Online Methods for Complex Stochastic Optimization Problems

我的研究主要包括在随机优化的背景下检查自适应步长算法的类别。近年来，这样的算法已经成为深度学习领域成功的一个组成部分，使以前不切实际的神经架构能够在大量数据上进行训练。随机优化的自适应步长算法扩展了随机梯度下降，这是一种用于拟合统计和ML模型类的技术，通过在训练时利用额外的数据，使其更加鲁棒和高效。然而，直到最近，人们对这些自适应步长算法的实际性能知之甚少，这些算法的许多重要性质，如稳定性和概率收敛性，都是不确定的。最近的工作已经开始尝试分离这些属性和它们所拥有的条件——我正在进行的研究将旨在扩大我们知道这些属性所拥有的条件，寻求削弱标准设置中的假设（也加强属性本身），并研究算法在依赖数据条件下的行为，主要集中在马尔可夫动力学上。这项工作将有助于提高对自适应步长算法性能的信心，鉴于在关键基础设施中使用它们的机器学习技术日益普及，这将变得越来越重要。这项工作还将增加可应用自适应步长算法的设置范围，例如通常需要马尔可夫条件的训练强化学习算法。

My research primarily consists of examining the class of adaptive stepsize algorithms in the context of stochastic optimisation. In recent years, such algorithms have been an integral component to the success of the field of deep learning, allowing previously impractical neural architectures to be trained on huge swathes of data. Adaptive stepsize algorithms for stochastic optimisation extend stochastic gradient descent, a technique for fitting classes of statistical and ML models, to be more robust and efficient by utilising additional data whilst training. Until recently, however, relatively little was known about the practical performance of these adaptive stepsize algorithms with many important properties, such as stability and probabilistic convergence, being undetermined. Recent work has been undertaken to try and isolate these properties and the conditions in which they hold - The research I am undertaking will aim to widen the conditions in which we know that these properties hold, looking toward weakening the assumptions in the standard setting (also strengthening the properties themselves), and also looking at how the algorithms behave in condition of dependent data, mostly focusing on markovian dynamics. This work will facilitate increased confidence in the performance of adaptive step size algorithms which will become increasingly more important given the growing prevalence of machine learning techniques using them being relied upon in critical infrastructure. This work will also increase the range of settings in which adaptive stepsize algorithms can be applied such as training reinforcement learning algorithms which often entail Markovian conditions.