Adaptively Incorporating Directional Hints into Zeroth-Order Optimization

• URL: http://arxiv.org/abs/2609.08277v1
• Date: Tue, 08 Sep 2026 05:42:02 GMT
• Title: Adaptively Incorporating Directional Hints into Zeroth-Order Optimization
• Abstract summary: We develop an algorithm that achieves zeroth-order optimization of non- functions with the aid directional hints.<n>We validate the method, demonstrating sustained progress on non- control tasks.
• Score: 49.940317286021696
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study zeroth-order optimization of non-convex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations of the true gradient direction, given by linear subspaces at each iteration. To leverage these hints adaptively while maintaining robustness to their quality, we introduce Control-Variate Zeroth-Order Descent (CV-ZOD), a new framework that refines the classical zeroth-order gradient estimator with a control variate that can be set based on the directional hints. We first show that the oracle algorithm that optimally sets the reference vector and step size at each iteration achieves a convergence rate that interpolates between the first-order $O(1/T)$ rate and the zeroth-order $O(d/T)$ rate, depending on the quality of the hints along the trajectory. We then develop a practical variant of CV-ZOD that achieves the same oracle guarantee up to logarithmic factors, without any prior knowledge of the hint quality. We validate the method empirically on simulation-based scientific optimization tasks, demonstrating sustained progress on non-convex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.

Related papers

• A Parameter-Free First-Order Algorithm for Non-Convex Optimization with $\tilde{\mkern1mu O}(ε^{-5/3})$ Global Rate [0.12744523252873352]
  We introduce PF-AGD, the first parameter-free, accelerated first-order method to achieve $O(-5)$ complexity on smooth non-log objectives.
  arXiv  Detail & Related papers  (2026-05-04T01:17:06Z)
• Prior-Informed Zeroth-Order Optimization with Adaptive Direction Alignment for Memory-Efficient LLM Fine-Tuning [4.278794376089146]
  We propose a plug-and-play method that incorporates prior-informed perturbations to refine gradient estimation.<n>Our method significantly accelerates convergence compared to standard ZO approaches.<n>We prove that our gradient estimator achieves stronger alignment with the true gradient direction.
  arXiv  Detail & Related papers  (2026-01-08T08:27:15Z)
• Single Point-Based Distributed Zeroth-Order Optimization with a Non-Convex Stochastic Objective Function [14.986031916712108]
  We introduce a zero-order distributed optimization method based on a one-point estimate of the gradient tracking technique. We prove that this new technique converges with a numerical function at a noisy setting.
  arXiv  Detail & Related papers  (2024-10-08T11:45:45Z)
• Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity [59.75300530380427]
  We consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.
  arXiv  Detail & Related papers  (2024-06-28T02:56:22Z)
• Double Variance Reduction: A Smoothing Trick for Composite Optimization Problems without First-Order Gradient [40.22217106270146]
  Variance reduction techniques are designed to decrease the sampling variance, thereby accelerating convergence rates of first-order (FO) and zeroth-order (ZO) optimization methods. In composite optimization problems, ZO methods encounter an additional variance called the coordinate-wise variance, which stems from the random estimation. This paper proposes the Zeroth-order Proximal Double Variance Reduction (ZPDVR) method, which utilizes the averaging trick to reduce both sampling and coordinate-wise variances.
  arXiv  Detail & Related papers  (2024-05-28T02:27:53Z)
• ELRA: Exponential learning rate adaption gradient descent optimization method [83.88591755871734]
  We present a novel, fast (exponential rate), ab initio (hyper-free) gradient based adaption. The main idea of the method is to adapt the $alpha by situational awareness. It can be applied to problems of any dimensions n and scales only linearly.
  arXiv  Detail & Related papers  (2023-09-12T14:36:13Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [61.98523595657983]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms.<n>An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Stochastic Zeroth order Descent with Structured Directions [10.604744518360464]
  We introduce and analyze Structured Zeroth order Descent (SSZD), a finite difference approach that approximates a gradient on a set $lleq d directions, where $d is the dimension of the ambient space. For convex convex we prove almost sure convergence of functions on $O( (d/l) k-c1/2$)$ for every $c1/2$, which is arbitrarily close to the one of the Gradient Descent (SGD) in terms of one number of iterations.
  arXiv  Detail & Related papers  (2022-06-10T14:00:06Z)
• An Accelerated Variance-Reduced Conditional Gradient Sliding Algorithm for First-order and Zeroth-order Optimization [111.24899593052851]
  Conditional gradient algorithm (also known as the Frank-Wolfe algorithm) has recently regained popularity in the machine learning community. ARCS is the first zeroth-order conditional gradient sliding type algorithms solving convex problems in zeroth-order optimization. In first-order optimization, the convergence results of ARCS substantially outperform previous algorithms in terms of the number of gradient query oracle.
  arXiv  Detail & Related papers  (2021-09-18T07:08:11Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

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.