qNBO: quasi-Newton Meets Bilevel Optimization

• URL: http://arxiv.org/abs/2502.01076v1
• Date: Mon, 03 Feb 2025 05:36:45 GMT
• Title: qNBO: quasi-Newton Meets Bilevel Optimization
• Authors: Sheng Fang, Yong-Jin Liu, Wei Yao, Chengming Yu, Jin Zhang,
• Abstract summary: Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. We introduce a general framework to address these computational challenges in a coordinated manner. Specifically, we leverage quasi-Newton algorithms to accelerate the resolution of the lower-level problem while efficiently approximating the inverse Hessian-vector product.
• Score: 26.0555315825777
• License:
• Abstract: Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational hurdles, notably the computation of the exact lower-level solution and the inverse Hessian of the lower-level objective. Although these two aspects are inherently connected, existing methods typically handle them separately by solving the lower-level problem and a linear system for the inverse Hessian-vector product. In this paper, we introduce a general framework to address these computational challenges in a coordinated manner. Specifically, we leverage quasi-Newton algorithms to accelerate the resolution of the lower-level problem while efficiently approximating the inverse Hessian-vector product. Furthermore, by exploiting the superlinear convergence properties of BFGS, we establish the non-asymptotic convergence analysis of the BFGS adaptation within our framework. Numerical experiments demonstrate the comparable or superior performance of the proposed algorithms in real-world learning tasks, including hyperparameter optimization, data hyper-cleaning, and few-shot meta-learning.

Related papers

• Provably Faster Algorithms for Bilevel Optimization via Without-Replacement Sampling [96.47086913559289]
  gradient-based algorithms are widely used in bilevel optimization. We introduce a without-replacement sampling based algorithm which achieves a faster convergence rate. We validate our algorithms over both synthetic and real-world applications.
  arXiv  Detail & Related papers  (2024-11-07T17:05:31Z)
• A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints [66.61399765513383]
  We develop a BLOCC algorithm to tackle BiLevel Optimization problems with Coupled Constraints. We demonstrate its effectiveness on two well-known real-world applications.
  arXiv  Detail & Related papers  (2024-06-14T15:59:36Z)
• Constrained Bi-Level Optimization: Proximal Lagrangian Value function Approach and Hessian-free Algorithm [8.479947546216131]
  We develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA) LV-HBA is especially well-suited for machine learning applications.
  arXiv  Detail & Related papers  (2024-01-29T13:50:56Z)
• Effective Bilevel Optimization via Minimax Reformulation [23.5093932552053]
  We propose a reformulation of bilevel optimization as a minimax problem. Under mild conditions, we show these two problems are equivalent. Our method outperforms state-of-the-art bilevel methods while significantly reducing the computational cost.
  arXiv  Detail & Related papers  (2023-05-22T15:41:33Z)
• 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)
• Efficient Gradient Approximation Method for Constrained Bilevel Optimization [2.0305676256390934]
  Bilevel optimization has been developed with large-scale high-dimensional data. This paper considers a constrained bilevel problem with convex and non-differentiable approximations.
  arXiv  Detail & Related papers  (2023-02-03T19:34:56Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• Bilevel Optimization for Machine Learning: Algorithm Design and Convergence Analysis [12.680169619392695]
  This thesis provides a comprehensive convergence rate analysis for bilevel optimization algorithms. For the problem-based formulation, we provide a convergence rate analysis for AID- and ITD-based bilevel algorithms. We then develop acceleration bilevel algorithms, for which we provide shaper convergence analysis with relaxed assumptions.
  arXiv  Detail & Related papers  (2021-07-31T22:05:47Z)
• A Value-Function-based Interior-point Method for Non-convex Bi-level Optimization [38.75417864443519]
  Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. We propose a new interior Bi-level Value-based Interior-point scheme, we penalize the regularized value function of the lower level problem into the upper level objective.
  arXiv  Detail & Related papers  (2021-06-15T09:10:40Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Cogradient Descent for Bilinear Optimization [124.45816011848096]
  We introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem. We solve one variable by considering its coupling relationship with the other, leading to a synchronous gradient descent. Our algorithm is applied to solve problems with one variable under the sparsity constraint.
  arXiv  Detail & Related papers  (2020-06-16T13:41:54Z)

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.