CADO：从模仿到成本最小化的组合优化热力图求解器
CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization
AI总结：
针对热力图求解器监督训练中模仿损失与成本最小化的目标不匹配问题，提出CADO框架，通过强化学习微调直接优化解码后解的成本，在多个基准上取得最优性能。
摘要：
基于热力图的求解器已成为组合优化（CO）的一种有前景的范式。然而，我们认为主流的监督学习（SL）训练范式存在根本性的目标不匹配：最小化模仿损失（例如交叉熵）并不能保证解的成本最小化。我们将这种不匹配分解为两个缺陷：解码器盲区（忽视不可微的解码过程）和成本盲区（优先考虑结构模仿而非解的质量）。我们通过实验证明，这些内在缺陷施加了硬性性能上限。为了克服这一限制，我们提出了CADO（成本感知的优化扩散模型），一个简化的强化学习微调框架，将扩散去噪过程建模为MDP，以直接优化解码后的解成本。我们引入了标签中心奖励，将真实标签重新用作无偏基线而非模仿目标，以及混合微调以实现参数高效的适应。CADO在多个基准上取得了最先进的性能，验证了目标对齐对于释放热力图求解器全部潜力的必要性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
