From Inexact Gradients to Byzantine Robustness: Acceleration and Optimization under Similarity

• URL: http://arxiv.org/abs/2602.03329v1
• Date: Tue, 03 Feb 2026 09:56:23 GMT
• Title: From Inexact Gradients to Byzantine Robustness: Acceleration and Optimization under Similarity
• Authors: Renaud Gaucher, Aymeric Dieuleveut, Hadrien Hendrikx,
• Abstract summary: We show that Byzantine-robust distributed optimization can be cast as a general optimization with inexact gradient oracles.<n>We propose two optimization schemes to speed up the convergence.
• Score: 12.097833603814252
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard federated learning algorithms are vulnerable to adversarial nodes, a.k.a. Byzantine failures. To solve this issue, robust distributed learning algorithms have been developed, which typically replace parameter averaging by robust aggregations. While generic conditions on these aggregations exist to guarantee the convergence of (Stochastic) Gradient Descent (SGD), the analyses remain rather ad-hoc. This hinders the development of more complex robust algorithms, such as accelerated ones. In this work, we show that Byzantine-robust distributed optimization can, under standard generic assumptions, be cast as a general optimization with inexact gradient oracles (with both additive and multiplicative error terms), an active field of research. This allows for instance to directly show that GD on top of standard robust aggregation procedures obtains optimal asymptotic error in the Byzantine setting. Going further, we propose two optimization schemes to speed up the convergence. The first one is a Nesterov-type accelerated scheme whose proof directly derives from accelerated inexact gradient results applied to our formulation. The second one hinges on Optimization under Similarity, in which the server leverages an auxiliary loss function that approximates the global loss. Both approaches allow to drastically reduce the communication complexity compared to previous methods, as we show theoretically and empirically.

Related papers

• VFOG: Variance-Reduced Fast Optimistic Gradient Methods for a Class of Nonmonotone Generalized Equations [3.6997773420183866]
  We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques.<n>We show that our method achieves $mathcalO (1/k2)$ convergence rates in expectation on the squared norm of residual under the Lipschitz continuity.<n>We show that the sequence of iterates of our method almost surely converges to a solution of the underlying problem.
  arXiv  Detail & Related papers  (2025-08-22T20:46:29Z)
• Elucidating Subspace Perturbation in Zeroth-Order Optimization: Theory and Practice at Scale [33.38543010618118]
  Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods.<n>We show that high dimensionality is the primary bottleneck and introduce the notion of textitsubspace alignment to explain how the subspace perturbations reduce gradient noise and accelerate convergence.<n>We propose an efficient ZO method using block coordinate descent (MeZO-BCD), which perturbs and updates only a subset of parameters at each step.
  arXiv  Detail & Related papers  (2025-01-31T12:46:04Z)
• Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stability [107.65337427333064]
  optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. In this work, we present the first trial in the single-dependent generalization of AUPRC optimization. Experiments on three image retrieval datasets on speak to the effectiveness and soundness of our framework.
  arXiv  Detail & Related papers  (2022-09-27T09:06:37Z)
• 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)
• Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity [49.66890309455787]
  We introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size. Our convergence guarantees hold under the arbitrary sampling paradigm, and we give insights into the complexity of minibatching.
  arXiv  Detail & Related papers  (2021-06-30T18:32:46Z)
• Robust Distributed Optimization With Randomly Corrupted Gradients [24.253191879453784]
  We propose a first-order distributed optimization algorithm that is provably robust to Byzantine failures-arbitrary and potentially adversarial behavior. Our algorithm achieves order normalization and trustworthy statistical error convergence rates.
  arXiv  Detail & Related papers  (2021-06-28T19:45:25Z)
• 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)
• Doubly Robust Off-Policy Actor-Critic: Convergence and Optimality [131.45028999325797]
  We develop a doubly robust off-policy AC (DR-Off-PAC) for discounted MDP. DR-Off-PAC adopts a single timescale structure, in which both actor and critics are updated simultaneously with constant stepsize. We study the finite-time convergence rate and characterize the sample complexity for DR-Off-PAC to attain an $epsilon$-accurate optimal policy.
  arXiv  Detail & Related papers  (2021-02-23T18:56:13Z)
• Provably Convergent Working Set Algorithm for Non-Convex Regularized Regression [0.0]
  This paper proposes a working set algorithm for non-regular regularizers with convergence guarantees. Our results demonstrate high gain compared to the full problem solver for both block-coordinates or a gradient solver.
  arXiv  Detail & Related papers  (2020-06-24T07:40:31Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• 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)
• Explicit Regularization of Stochastic Gradient Methods through Duality [9.131027490864938]
  We propose randomized Dykstra-style algorithms based on randomized dual coordinate ascent. For accelerated coordinate descent, we obtain a new algorithm that has better convergence properties than existing gradient methods in the interpolating regime.
  arXiv  Detail & Related papers  (2020-03-30T20:44:56Z)

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.