Recent years have seen a growing interest in accelerating optimization algorithms with machine-learned predictions. Sakaue and Oki (NeurIPS 2022) have developed a general framework that warm-starts the L-convex function minimization method with predictions, revealing the idea's usefulness for various discrete optimization problems. In this paper, we present a framework for using predictions to accelerate M-convex function minimization, thus complementing previous research and extending the range of discrete optimization algorithms that can benefit from predictions. Our framework is particularly effective for an important subclass called laminar convex minimization, which appears in many operations research applications. Our methods can improve time complexity bounds upon the best worst-case results by using predictions and even have potential to go beyond a lower-bound result.

翻译：近年来，利用机器学习预测加速优化算法的方法日益受到关注。Sakaue与Oki（NeurIPS 2022）开发了一个通用框架，通过预测对L-凸函数最小化方法进行热启动，揭示了该思想在多种离散优化问题中的有效性。本文提出一个利用预测加速M-凸函数最小化的框架，既补充了先前研究，又扩展了可从预测中获益的离散优化算法范畴。我们的框架对名为层次凸最小化的重要子类尤为有效——该子类常见于诸多运筹学应用中。我们的方法能通过预测突破最差情况下的最佳时间复杂度上界，甚至具备超越下界结果的潜力。