Algorithms that solve zero-sum games, multi-objective agent objectives, or, more generally, variational inequality (VI) problems are notoriously unstable on general problems. Owing to the increasing need for solving such problems in machine learning, this instability has been highlighted in recent years as a significant research challenge. In this paper, we provide an overview of recent progress in the use of continuous-time perspectives in the analysis and design of methods targeting the broad VI problem class. Our presentation draws parallels between single-objective problems and multi-objective problems, highlighting the challenges of the latter. We also formulate various desiderata for algorithms that apply to general VIs and we argue that achieving these desiderata may profit from an understanding of the associated continuous-time dynamics.

翻译：解决零和游戏、多目标代理目标,或更一般而言,差异性不平等问题的计算方法在一般问题上臭名昭著地不稳定。由于在机器学习中日益需要解决这类问题,近年来这种不稳定被强调为一项重大的研究挑战。本文概述了在分析和设计针对广泛的六类问题的方法时使用连续时间观点的最新进展。我们的发言将单一目标问题与多目标问题相提并论,突出了后者的挑战。我们还为适用于六类通用的算法制定了各种偏差,并争论说,实现这些偏差可能得益于对相关连续时间动态的理解。