A Generic Descent Aggregation Framework for Gradient-based Bi-level Optimization

• URL: http://arxiv.org/abs/2102.07976v1
• Date: Tue, 16 Feb 2021 06:58:12 GMT
• Title: A Generic Descent Aggregation Framework for Gradient-based Bi-level Optimization
• Authors: Risheng Liu, Pan Mu, Xiaoming Yuan, Shangzhi Zeng, Jin Zhang
• Abstract summary: We develop a novel Bi-level Descent Aggregation (BDA) framework for bi-level learning tasks. BDA aggregates hierarchical objectives of both upper level and lower level. We propose a new proof recipe to improve the convergence results of conventional gradient-based bi-level methods.
• Score: 41.894281911990554
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, gradient-based methods for solving bi-level optimization tasks have drawn a great deal of interest from the machine learning community. However, to calculate the gradient of the best response, existing research always relies on the singleton of the lower-level solution set (a.k.a., Lower-Level Singleton, LLS). In this work, by formulating bi-level models from an optimistic bi-level viewpoint, we first establish a novel Bi-level Descent Aggregation (BDA) framework, which aggregates hierarchical objectives of both upper level and lower level. The flexibility of our framework benefits from the embedded replaceable task-tailored iteration dynamics modules, thereby capturing a wide range of bi-level learning tasks. Theoretically, we derive a new methodology to prove the convergence of BDA framework without the LLS restriction. Besides, the new proof recipe we propose is also engaged to improve the convergence results of conventional gradient-based bi-level methods under the LLS simplification. Furthermore, we employ a one-stage technique to accelerate the back-propagation calculation in a numerical manner. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed algorithm for hyper-parameter optimization and meta-learning tasks.

Related papers

• A First-order Generative Bilevel Optimization Framework for Diffusion Models [57.40597004445473]
  Diffusion models iteratively denoise data samples to synthesize high-quality outputs. Traditional bilevel methods fail due to infinite-dimensional probability space and prohibitive sampling costs. We formalize this challenge as a generative bilevel optimization problem. Our first-order bilevel framework overcomes the incompatibility of conventional bilevel methods with diffusion processes.
  arXiv  Detail & Related papers  (2025-02-12T21:44:06Z)
• qNBO: quasi-Newton Meets Bilevel Optimization [26.0555315825777]
  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.
  arXiv  Detail & Related papers  (2025-02-03T05:36:45Z)
• 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)
• Averaged Method of Multipliers for Bi-Level Optimization without Lower-Level Strong Convexity [43.092883358935545]
  We propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for Bi-Level Optimization (BLO) We provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption.
  arXiv  Detail & Related papers  (2023-02-07T11:29:05Z)
• Value-Function-based Sequential Minimization for Bi-level Optimization [52.39882976848064]
  gradient-based Bi-Level Optimization (BLO) methods have been widely applied to handle modern learning tasks. There are almost no gradient-based methods able to solve BLO in challenging scenarios, such as BLO with functional constraints and pessimistic BLO. We provide Bi-level Value-Function-based Sequential Minimization (BVFSM) to address the above issues.
  arXiv  Detail & Related papers  (2021-10-11T03:13:39Z)
• 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)
• A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton [49.23948907229656]
  Bi-level Descent Aggregation is a flexible and modularized algorithmic framework for generic bi-level optimization. We derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules.
  arXiv  Detail & Related papers  (2020-06-07T05:18:50Z)

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.