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

Published 28 Feb 2024 in cs.LG, cs.SY, and eess.SY | (2402.17967v2)

Abstract: 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.

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References (38)
  1. Graph-theoretic connectivity control of mobile robot networks. Proceedings of the IEEE, 99(9):1525–1540, 2011.
  2. Albert-László Barabási. Network science. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1987):20120375, 2013.
  3. The power grid as a complex network: A survey. Physica A: Statistical Mechanics and its Applications, 392(11):2688–2700, 2013.
  4. Tsan-Ming Choi. Guest editorial to the special issue on logistics and supply chain systems engineering. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(12):4852–4855, 2020.
  5. Recent advances in robust optimization: An overview. European Journal of Operational Research, 235(3):471–483, 2014.
  6. Energy equipartition stabilization and cascading resilience optimization for geospatially distributed cyber-physical network systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(1):25–43, 2015.
  7. Robust transport over networks. IEEE transactions on automatic control, 62(9):4675–4682, 2016.
  8. Efficient robust routing for single commodity network flows. IEEE Transactions on Automatic Control, 63(7):2287–2294, 2017.
  9. Yilun Shang. Subgraph robustness of complex networks under attacks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(4):821–832, 2019.
  10. Robustness evaluation of multipartite complex networks based on percolation theory. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(10):6244–6257, 2021.
  11. Enhancing robustness and resilience of multiplex networks against node-community cascading failures. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(6):3808–3821, 2022.
  12. Enhancing the robustness of networks against multiple damage models using a multifactorial evolutionary algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 53(7):4176–4188, 2023.
  13. Cédric Villani. Topics in Optimal Transportation, volume 58. American Mathematical Soc., 2021.
  14. E. Schrödinger. Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique. Annales de l’institut Henri Poincaré, 2(4):269–310, 1932.
  15. Christian Léonard. A survey of the schrödinger problem and some of its connections with optimal transport. Discrete and Continuous Dynamical Systems, 34(4):1533–1574, 2014.
  16. Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. Advances in neural information processing systems, 26, 2013.
  17. Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning, 11(5-6):355–607, 2019.
  18. Maximum entropy rl (provably) solves some robust rl problems. arXiv preprint arXiv:2103.06257, 2021.
  19. Entropic model predictive optimal transport over dynamical systems. Automatica, 152:110980, June 2023.
  20. Resilience evaluation of entropy regularized logistic networks with probabilistic cost. IFAC-PapersOnLine, 56(2):3106–3111, 2023.
  21. Taming the noise in reinforcement learning via soft updates. arXiv preprint arXiv:1512.08562, 2015.
  22. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International conference on machine learning, pages 1861–1870. PMLR, 2018.
  23. Equivalence between policy gradients and soft q-learning. arXiv preprint arXiv:1704.06440, 2017.
  24. An algorithmic perspective on imitation learning. Foundations and Trends® in Robotics, 7(1-2):1–179, 2018.
  25. Centrality measures and thermodynamic formalism for complex networks. Physical Review E, 83(4):046117, 2011.
  26. William Parry. Intrinsic markov chains. Transactions of the American Mathematical Society, 112(1):55–66, 1964.
  27. David Ruelle. Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics. Cambridge University Press, 2004.
  28. Logistics and supply chain management. Research in transportation economics, 41(1):3–16, 2013.
  29. Lu Zhen. A bi-objective model on multiperiod green supply chain network design. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(3):771–784, 2020.
  30. Online multimodal transportation planning using deep reinforcement learning. In 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pages 1691–1698. IEEE, 2021.
  31. Logistics distribution path planning based on fireworks differential algorithm. In 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pages 2797–2802. IEEE, 2020.
  32. Positive contraction mappings for classical and quantum schrödinger systems. Journal of Mathematical Physics, 56(3), March 2015.
  33. Paul E. Black. repeated squareing, 2021. https://xlinux.nist.gov/dads/HTML/repeatedSquaring.html.
  34. Autonomous control methods in logistics – a mathematical perspective. Applied Mathematical Modelling, 36(7):2947–2960, 2012.
  35. A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays. International Journal of Systems Science, 43(5):845–853, 2012.
  36. Jos F Sturm. Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optimization methods and software, 11(1-4):625–653, 1999.
  37. CVX: Matlab software for disciplined convex programming, version 2.1. http://cvxr.com/cvx, March 2014.
  38. Graph implementations for nonsmooth convex programs. In V. Blondel, S. Boyd, and H. Kimura, editors, Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences, pages 95–110. Springer-Verlag Limited, 2008. http://stanford.edu/~boyd/graph_dcp.html.
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