We present a massively parallel Lagrange decomposition method for solving 0-1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique for decoding primal solutions. For representing subproblems we follow Lange et al. (2021) and use binary decision diagrams (BDDs). Our primal and dual algorithms require little synchronization between subproblems and optimization over BDDs needs only elementary operations without complicated control flow. This allows us to exploit the parallelism offered by GPUs for all components of our method. We present experimental results on combinatorial problems from MAP inference for Markov Random Fields, quadratic assignment and cell tracking for developmental biology. Our highly parallel GPU implementation improves upon the running times of the algorithms from Lange et al. (2021) by up to an order of magnitude. In particular, we come close to or outperform some state-of-the-art specialized heuristics while being problem agnostic.

翻译：我们提出了解决结构化预测中0-1整形线性程序的大规模平行拉格朗格分解方法。 我们提出了解决拉格兰格双向和分解原始解决方案的扰动技术的新的迭代更新方案。 为了代表子问题,我们遵循Lange等人(2021年)并使用二进制决定图(BDDs )。 我们的原始和双重算法要求子问题和对BDDs的优化很少同步,只需要简单的操作,而没有复杂的控制流。 这使我们能够利用GPUs为我们方法的所有组成部分提供的平行功能。 我们介绍了MAP对Markov随机场的推断、四进制任务和发育生物学的细胞跟踪的组合问题实验结果。 我们高度平行的GPU的运用在Lange等人(2021年)的算法运行时,通过一个程度的顺序得到了改进。 特别是, 我们接近或超越了某种状态的专业化的超音量技术,而同时又有问题。