Optimization and game dynamics in machine learning

这项建议侧重于在ML的优化和博弈的数值方法的背景下研究动力学和加速度。有大量关于优化的文献，特别是关于机器学习(ML)的优化。然而，还有一些根本性的问题仍然没有得到回答。令人惊讶的是，这些悬而未决的问题包括广泛使用的方法的基本性质，加速度和随机性的相互作用，游戏的动力学，以及加速度、适应性和泛化之间的联系。这种缺乏理解的后果是，我们没有充分受益于现有的方法，并进一步忽视了改进方法的可能性。我提议对优化和游戏动力学进行基础研究，因为它们与机器学习和深度学习的现代挑战有关。这项工作包括对经典动量动力学的更深入的研究，重点是一些以前未知的和非常奇怪的性质；加速随机优化的简单方法；关于游戏动力学的加速度和随机性的研究；以及对自适应优化方法的泛化能力的调查，重点放在动力学的镜头上。

This proposal focuses on the investigation of dynamics and acceleration in the context of numerical methods for optimization and games in ML. There is vast literature on optimization and specifically on optimization for machine learning (ML). However, there are a number of fundamental questions that are still unanswered. Those unanswered questions surprisingly include fundamental properties of widely used methods, the interaction of acceleration and stochasticity, the dynamics of games, and the connection between acceleration, adaptivity and generalization. A consequence of this lack of understanding is that we do not fully benefit from existing methods, and further ignore the possibility of improved methods. I am proposing fundamental research on optimization and game dynamics, as they pertain to modern challenges in machine learning and deep learning. The work includes a deeper study of classic momentum dynamics, emphasizing on some previously unknown and very curious properties; a simple approach to accelerated stochastic optimization; the study of acceleration and stochasticity on game dynamics; and an investigation of the generalization abilities of adaptive optimization methods with emphases on the lens of dynamics.