模仿学习在不确定条件下的组合优化
Imitation Learning for Combinatorial Optimisation under Uncertainty
AI总结：
本文研究了在不确定条件下组合优化的模仿学习，提出了一种系统专家分类方法，分析了不确定性处理、最优性水平和学习者交互模式，并提出了一种通用的数据集聚合框架。
摘要：
模仿学习（IL）提供了一种数据驱动的框架，用于近似解决大规模组合优化问题，这些问题被表述为序列决策问题（SDPs），其中精确求解方法在计算上不可行。在这一背景下，IL的一个核心但未被充分研究的方面是专家的作用，即生成训练演示的专家。现有研究采用了各种专家构造，但缺乏统一的框架来表征其建模假设、计算属性和对学习性能的影响。本文介绍了一种系统化的专家分类方法，用于在不确定条件下组合优化的模仿学习。文献沿三个主要维度进行分类：（i）不确定性的处理；（ii）最优性水平，区分任务最优和近似专家；（iii）与学习者的交互模式，从一次性监督到迭代、互动方案。我们进一步识别了其他相关专家特征的额外类别。基于此分类，我们提出了一种通用的数据集聚合（DAgger）框架，能够容纳多种专家查询、专家聚合和灵活的交互策略。所提出的框架在具有随机到达和容量限制的动态医生-患者分配问题上进行了评估。计算实验比较了不同专家类型和交互模式的学习结果。结果表明，从随机专家学习的策略在性能上始终优于从确定性或完全信息专家学习的策略，而互动学习使用更少的专家演示提高了解决方案的质量。聚合的确定性专家在随机优化变得计算上具有挑战性时提供了一个有效的替代方案。
英文摘要：
Imitation learning (IL) provides a data-driven framework for approximating policies for large-scale combinatorial optimisation problems formulated as sequential decision problems (SDPs), where exact solution methods are computationally intractable. A central but underexplored aspect of IL in this context is the role of the \emph{expert} that generates training demonstrations. Existing studies employ a wide range of expert constructions, yet lack a unifying framework to characterise their modelling assumptions, computational properties, and impact on learning performance. This paper introduces a systematic taxonomy of experts for imitation learning in combinatorial optimisation under uncertainty. The literature is classified along three principal dimensions: (i) treatment of uncertainty; (ii) level of optimality, distinguishing task-optimal and approximate experts; and (iii) interaction mode with the learner, ranging from one-shot supervision to iterative, interactive schemes. We further identify additional categories capturing other relevant expert characteristics. Building on this taxonomy, we propose a generalised Dataset Aggregation (DAgger) framework that accommodates multiple expert queries, expert aggregation, and flexible interaction strategies. The proposed framework is evaluated on a dynamic physician-to-patient assignment problem with stochastic arrivals and capacity constraints. Computational experiments compare learning outcomes across expert types and interaction regimes. The results show that policies learned from stochastic experts consistently outperform those learned from deterministic or full-information experts, while interactive learning improves solution quality using fewer expert demonstrations. Aggregated deterministic experts provide an effective alternative when stochastic optimisation becomes computationally challenging.
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