On the Convergence of Momentum-Based Algorithms for Federated Stochastic Bilevel Optimization Problems

• URL: http://arxiv.org/abs/2204.13299v1
• Date: Thu, 28 Apr 2022 06:14:21 GMT
• Title: On the Convergence of Momentum-Based Algorithms for Federated Stochastic Bilevel Optimization Problems
• Authors: Hongchang Gao
• Abstract summary: In particular, we developed two momentum-based algorithms for optimizing this kind of problem. We established the convergence rate of these two algorithms, providing their sample and communication complexities.
• Score: 22.988563731766586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we studied the federated stochastic bilevel optimization problem. In particular, we developed two momentum-based algorithms for optimizing this kind of problem. In addition, we established the convergence rate of these two algorithms, providing their sample and communication complexities. To the best of our knowledge, this is the first work achieving such favorable theoretical results.

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)
• A Single-Loop Algorithm for Decentralized Bilevel Optimization [11.67135350286933]
  We propose a novel single-loop algorithm for solving decentralized bilevel optimization with a strongly convex lower-level problem. Our approach is a fully single-loop method that approximates the hypergradient using only two matrix-vector multiplications per iteration. Our analysis demonstrates that the proposed algorithm achieves the best-known convergence rate for bilevel optimization algorithms.
  arXiv  Detail & Related papers  (2023-11-15T13:29:49Z)
• Decentralized Multi-Level Compositional Optimization Algorithms with Level-Independent Convergence Rate [26.676582181833584]
  Decentralized multi-level optimization is challenging because of the multilevel structure and decentralized communication. We develop two novel decentralized optimization algorithms to optimize the multi-level compositional problem.
  arXiv  Detail & Related papers  (2023-06-06T00:23:28Z)
• Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems [118.00379425831566]
  We propose a communication-efficient algorithm, named FedBiOAcc. We prove that FedBiOAcc-Local converges at the same rate for this type of problems. Empirical results show superior performance of our algorithms.
  arXiv  Detail & Related papers  (2023-02-13T21:28:53Z)
• On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network [55.56019538079826]
  Bilevel optimization has been applied to a wide variety of machine learning models. Most existing algorithms restrict their single-machine setting so that they are incapable of handling distributed data. We develop novel decentralized bilevel optimization algorithms based on a gradient tracking communication mechanism and two different gradients.
  arXiv  Detail & Related papers  (2022-06-30T05:29:52Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• 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)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)

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.