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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.08210 |
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| _version_ | 1866914315408244736 |
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| author | Song, Hyungseok Yoon, Deunsol Lee, Kanghoon Jeong, Han-Seul Lee, Soonyoung Lim, Woohyung |
| author_facet | Song, Hyungseok Yoon, Deunsol Lee, Kanghoon Jeong, Han-Seul Lee, Soonyoung Lim, Woohyung |
| contents | Heatmap-based solvers have emerged as a promising paradigm for Combinatorial Optimization (CO). However, we argue that the dominant Supervised Learning (SL) training paradigm suffers from a fundamental objective mismatch: minimizing imitation loss (e.g., cross-entropy) does not guarantee solution cost minimization. We dissect this mismatch into two deficiencies: Decoder-Blindness (being oblivious to the non-differentiable decoding process) and Cost-Blindness (prioritizing structural imitation over solution quality). We empirically demonstrate that these intrinsic flaws impose a hard performance ceiling. To overcome this limitation, we propose CADO (Cost-Aware Diffusion models for Optimization), a streamlined Reinforcement Learning fine-tuning framework that formulates the diffusion denoising process as an MDP to directly optimize the post-decoded solution cost. We introduce Label-Centered Reward, which repurposes ground-truth labels as unbiased baselines rather than imitation targets, and Hybrid Fine-Tuning for parameter-efficient adaptation. CADO achieves state-of-the-art performance across diverse benchmarks, validating that objective alignment is essential for unlocking the full potential of heatmap-based solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08210 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization Song, Hyungseok Yoon, Deunsol Lee, Kanghoon Jeong, Han-Seul Lee, Soonyoung Lim, Woohyung Machine Learning Heatmap-based solvers have emerged as a promising paradigm for Combinatorial Optimization (CO). However, we argue that the dominant Supervised Learning (SL) training paradigm suffers from a fundamental objective mismatch: minimizing imitation loss (e.g., cross-entropy) does not guarantee solution cost minimization. We dissect this mismatch into two deficiencies: Decoder-Blindness (being oblivious to the non-differentiable decoding process) and Cost-Blindness (prioritizing structural imitation over solution quality). We empirically demonstrate that these intrinsic flaws impose a hard performance ceiling. To overcome this limitation, we propose CADO (Cost-Aware Diffusion models for Optimization), a streamlined Reinforcement Learning fine-tuning framework that formulates the diffusion denoising process as an MDP to directly optimize the post-decoded solution cost. We introduce Label-Centered Reward, which repurposes ground-truth labels as unbiased baselines rather than imitation targets, and Hybrid Fine-Tuning for parameter-efficient adaptation. CADO achieves state-of-the-art performance across diverse benchmarks, validating that objective alignment is essential for unlocking the full potential of heatmap-based solvers. |
| title | CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.08210 |