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The nested Sinkhorn divergence to learn the nested distance

Author

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  • Alois Pichler

    (University of Technology, Chemnitz)

  • Michael Weinhardt

    (University of Technology, Chemnitz)

Abstract

The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the evolution of information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which can be computed considerably faster. For this reason we employ the Sinkhorn divergence and take advantage of the related (fixed point) iteration algorithm. Furthermore, we investigate the transition of the entropy throughout the stages of the stochastic process and provide an entropy-regularized nested distance formulation, including a characterization of its dual. Numerical experiments affirm the computational advantage and supremacy.

Suggested Citation

  • Alois Pichler & Michael Weinhardt, 2022. "The nested Sinkhorn divergence to learn the nested distance," Computational Management Science, Springer, vol. 19(2), pages 269-293, June.
    • Handle: RePEc:spr:comgts:v:19:y:2022:i:2:d:10.1007_s10287-021-00415-7
    DOI: 10.1007/s10287-021-00415-7
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    References listed on IDEAS

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    1. Brodt, Abraham I., 1983. "MIN-MAD life: A multi-period optimization model for life insurance company investment decisions," Insurance: Mathematics and Economics, Elsevier, vol. 2(2), pages 91-102, April.
    2. Pierre Carpentier & Jean-Philippe Chancelier & Guy Cohen & Michel Lara & Pierre Girardeau, 2012. "Dynamic consistency for stochastic optimal control problems," Annals of Operations Research, Springer, vol. 200(1), pages 247-263, November.
    3. Raimund Kovacevic & Alois Pichler, 2015. "Tree approximation for discrete time stochastic processes: a process distance approach," Annals of Operations Research, Springer, vol. 235(1), pages 395-421, December.
    4. Markéta Horejšová & Sebastiano Vitali & Miloš Kopa & Vittorio Moriggia, 2020. "Evaluation of scenario reduction algorithms with nested distance," Computational Management Science, Springer, vol. 17(2), pages 241-275, June.
    5. Bita Analui & Georg Pflug, 2014. "On distributionally robust multiperiod stochastic optimization," Computational Management Science, Springer, vol. 11(3), pages 197-220, July.
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    Cited by:

    1. Erhan Bayraktar & Bingyan Han, 2023. "Fitted Value Iteration Methods for Bicausal Optimal Transport," Papers 2306.12658, arXiv.org, revised Nov 2023.

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