DiOpt: Self-supervised Diffusion for Constrained Optimization

• URL: http://arxiv.org/abs/2502.10330v1
• Date: Fri, 14 Feb 2025 17:43:08 GMT
• Title: DiOpt: Self-supervised Diffusion for Constrained Optimization
• Authors: Shutong Ding, Yimiao Zhou, Ke Hu, Xi Yao, Junchi Yan, Xiaoying Tang, Ye Shi,
• Abstract summary: DiOpt is a novel diffusion paradigm that systematically learns near-optimal feasible solution distributions through iterative self-training.<n>To our knowledge, DiOpt represents the first successful integration of self-supervised diffusion with hard constraint satisfaction.
• Score: 46.75288477458697
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advances in diffusion models show promising potential for learning-based optimization by leveraging their multimodal sampling capability to escape local optima. However, existing diffusion-based optimization approaches, often reliant on supervised training, lacks a mechanism to ensure strict constraint satisfaction which is often required in real-world applications. One resulting observation is the distributional misalignment, i.e. the generated solution distribution often exhibits small overlap with the feasible domain. In this paper, we propose DiOpt, a novel diffusion paradigm that systematically learns near-optimal feasible solution distributions through iterative self-training. Our framework introduces several key innovations: a target distribution specifically designed to maximize overlap with the constrained solution manifold; a bootstrapped self-training mechanism that adaptively weights candidate solutions based on the severity of constraint violations and optimality gaps; and a dynamic memory buffer that accelerates convergence by retaining high-quality solutions over training iterations. To our knowledge, DiOpt represents the first successful integration of self-supervised diffusion with hard constraint satisfaction. Evaluations on diverse tasks, including power grid control, motion retargeting, wireless allocation demonstrate its superiority in terms of both optimality and constraint satisfaction.

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