Imitating Cost-Constrained Behaviors in Reinforcement Learning

Complex planning and scheduling problems have long been solved using various optimization or heuristic approaches. In recent years, imitation learning that aims to learn from expert demonstrations has been proposed as a viable alternative to solving these problems. Generally speaking, imitation learning is designed to learn either the reward (or preference) model or directly the behavioral policy by observing the behavior of an expert. Existing work in imitation learning and inverse reinforcement learning has focused on imitation primarily in unconstrained settings (e.g., no limit on fuel consumed by the vehicle). However, in many real-world domains, the behavior of an expert is governed not only by reward (or preference) but also by constraints. For instance, decisions on self-driving delivery vehicles are dependent not only on the route preferences/rewards (depending on past demand data) but also on the fuel in the vehicle and the time available. In such problems, imitation learning is challenging as decisions are not only dictated by the reward model but are also dependent on a cost-constrained model. In this paper, we provide multiple methods that match expert distributions in the presence of trajectory cost constraints through (a) Lagrangian-based method; (b) Meta-gradients to find a good trade-off between expected return and minimizing constraint violation; and (c) Cost-violation-based alternating gradient. We empirically show that leading imitation learning approaches imitate cost-constrained behaviors poorly and our meta-gradient-based approach achieves the best performance.