A Stochastic Approximation Approach for Efficient Decentralized Optimization on Random Networks

• URL: http://arxiv.org/abs/2410.18774v2
• Date: Wed, 28 May 2025 04:13:41 GMT
• Title: A Stochastic Approximation Approach for Efficient Decentralized Optimization on Random Networks
• Authors: Chung-Yiu Yau, Haoming Liu, Hoi-To Wai,
• Abstract summary: A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random time topologies under unreliable bandwidth-constrained communication network.<n>This paper introduces a novel approximation approach with a Fully Primal Dual Algorithm (FSPDA) framework.<n> Numerical experiments show the benefits of the FSPDA algorithms.
• Score: 21.66341372216097
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic approximation approach with a Fully Stochastic Primal Dual Algorithm (FSPDA) framework. Our framework relies on a novel observation that randomness in time varying topology can be incorporated in a stochastic augmented Lagrangian formulation, whose expected value admits saddle points that coincide with stationary solutions of the decentralized optimization problem. With the FSPDA framework, we develop two new algorithms supporting efficient sparsified communication on random time varying topologies -- FSPDA-SA allows agents to execute multiple local gradient steps depending on the time varying topology to accelerate convergence, and FSPDA-STORM further incorporates a variance reduction step to improve sample complexity. For problems with smooth (possibly non-convex) objective function, within $T$ iterations, we show that FSPDA-SA (resp. FSPDA-STORM) finds an $\mathcal{O}( 1/\sqrt{T} )$-stationary (resp. $\mathcal{O}( 1/T^{2/3} )$) solution. Numerical experiments show the benefits of the FSPDA algorithms.

Related papers

• Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping [21.865728815935665]
  We provide the first convergence under heavy-tailed noises but without clipping. We also establish first $mathcalO(Tfrac1-mathfrakp3mathfrakp-2)$ convergence rate in the case where the tail index $mathfrakp$ is unknown in advance.
  arXiv  Detail & Related papers  (2024-12-27T08:46:46Z)
• Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization [77.3396841985172]
  We provide a unified analysis of two-timescale gradient ascent (TTGDA) for solving structured non minimax optimization problems. Our contribution is to design TTGDA algorithms are effective beyond the setting.
  arXiv  Detail & Related papers  (2024-08-21T20:14:54Z)
• High Probability Convergence of Stochastic Gradient Methods [15.829413808059124]
  We show convergence with bounds depending on the initial distance to the optimal solution. We demonstrate that our techniques can be used to obtain high bound for AdaGrad-Norm.
  arXiv  Detail & Related papers  (2023-02-28T18:42:11Z)
• ReSQueing Parallel and Private Stochastic Convex Optimization [59.53297063174519]
  We introduce a new tool for BFG convex optimization (SCO): a Reweighted Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. We develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings.
  arXiv  Detail & Related papers  (2023-01-01T18:51:29Z)
• Faster Adaptive Federated Learning [84.38913517122619]
  Federated learning has attracted increasing attention with the emergence of distributed data. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on momentum-based variance reduced technique in cross-silo FL.
  arXiv  Detail & Related papers  (2022-12-02T05:07:50Z)
• Adaptive Federated Minimax Optimization with Lower Complexities [82.51223883622552]
  We propose an efficient adaptive minimax optimization algorithm (i.e., AdaFGDA) to solve these minimax problems. It builds our momentum-based reduced and localSGD techniques, and it flexibly incorporate various adaptive learning rates.
  arXiv  Detail & Related papers  (2022-11-14T12:32:18Z)
• An Optimal Stochastic Algorithm for Decentralized Nonconvex Finite-sum Optimization [25.21457349137344]
  We show a proof to show DEAREST requires at most $mathcal O(+sqrtmnLvarepsilon-2)$ first-order oracle (IFO) calls and $mathcal O(Lvarepsilon-2/sqrt1-lambda_W)$ communication rounds.
  arXiv  Detail & Related papers  (2022-10-25T11:37:11Z)
• Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization [116.89941263390769]
  We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $min_mathbfxmax_mathbfyF(mathbfx) + H(mathbfx,mathbfy)$, where one has access to first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. We present a emphaccelerated gradient-extragradient (AG-EG) descent-ascent algorithm that combines extragrad
  arXiv  Detail & Related papers  (2022-06-17T06:10:20Z)
• Sharper Convergence Guarantees for Asynchronous SGD for Distributed and Federated Learning [77.22019100456595]
  We show a training algorithm for distributed computation workers with varying communication frequency. In this work, we obtain a tighter convergence rate of $mathcalO!!!(sigma2-2_avg!! . We also show that the heterogeneity term in rate is affected by the average delay within each worker.
  arXiv  Detail & Related papers  (2022-06-16T17:10:57Z)
• Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization [28.862321453597918]
  Non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed proximal-gradient algorithm with random reshuffling to solve the problem.
  arXiv  Detail & Related papers  (2021-11-06T07:29:55Z)
• Distributed stochastic optimization with large delays [59.95552973784946]
  One of the most widely used methods for solving large-scale optimization problems is distributed asynchronous gradient descent (DASGD) We show that DASGD converges to a global optimal implementation model under same delay assumptions.
  arXiv  Detail & Related papers  (2021-07-06T21:59:49Z)
• Asynchronous Stochastic Optimization Robust to Arbitrary Delays [54.61797739710608]
  We consider optimization with delayed gradients where, at each time stept$, the algorithm makes an update using a stale computation - d_t$ for arbitrary delay $d_t gradient. Our experiments demonstrate the efficacy and robustness of our algorithm in cases where the delay distribution is skewed or heavy-tailed.
  arXiv  Detail & Related papers  (2021-06-22T15:50:45Z)
• 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)
• Improving the Transient Times for Distributed Stochastic Gradient Methods [5.215491794707911]
  We study a distributed gradient algorithm, called exact diffusion adaptive stepsizes (EDAS) We show EDAS achieves the same network independent convergence rate as centralized gradient descent (SGD) To the best of our knowledge, EDAS achieves the shortest time when the average of the $n$ cost functions is strongly convex.
  arXiv  Detail & Related papers  (2021-05-11T08:09:31Z)
• Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling [86.85697555068168]
  Two-stage algorithmic optimization plays a critical role in various engineering and scientific applications. There still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. We show that PDD-SSCA can achieve superior performance over existing solutions.
  arXiv  Detail & Related papers  (2021-05-05T03:36:00Z)
• Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization [59.65871549878937]
  We prove that the practical single loop accelerated gradient tracking needs $O(fracgamma1-sigma_gamma)2sqrtfracLepsilon)$. Our convergence rates improve significantly over the ones of $O(frac1epsilon5/7)$ and $O(fracLmu)5/7frac1 (1-sigma)1.5logfrac1epsilon)$.
  arXiv  Detail & Related papers  (2021-04-06T15:34:14Z)
• Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method [3.860616339202303]
  This paper investigates the distributed non optimization problem of minimizing a global cost function formed by the summation of $ZOn$ local cost functions. Agents approximate their own ZO coordinate method to solve the problem.
  arXiv  Detail & Related papers  (2021-03-24T03:07:46Z)
• Distributed Stochastic Consensus Optimization with Momentum for Nonconvex Nonsmooth Problems [45.88640334610308]
  This paper presents a new distributed optimization algorithm for non-smooth problems. We show that the proposed algorithm can achieve an overcal communication. Experiments are presented to illustrate the effectiveness of the proposed algorithms.
  arXiv  Detail & Related papers  (2020-11-10T13:12:21Z)
• 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)
• S-ADDOPT: Decentralized stochastic first-order optimization over directed graphs [16.96562173221624]
  Decentralized convex optimization is proposed to minimize a sum of smooth and strongly cost functions when the functions are distributed over a directed network nodes. In particular, we propose thetextbftextttS-ADDOPT algorithm that assumes a first-order oracle at each node. For decaying step-sizes$mathcalO (1/k)$, we show thattextbfttS-ADDOPT reaches the exact solution subly at$mathcalO (1/k)$ and its convergence is networkally-independent
  arXiv  Detail & Related papers  (2020-05-15T21:14:22Z)

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.