RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation

• URL: http://arxiv.org/abs/2603.22155v1
• Date: Mon, 23 Mar 2026 16:18:31 GMT
• Title: RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation
• Abstract summary: Extragradient (EG) may suffer from discretization bias when applied to non-linear fields, conservative or otherwise.<n>We introduce RAndomized Mid-Point for debiAsed Gradient Extrapolation (RAMPAGE) and its variance-reduced counterpart, RAM+.
• Score: 10.213412445129089
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when applied to non-linear vector fields, conservative or otherwise. To resolve this discretization shortcoming, we introduce RAndomized Mid-Point for debiAsed Gradient Extrapolation (RAMPAGE) and its variance-reduced counterpart, RAMPAGE+ which leverages antithetic sampling. In contrast with EG, both methods are unbiased. Furthermore, leveraging negative correlation, RAMPAGE+ acts as an unbiased, geometric path-integrator that completely removes internal first-order terms from the variance, provably improving upon RAMPAGE. We further demonstrate that both methods enjoy provable $\mathcal{O}(1/k)$ convergence guarantees for a range of problems including root finding under co-coercive, co-hypomonotone, and generalized Lipschitzness regimes. Furthermore, we introduce symmetrically scaled variants to extend our results to constrained VIs. Finally, we provide convergence guarantees of both methods for stochastic and deterministic smooth convex-concave games. Somewhat interestingly, despite being a randomized method, RAMPAGE+ attains purely deterministic bounds for a number of the studied settings.

Related papers

• Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere [11.087393998848254]
  In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective.<n>Current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHEREJEPA)<n>This injects projection variance into the training gradients, destabilizing optimization, and hindering convergence.<n>In this work, we first show that analytically integrating out these random projections yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods.
  arXiv  Detail & Related papers  (2026-06-16T07:10:05Z)
• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Pivotal CLTs for Pseudolikelihood via Conditional Centering in Dependent Random Fields [1.3875545441867139]
  We study fluctuations of conditionally centered statistics of the form $$N-1/2sum_i=1N c_i(g(sigma_i)-mathbbE_N[g(sigma_i)|sigma_j,jneq i])$$ where $(sigma_j,ldots,sigma_N) are sampled from a dependent random field.<n>We develop a general framework for maximum pseudolikelihood inference in dependent random fields.
  arXiv  Detail & Related papers  (2025-10-06T16:06:45Z)
• Entropic Mirror Descent for Linear Systems: Polyak's Stepsize and Implicit Bias [55.72269695392027]
  This paper focuses on applying entropic mirror descent to solve linear systems.<n>The main challenge for the convergence analysis stems from the unboundedness of the domain.<n>To overcome this without imposing restrictive assumptions, we introduce a variant of Polyak-type stepsizes.
  arXiv  Detail & Related papers  (2025-05-05T12:33:18Z)
• Convergence Analysis of Federated Learning Methods Using Backward Error Analysis [5.954488351438149]
  In this paper, we attempt to find the implicit regularizer for various federated learning algorithms.<n>We show that the implicit regularizer hampers its convergence.<n>Similarly, we compute the implicit regularizers FedSAM SCAFFOLD, and explain why they converge better.
  arXiv  Detail & Related papers  (2025-03-05T03:26:48Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Spectrum-Aware Debiasing: A Modern Inference Framework with Applications to Principal Components Regression [1.342834401139078]
  We introduce SpectrumAware Debiasing, a novel method for high-dimensional regression. Our approach applies to problems with structured, heavy tails, and low-rank structures. We demonstrate our method through simulated and real data experiments.
  arXiv  Detail & Related papers  (2023-09-14T15:58:30Z)
• Bridging Discrete and Backpropagation: Straight-Through and Beyond [62.46558842476455]
  We propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. We propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs.
  arXiv  Detail & Related papers  (2023-04-17T20:59:49Z)
• Solving Constrained Variational Inequalities via an Interior Point Method [88.39091990656107]
  We develop an interior-point approach to solve constrained variational inequality (cVI) problems. We provide convergence guarantees for ACVI in two general classes of problems. Unlike previous work in this setting, ACVI provides a means to solve cVIs when the constraints are nontrivial.
  arXiv  Detail & Related papers  (2022-06-21T17:55:13Z)
• Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation [64.92152574895111]
  We propose a simple Orthogonal Jacobian Regularization (OroJaR) to encourage deep generative model to learn disentangled representations. Our method is effective in disentangled and controllable image generation, and performs favorably against the state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-08-17T15:01:46Z)
• Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck [14.309243378538012]
  We propose an online compression scheme that fixes an error neighborhood with respect to the Hellinger metric centered at the current posterior. For constant error radius, POG converges to a neighborhood of the population posterior (Theorem 1(ii))but with finite memory at-worst determined by the metric entropy of the feature space.
  arXiv  Detail & Related papers  (2020-04-23T11:52:06Z)
• GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values [75.17074235764757]
  We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution. GenDICE is the state-of-the-art for estimating such density ratios.
  arXiv  Detail & Related papers  (2020-01-29T22:10:11Z)

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.