An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

• URL: http://arxiv.org/abs/2208.00956v5
• Date: Sun, 24 Mar 2024 05:01:56 GMT
• Title: An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
• Authors: Bin Shi, Guodong Sun,
• Abstract summary: We propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs) The sampling approach directly reduces the gradient to the objective function value (zeroth-order information) We demonstrate the CNOPs obtained with their spatial patterns, objective values, quantifying computation times, and nonlinear error growth.
• Score: 5.758073912084367
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive, since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times, and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is much shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy.

Related papers

• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Generative modeling of time-dependent densities via optimal transport and projection pursuit [3.069335774032178]
  We propose a cheap alternative to popular deep learning algorithms for temporal modeling. Our method is highly competitive compared with state-of-the-art solvers.
  arXiv  Detail & Related papers  (2023-04-19T13:50:13Z)
• Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning [45.78238792836363]
  We present a single-loop algorithm named SLEDGE (Single-Loop-E Gradient Estimator) for periodic convergence. Unlike existing methods, SLEDGE has the advantage of versatility; (ii) second-order optimal, (ii) in the PL region, and (iii) smaller complexity under less of data.
  arXiv  Detail & Related papers  (2022-09-01T11:05:26Z)
• Sparse Bayesian Learning for Complex-Valued Rational Approximations [0.03392423750246091]
  Surrogate models are used to alleviate the computational burden in engineering tasks. These models show a strongly non-linear dependence on their input parameters. We apply a sparse learning approach to the rational approximation.
  arXiv  Detail & Related papers  (2022-06-06T12:06:13Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• Local policy search with Bayesian optimization [73.0364959221845]
  Reinforcement learning aims to find an optimal policy by interaction with an environment. Policy gradients for local search are often obtained from random perturbations. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient.
  arXiv  Detail & Related papers  (2021-06-22T16:07:02Z)
• Effective Proximal Methods for Non-convex Non-smooth Regularized Learning [27.775096437736973]
  We show that the independent sampling scheme tends to improve performance of the commonly-used uniform sampling scheme. Our new analysis also derives a speed for the sampling than best one available so far.
  arXiv  Detail & Related papers  (2020-09-14T16:41:32Z)
• 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)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)

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.