Exploring the Boundary of Diffusion-based Methods for Solving Constrained Optimization

• URL: http://arxiv.org/abs/2502.10330v3
• Date: Tue, 27 May 2025 09:05:01 GMT
• Title: Exploring the Boundary of Diffusion-based Methods for Solving Constrained Optimization
• Authors: Shutong Ding, Yimiao Zhou, Ke Hu, Xi Yao, Junchi Yan, Xiaoying Tang, Ye Shi,
• Abstract summary: We propose a novel diffusion-based framework for Continuous Constrained Optimization problems called DiOpt.<n>DiOpt operates in two distinct phases: an initial warm-start phase, implemented via supervised learning, followed by a bootstrapping phase.<n>It is designed to iteratively refine solutions, thereby improving the objective function while rigorously satisfying problem constraints.
• Score: 46.75288477458697
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models have achieved remarkable success in generative tasks such as image and video synthesis, and in control domains like robotics, owing to their strong generalization capabilities and proficiency in fitting complex multimodal distributions. However, their full potential in solving Continuous Constrained Optimization problems remains largely underexplored. Our work commences by investigating a two-dimensional constrained quadratic optimization problem as an illustrative example to explore the inherent challenges and issues when applying diffusion models to such optimization tasks and providing theoretical analyses for these observations. To address the identified gaps and harness diffusion models for Continuous Constrained Optimization, we build upon this analysis to propose a novel diffusion-based framework for optimization problems called DiOpt. This framework operates in two distinct phases: an initial warm-start phase, implemented via supervised learning, followed by a bootstrapping phase. This dual-phase architecture is designed to iteratively refine solutions, thereby improving the objective function while rigorously satisfying problem constraints. Finally, multiple candidate solutions are sampled, and the optimal one is selected through a screening process. We present extensive experiments detailing the training dynamics of DiOpt, its performance across a diverse set of Continuous Constrained Optimization problems, and an analysis of the impact of DiOpt's various hyperparameters.

Related papers

• Preference-Guided Diffusion for Multi-Objective Offline Optimization [64.08326521234228]
  We propose a preference-guided diffusion model for offline multi-objective optimization. Our guidance is a preference model trained to predict the probability that one design dominates another. Our results highlight the effectiveness of classifier-guided diffusion models in generating diverse and high-quality solutions.
  arXiv  Detail & Related papers  (2025-03-21T16:49:38Z)
• Test-time Alignment of Diffusion Models without Reward Over-optimization [8.981605934618349]
  Diffusion models excel in generative tasks, but aligning them with specific objectives remains challenging.<n>We propose a training-free, test-time method based on Sequential Monte Carlo (SMC) to sample from the reward-aligned target distribution.<n>We demonstrate its effectiveness in single-reward optimization, multi-objective scenarios, and online black-box optimization.
  arXiv  Detail & Related papers  (2025-01-10T09:10:30Z)
• Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks [4.124390946636935]
  Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly.<n>We propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks.<n>Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space.
  arXiv  Detail & Related papers  (2024-12-23T06:05:45Z)
• Diffusion Models as Network Optimizers: Explorations and Analysis [71.69869025878856]
  generative diffusion models (GDMs) have emerged as a promising new approach to network optimization.<n>In this study, we first explore the intrinsic characteristics of generative models.<n>We provide a concise theoretical and intuitive demonstration of the advantages of generative models over discriminative network optimization.
  arXiv  Detail & Related papers  (2024-11-01T09:05:47Z)
• DiffSG: A Generative Solver for Network Optimization with Diffusion Model [75.27274046562806]
  Diffusion generative models can consider a broader range of solutions and exhibit stronger generalization by learning parameters. We propose a new framework, which leverages intrinsic distribution learning of diffusion generative models to learn high-quality solutions.
  arXiv  Detail & Related papers  (2024-08-13T07:56:21Z)
• HUWSOD: Holistic Self-training for Unified Weakly Supervised Object Detection [66.42229859018775]
  We introduce a unified, high-capacity weakly supervised object detection (WSOD) network called HUWSOD. HUWSOD incorporates a self-supervised proposal generator and an autoencoder proposal generator with a multi-rate re-supervised pyramid to replace traditional object proposals. Our findings indicate that randomly boxes, although significantly different from well-designed offline object proposals, are effective for WSOD training.
  arXiv  Detail & Related papers  (2024-06-27T17:59:49Z)
• Quantization Avoids Saddle Points in Distributed Optimization [1.579622195923387]
  Distributed non optimization underpins key functionalities of numerous distributed systems. The aim of this paper is to prove that it can effectively escape saddle points convergence to a second-order stationary point convergence. With an easily adjustable quantization, the approach allows a user control to aggressively reduce communication overhead.
  arXiv  Detail & Related papers  (2024-03-15T15:58:20Z)
• Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints [42.47298301874283]
  We propose to perform optimization within the data manifold using diffusion models. Depending on the differentiability of the objective function, we propose two different sampling methods. Our method achieves better or comparable performance with previous state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-02-28T03:09:12Z)
• DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization [9.28162057044835]
  Optimal trajectory local is computationally expensive for nonlinear and high-dimensional dynamical systems. In this paper we introduce Diffu-based general model for non-dimensional optima problems. We also present Diff+, a novel constrained diffusion model with an additional loss in that further reduces the problem violations.
  arXiv  Detail & Related papers  (2024-02-22T03:52:17Z)
• Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints [17.392113376816788]
  Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. We present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. Our framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population.
  arXiv  Detail & Related papers  (2024-01-02T00:38:20Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems [1.6709415233613623]
  This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set. We also introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.
  arXiv  Detail & Related papers  (2021-02-18T01:49:06Z)

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.