We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in (Swoboda, Kolmogorov 2019; Kolmogorov, Pock 2021). As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subproutine based on in-face Frank-Wolfe directions, introduced in (Freund et al. 2017) in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at https://pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html.

翻译：我们研究求解MAP-MRF推理问题的LP松弛问题，特别是近期在(Swoboda, Kolmogorov 2019; Kolmogorov, Pock 2021)中提出的方法。该方法的关键计算子程序使用Frank-Wolfe(FW)方法的一种变体，在组合多面体上最小化光滑凸函数。我们基于(Freund等 2017)在不同背景下提出的内面Frank-Wolfe方向，提出该子程序的高效实现。更一般地，我们为支持内面FW方向的组合子问题定义了一种抽象数据结构，并描述了其在树结构MAP-MRF推理子问题中的具体化。实验结果表明，对于某些问题类别，所提方法是当前最先进的LP求解器。我们的代码见https://pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html。