Wasserstein分布鲁棒优化的正则化

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-05-18 DOI:10.1051/cocv/2023019

Waïss Azizian, F. Iutzeler, J. Malick

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引用次数: 6

摘要

最优传输最近被证明是各种机器学习应用中一个有用的工具，需要对概率度量进行比较。其中，分布鲁棒优化的应用自然涉及不确定性模型中的沃瑟斯坦距离，捕获数据移动或最坏情况。受最优输运中Wasserstein距离正则化成功的启发，本文研究了Wasserstein分布鲁棒优化的正则化问题。首先，我们得到了正则化Wasserstein分布鲁棒问题的一般强对偶结果。其次，我们改进了熵正则化情况下的对偶性结果，并提供了正则化参数消失时的近似结果。

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Regularization for Wasserstein distributionally robust optimization

Optimal transport has recently proved to be a useful tool in various machine learning applications, needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein distances in their models of uncertainty, capturing data shifts or worst-case scenarios. Inspired by the success of the regularization of Wasserstein distances in optimal transport, we study in this paper the regularization of Wassserstein distributionally robust optimization. First, we derive a general strong duality result of regularized Wasserstein distributionally robust problems. Second, we refine this duality result in the case of entropic regularization and provide an approximation result when the regularization parameters vanish.

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

自引率

7.10%

发文量

期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.