Imitation-regularized Optimal Transport on Networks: Provable Robustness
  and Application to Logistics Planning
Koshi Oishi Yota Hashizume Tomohiko Jimbo Hirotaka Kaji Kenji Kashima
Network systems form the foundation of modern society, playing a critical
role in various applications. However, these systems are at significant risk of
being adversely affected by unforeseen circumstances, such as disasters.
Considering this, there is a pressing need for research to enhance the
robustness of network systems. Recently, in reinforcement learning, the
relationship between acquiring robustness and regularizing entropy has been
identified. Additionally, imitation learning is used within this framework to
reflect experts' behavior. However, there are no comprehensive studies on the
use of a similar imitation framework for optimal transport on networks.
Therefore, in this study, imitation-regularized optimal transport (I-OT) on
networks was investigated. It encodes prior knowledge on the network by
imitating a given prior distribution. The I-OT solution demonstrated robustness
in terms of the cost defined on the network. Moreover, we applied the I-OT to a
logistics planning problem using real data. We also examined the imitation and
apriori risk information scenarios to demonstrate the usefulness and
implications of the proposed method.