# Imitation-regularized Optimal Transport on Networks: Provable Robustness and Application to Logistics Planning

arXiv: https://arxiv.org/abs/2402.17967 · HTML: https://mlsanity.com/paper/2402.17967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [Taming the Noise in Reinforcement Learning via Soft Updates](https://mlsanity.com/paper/1512.08562/) (2015)
- [Robust transport over networks](https://mlsanity.com/paper/1603.08129/) (2016)
- [Estimating ensemble flows on a hidden Markov chain](https://mlsanity.com/paper/1905.09119/) (2019)
- [Entropic Model Predictive Optimal Transport over Dynamical Systems](https://mlsanity.com/paper/2301.06492/) (2023)
- [Online Multimodal Transportation Planning using Deep Reinforcement Learning](https://mlsanity.com/paper/2105.08374/) (2021)
- [Resilience Evaluation of Entropy Regularized Logistic Networks with Probabilistic Cost](https://mlsanity.com/paper/2212.02060/) (2022)

## Abstract (arXiv)

Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph structures has been investigated to enhance the robustness of transport on such networks. In this study, we propose an imitation-regularized OT (I-OT) that mathematically incorporates prior knowledge into the robustness of OT. This method is expected to enhance interpretability by integrating human insights into robustness and to accelerate practical applications. Furthermore, we mathematically verify the robustness of I-OT and discuss how these robustness properties relate to real-world applications. The effectiveness of this method is validated through a logistics simulation using automotive parts data.