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Main Authors: Song, Hyungseok, Yoon, Deunsol, Lee, Kanghoon, Jeong, Han-Seul, Lee, Soonyoung, Lim, Woohyung
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2602.08210
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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.
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publishDate 2026
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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