of these methods under the Polyak-{\L} ojasiewicz condition. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.

Related papers

• The Cost of Shuffling in Private Gradient Based Optimization [40.31928071333575]
  We show that data shuffling results in worse empirical excess risk for textitDP-ShuffleG compared to DP-SGD. We propose textitInterleaved-ShuffleG, a hybrid approach that integrates public data samples in private optimization.
  arXiv  Detail & Related papers  (2025-02-05T22:30:00Z)
• Error Feedback under $(L_0,L_1)$-Smoothness: Normalization and Momentum [56.37522020675243]
  We provide the first proof of convergence for normalized error feedback algorithms across a wide range of machine learning problems. We show that due to their larger allowable stepsizes, our new normalized error feedback algorithms outperform their non-normalized counterparts on various tasks.
  arXiv  Detail & Related papers  (2024-10-22T10:19:27Z)
• Riemannian stochastic optimization methods avoid strict saddle points [68.80251170757647]
  We show that policies under study avoid strict saddle points / submanifolds with probability 1. This result provides an important sanity check as it shows that, almost always, the limit state of an algorithm can only be a local minimizer.
  arXiv  Detail & Related papers  (2023-11-04T11:12:24Z)
• Fine-grained analysis of non-parametric estimation for pairwise learning [9.676007573960383]
  We are concerned with the generalization performance of non-parametric estimation for pairwise learning. Our results can be used to handle a wide range of pairwise learning problems including ranking, AUC, pairwise regression and metric and similarity learning.
  arXiv  Detail & Related papers  (2023-05-31T08:13:14Z)
• SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance [33.593203156666746]
  We show that AdaGrad stepsizes a popular adaptive (self-tuning) method for first-order optimization. In both the low-noise and high-regimes we find sharp rates of convergence in both the low-noise and high-regimes.
  arXiv  Detail & Related papers  (2023-02-17T09:46:08Z)
• A general sample complexity analysis of vanilla policy gradient [101.16957584135767]
  Policy gradient (PG) is one of the most popular reinforcement learning (RL) problems. "vanilla" theoretical understanding of PG trajectory is one of the most popular methods for solving RL problems.
  arXiv  Detail & Related papers  (2021-07-23T19:38:17Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Gradient-Free Methods for Saddle-Point Problem [125.99533416395765]
  We generalize the approach Gasnikov et. al., 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle. Our approach reduces $fracnlog n$ times the required number of oracle calls. In the second part of the paper, we analyze the case when such an assumption cannot be made, we propose a general approach on how to modernize the method to solve this problem.
  arXiv  Detail & Related papers  (2020-05-12T16:44:27Z)

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.