A Superlinearly Convergent Evolution Strategy

• URL: http://arxiv.org/abs/2505.10987v1
• Date: Fri, 16 May 2025 08:33:30 GMT
• Title: A Superlinearly Convergent Evolution Strategy
• Authors: Tobias Glasmachers,
• Abstract summary: We present a hybrid algorithm between an evolution strategy and a quasi Newton method.<n>The proposed method replaces the global recombination step commonly found in non-elitist evolution strategies with a quasi-Newton step.<n> Numerical results show superlinear convergence, resulting in improved performance in particular on smooth convex problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a hybrid algorithm between an evolution strategy and a quasi Newton method. The design is based on the Hessian Estimation Evolution Strategy, which iteratively estimates the inverse square root of the Hessian matrix of the problem. This is akin to a quasi-Newton method and corresponding derivative-free trust-region algorithms like NEWUOA. The proposed method therefore replaces the global recombination step commonly found in non-elitist evolution strategies with a quasi-Newton step. Numerical results show superlinear convergence, resulting in improved performance in particular on smooth convex problems.

Related papers

• An Efficient Reconstructed Differential Evolution Variant by Some of the Current State-of-the-art Strategies for Solving Single Objective Bound Constrained Problems [5.095287502726488]
  We propose a strategy recombination and reconstruction differential evolution algorithm called reconstructed differential evolution (RDE) to solve single-objective bounded optimization problems. Based on the benchmark suite of the 2024 IEEE Congress on Evolutionary Computation, we tested RDE and several other advanced differential evolution variants.
  arXiv  Detail & Related papers  (2024-04-25T01:48:44Z)
• Incremental Quasi-Newton Methods with Faster Superlinear Convergence Rates [50.36933471975506]
  We consider the finite-sum optimization problem, where each component function is strongly convex and has Lipschitz continuous gradient and Hessian. The recently proposed incremental quasi-Newton method is based on BFGS update and achieves a local superlinear convergence rate. This paper proposes a more efficient quasi-Newton method by incorporating the symmetric rank-1 update into the incremental framework.
  arXiv  Detail & Related papers  (2024-02-04T05:54:51Z)
• Stochastic Gradient Descent for Gaussian Processes Done Right [86.83678041846971]
  We show that when emphdone right -- by which we mean using specific insights from optimisation and kernel communities -- gradient descent is highly effective. We introduce a emphstochastic dual descent algorithm, explain its design in an intuitive manner and illustrate the design choices. Our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.
  arXiv  Detail & Related papers  (2023-10-31T16:15:13Z)
• Variance-Reduced Gradient Estimation via Noise-Reuse in Online Evolution Strategies [50.10277748405355]
  Noise-Reuse Evolution Strategies (NRES) is a general class of unbiased online evolution strategies methods. We show NRES results in faster convergence than existing AD and ES methods in terms of wall-clock time and number of steps across a variety of applications.
  arXiv  Detail & Related papers  (2023-04-21T17:53:05Z)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• Online Learning Guided Curvature Approximation: A Quasi-Newton Method with Global Non-Asymptotic Superlinear Convergence [22.286753988825048]
  We present the first globally convergent quasi-Newton method with an explicit non-asymptotic superlinear convergence rate. Unlike classical quasi-Newton methods, we build our algorithm upon the hybrid proximal extragradient method.
  arXiv  Detail & Related papers  (2023-02-16T20:58:09Z)
• Robust empirical risk minimization via Newton's method [9.797319790710711]
  A new variant of Newton's method for empirical risk minimization is studied. The gradient and Hessian of the objective function are replaced by robust estimators. An algorithm for obtaining robust Newton directions based on the conjugate gradient method is also proposed.
  arXiv  Detail & Related papers  (2023-01-30T18:54:54Z)
• Distributed Evolution Strategies for Black-box Stochastic Optimization [42.90600124972943]
  This work concerns the evolutionary approaches to distributed black-box optimization. Each worker can individually solve an approximation of the problem with algorithms. We propose two alternative simulation schemes which significantly improve robustness of problems.
  arXiv  Detail & Related papers  (2022-04-09T11:18:41Z)
• First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems [88.58409977434269]
  We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) Our contribution is to provide two simple first-order algorithmic frameworks based on the quadratic penalty method and the augmented Lagrangian method. We provide nonasymptotic theoretical guarantees for these algorithms.
  arXiv  Detail & Related papers  (2022-04-07T00:11:05Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)
• A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems [3.888272676868008]
  We propose a novel type to solve inverse problems consisting general architecture and neural intimating. Results that the proposed network outperforms the state reconstruction methods on different image problems in terms of efficiency and results.
  arXiv  Detail & Related papers  (2020-03-15T03:44:43Z)

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.