Disciplined Bilevel Programming

• URL: http://arxiv.org/abs/2609.00644v1
• Date: Tue, 01 Sep 2026 03:22:48 GMT
• Title: Disciplined Bilevel Programming
• Abstract summary: Bilevel optimization provides a natural modeling language for hierarchical decision problems.<n>Applying existing numerical solvers usually requires substantial manual analysis and reformulation.<n>We introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems.
• Score: 9.272977870242562
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bilevel optimization provides a natural modeling language for hierarchical decision problems. However, applying existing numerical solvers usually requires substantial manual analysis and reformulation. In this paper, we introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems in a high-level, human-readable way that is close to the mathematical formulation. For problems with a disciplined nonlinear upper problem and a convex lower problem satisfying the disciplined parameterized programming rules, DBLP automatically canonicalizes the lower problem into conic form and constructs an equivalent single-level reformulation using the conic Karush-Kuhn-Tucker conditions. We relax the resulting complementarity constraint and use a gap continuation procedure to approximately solve a sequence of smooth nonlinear problems. We implement DBLP in the open-source Python package BLVPY, an extension of CVXPY for bilevel programming. We demonstrate the modeling and solution capabilities of BLVPY on a range of bilevel optimization problems from several application domains. The proposed framework and implementation allow users to specify and solve bilevel optimization problems within a few lines of code, without prior expertise in bilevel modeling and numerical optimization.

Related papers

• Disciplined Biconvex Programming [9.272977870242562]
  We introduce disciplined bi programming (DBCP) for specifying solving bi computational processing problems.<n>Bi optimization problems arise in various applications, including machine learning signal, and science, and control.
  arXiv  Detail & Related papers  (2025-11-03T18:20:03Z)
• A Method for Learning to Solve Parametric Bilevel Optimization with Coupling Constraints [46.74496760711108]
  This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems.<n>The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems.
  arXiv  Detail & Related papers  (2025-07-11T21:48:21Z)
• 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)
• Contextual Stochastic Bilevel Optimization [50.36775806399861]
  We introduce contextual bilevel optimization (CSBO) -- a bilevel optimization framework with the lower-level problem minimizing an expectation on some contextual information and the upper-level variable. It is important for applications such as meta-learning, personalized learning, end-to-end learning, and Wasserstein distributionally robustly optimization with side information (WDRO-SI)
  arXiv  Detail & Related papers  (2023-10-27T23:24:37Z)
• A Generalized Alternating Method for Bilevel Learning under the Polyak-{\L}ojasiewicz Condition [63.66516306205932]
  Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields. Recent results have shown that simple alternating iteration-based iterations can match interest owing to convex lower-level objective.
  arXiv  Detail & Related papers  (2023-06-04T17:54:11Z)
• On Penalty-based Bilevel Gradient Descent Method [35.83102074785861]
  Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems.<n>Recent progress on bilevel algorithms mainly focuses on bilevel optimization problems through the lens of the implicit-gradient method.<n>In this work, we tackle a challenging class of bilevel problems through the lens of the penalty method.
  arXiv  Detail & Related papers  (2023-02-10T11:30:19Z)
• Communication-Efficient Robust Federated Learning with Noisy Labels [144.31995882209932]
  Federated learning (FL) is a promising privacy-preserving machine learning paradigm over distributed located data. We propose a learning-based reweighting approach to mitigate the effect of noisy labels in FL. Our approach has shown superior performance on several real-world datasets compared to various baselines.
  arXiv  Detail & Related papers  (2022-06-11T16:21:17Z)
• Enhanced Bilevel Optimization via Bregman Distance [104.96004056928474]
  We propose a bilevel optimization method based on Bregman Bregman functions. We also propose an accelerated version of SBiO-BreD method (ASBiO-BreD) by using the variance-reduced technique.
  arXiv  Detail & Related papers  (2021-07-26T16:18:43Z)

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.