从路线数据反推成本分布，让模型学会生成多样可行解
Inverse Optimization Latent Variable Models for Learning Costs Applied to Route Problems
- 用逆优化+潜变量建模，从可观测路径反推成本函数分布
- 在真实船运、出租车路线数据上重建路径并预测分布，准确率超基准方法
- 适合研究交通规划、行为建模的读者，可解释性强
在成本函数未知的情况下学习约束优化问题（COP）的解表示极具挑战性，因为传统变分自编码器等模型在解码结构化输出时难以满足约束。我们提出逆优化潜变量模型（IO-LVM），通过观测到的解来学习COP成本函数的潜空间，并利用求解器在循环中重构可行解。该方法通过非可微确定性求解器估计Fenchel-Young损失的梯度，塑造潜空间。与传统逆优化或逆强化学习仅恢复单一或特定上下文的成本函数不同，IO-LVM捕捉成本函数的分布，从而识别训练阶段未见的代理或条件带来的多样化解行为。我们在真实世界船舶和出租车路线数据集，以及合成图路径上验证了该方法，证明其能有效重构路径与环路，预测解的分布，并生成可解释的潜表示。
原文摘要 · Abstract (English)
Learning representations for solutions of constrained optimization problems (COPs) with unknown cost functions is challenging, as models like (Variational) Autoencoders struggle to enforce constraints when decoding structured outputs. We propose an Inverse Optimization Latent Variable Model (IO-LVM) that learns a latent space of COP cost functions from observed solutions and reconstructs feasible outputs by solving a COP with a solver in the loop. Our approach leverages estimated gradients of a Fenchel-Young loss through a non-differentiable deterministic solver to shape the latent space. Unlike standard Inverse Optimization or Inverse Reinforcement Learning methods, which typically recover a single or context-specific cost function, IO-LVM captures a distribution over cost functions, enabling the identification of diverse solution behaviors arising from different agents or conditions not available during the training process. We validate our method on real-world datasets of ship and taxi routes, as well as paths in synthetic graphs, demonstrating its ability to reconstruct paths and cycles, predict their distributions, and yield interpretable latent representations.
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