Imitation Learning for Combinatorial Optimisation under Uncertainty

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 IL in combinatorial optimisation under uncertainty. Experts are classified along three dimensions: (i) their treatment of uncertainty, including myopic, deterministic, full-information, two-stage stochastic, and multi-stage stochastic formulations; (ii) their level of optimality, distinguishing task-optimal and approximate experts; and (iii) their interaction mode with the learner, ranging from one-shot supervision to iterative, interactive schemes. Building on this taxonomy, we propose a generalised Dataset Aggregation (DAgger) algorithm that supports 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.